CLASS NOTES ON

ELECTRICAL MEASUREMENTS & INSTRUMENTATION

FOR

4th SEMESTER OF

ELECTRICAL ENGINEERING

(B.TECH PROGRAMME)

UNIT-1

1
 SYLLABUS

ELECTRICAL MEASUREMENTS & INSTRUMENTATION (2-0-0)

➢ Introduction: Objective, scope and outcome of the course.

➢ Measuring Instruments: Moving coil, moving iron, electrodynamic and induction
instruments-construction, operation, torque equation and errors. Applications of
instruments for measurement of current, voltage, single-phase power and single-phase
energy. Errors in wattmeter and energy meter and their compensation and adjustment.
Testing and calibration of single-phase energy meter by phantom loading.
➢ Polyphase Metering: Blondel's Theorem for n-phase, p-wire system. Measurement of power and
reactive kVA in 3-phase balanced and unbalanced systems: One-wattmeter, two- wattmeter and
three-wattmeter methods. 3-phase induction type energy meter. Instrument Transformers:
Construction and operation of current and potential transformers. Ratio and phase angle errors
and their minimization. Effect of variation of power factor, secondary burden and frequency on
errors. Testing of CTs and PTs. Applications of CTs and PTs for the measurement of current,
voltage, power and energy.
➢ Potentiometers: Construction, operation and standardization of DC potentiometers– slide wire
and Crompton potentiometers. Use of potentiometer for measurement of resistance and voltmeter
and ammeter calibrations. Volt ratio boxes. Construction, operation and standardization of AC
potentiometer in-phase and quadrature potentiometers. Applications of AC potentiometers.
➢ Measurement of Resistances: Classification of resistance. Measurement of medium resistances –
ammeter and voltmeter method, substitution method, Wheatstone bridge method. Measurement
of low resistances – Potentiometer method and Kelvin's double bridge method. Measurement of
high resistance: Price's Guardwire method. Measurement of earth resistance.
➢ AC Bridges: Generalized treatment of four-arm AC bridges. Sources and detectors. Maxwell's
bridge, Hay's bridge and Anderson bridge for self inductance measurement. Heaviside's bridge
for mutual inductance measurement. De Sauty Bridge for capacitance measurement. Wien's
bridge for capacitance and frequency measurements. Sources of error in bridge measurements
and precautions. Screening of bridge components. Wagner earth device.
TEXT BOOKS
[1]. A Course in Elec. & Electronics Measurements & Instrumentation: A K.
Sawhney [2]. Modern Electronic Instrumentation and Measurement Techniques:
Helfrick & Cooper [3]. Electrical Measurement and Measuring Instruments -
Golding & Waddis

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Course Outcome For Electronic Measurement & Instrumentation

CO1 Acquire detailed knowledge of different-different instruments.

CO2 Develop the ability to select measuring instruments for a given application.
CO3 Design the different AC and DC bridges and the application of different bridges for
measurements

3
4
 MEASURING INSTRUMENTS

1.1 Definition of instruments

An instrument is a device in which we can determine the magnitude or value of the quantity
to be measured. The measuring quantity can be voltage, current, power and energy etc. Generally
instruments are classified in to two categories.

Instrument

Absolute Instrument Secondary Instrument

1.2 Absolute instrument

An absolute instrument determines the magnitude of the quantity to be measured in terms of the
instrument parameter. This instrument is really used, because each time the value of the measuring
quantities varies. So we have to calculate the magnitude of the measuring quantity, analytically
which is time consuming. These types of instruments are suitable for laboratory use. Example:
Tangent galvanometer.

1.3 Secondary instrument

This instrument determines the value of the quantity to be measured directly. Generally these
instruments are calibrated by comparing with another standard secondary instrument.
Examples of such instruments are voltmeter, ammeter and wattmeter etc. Practically
secondary instruments are suitable for measurement.

Secondary instruments

Indicating instruments Recording Integrating Electromechanically

Indicating instruments

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 1.3.1 Indicating instrument

This instrument uses a dial and pointer to determine the value of measuring quantity. The pointer
indication gives the magnitude of measuring quantity.

1.3.2 Recording instrument

This type of instruments records the magnitude of the quantity to be measured continuously over
a specified period of time.

1.3.3 Integrating instrument

This type of instrument gives the total amount of the quantity to be measured over a specified
period of time.
1.3.4 Electromechanical indicating instrument

For satisfactory operation electromechanical indicating instrument, three forces are necessary.
They are
(a) Deflecting force

(b) Controlling force

(c)Damping force

1.4 Deflecting force

When there is no input signal to the instrument, the pointer will be at its zero position. To deflect
the pointer from its zero position, a force is necessary which is known as deflecting force. A system
which produces the deflecting force is known as a deflecting system. Generally a deflecting system
converts an electrical signal to a mechanical force.

Fig. 1.1 Pointer scale

6
1.4.1 Magnitude effect

When a current passes through the coil (Fig.1.2), it produces a imaginary bar magnet. When a soft-
iron piece is brought near this coil it is magnetized. Depending upon the current direction the poles
are produced in such a way that there will be a force of attraction between the coil and the soft iron
piece. This principle is used in moving iron attraction type instrument.

Fig. 1.2

If two soft iron pieces are place near a current carrying coil there will be a force of repulsion
between the two soft iron pieces. This principle is utilized in the moving iron repulsion type
instrument.

1.4.2 Force between a permanent magnet and a current carrying coil

When a current carrying coil is placed under the influence of magnetic field produced by a
permanent magnet and a force is produced between them. This principle is utilized in the moving
coil type instrument.

Fig. 1.3

1.4.3 Force between two current carrying coil

When two current carrying coils are placed closer to each other there will be a force of repulsion
between them. If one coil is movable and other is fixed, the movable coil will move away from the
fixed one. This principle is utilized in electrodynamometer type instrument.

7
 Fig. 1.4

1.5 Controlling force

To make the measurement indicated by the pointer definite (constant) a force is necessary which
will be acting in the opposite direction to the deflecting force. This force is known as controlling
force. A system which produces this force is known as a controlled system. When the external
signal to be measured by the instrument is removed, the pointer should return back to the zero
position. This is possibly due to the controlling force and the pointer will be indicating a steady
value when the deflecting torque is equal to controlling torque.

Td (1.1)
Tc

1.5.1 Spring control

Two springs are attached on either end of spindle (Fig. 1.5).The spindle is placed in jewelled
bearing, so that the frictional force between the pivot and spindle will be minimum. Two springs
are provided in opposite direction to compensate the temperature error. The spring is made of
phosphorous bronze.

When a current is supply, the pointer deflects due to rotation of the spindle. While spindle is rotate,
the spring attached with the spindle will oppose the movements of the pointer. The torque produced
by the spring is directly proportional to the pointer deflection .

TC (1.2)

The deflecting torque produced Td proportional to ‘I’. When TC Td , the pointer will come to a

8
steady position. Therefore
(1.3)
I

9
 Fig. 1.5

Since, and I are directly proportional to the scale of such instrument which uses spring controlled
is uniform.
1.6 Damping force

The deflection torque and controlling torque produced by systems are electro mechanical.
Due to inertia produced by this system, the pointer oscillates about it final steady position before
coming to rest. The time required to take the measurement is more. To damp out the oscillation is
quickly, a damping force is necessary. This force is produced by different systems.

(a) Air friction damping

(b) Fluid friction damping
(c) Eddy current damping
1.6.1 Air friction damping

The piston is mechanically connected to a spindle through the connecting rod (Fig. 1.6). The
pointer is fixed to the spindle moves over a calibrated dial. When the pointer oscillates in clockwise
direction, the piston goes inside and the cylinder gets compressed. The air pushes the piston
upwards and the pointer tends to move in anticlockwise direction.

10
 Fig. 1.6

If the pointer oscillates in anticlockwise direction the piston moves away and the pressure of the
air inside cylinder gets reduced. The external pressure is more than that of the internal pressure.
Therefore the piston moves down wards. The pointer tends to move in clock wise direction.

1.6.2 Eddy current damping

Fig. 1.6 Disc type

An aluminum circular disc is fixed to the spindle (Fig. 1.6). This disc is made to move in the
magnetic field produced by a permanent magnet.

11
When the disc oscillates it cuts the magnetic flux produced by damping magnet. An emf is induced
in the circular disc by faradays law. Eddy currents are established in the disc since it has several
closed paths. By Lenz’s law, the current carrying disc produced a force in a direction opposite to
oscillating force. The damping force can be varied by varying the projection of the magnet over
the circular disc.

Fig. 1.6 Rectangular type

1.7 Permanent Magnet Moving Coil (PMMC) instrument

One of the most accurate type of instrument used for D.C. measurements is PMMC instrument.
Construction: A permanent magnet is used in this type instrument. Aluminum former is
provided in the cylindrical in between two poles of the permanent magnet (Fig. 1.7). Coils are
wound on the aluminum former which is connected with the spindle. This spindle is supported
with jeweled bearing. Two springs are attached on either end of the spindle. The terminals of the
moving coils are connected to the spring. Therefore the current flows through spring 1, moving
coil and spring 2.

Damping: Eddy current damping is used. This is produced by aluminum former.

Control: Spring control is used.

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 Fig. 1.7

Principle of operation
When D.C. supply is given to the moving coil, D.C. current flows through it. When the current
carrying coil is kept in the magnetic field, it experiences a force. This force produces a torque and
the former rotates. The pointer is attached with the spindle. When the former rotates, the pointer
moves over the calibrated scale. When the polarity is reversed a torque is produced in the opposite
direction. The mechanical stopper does not allow the deflection in the opposite direction. Therefore
the polarity should be maintained with PMMC instrument.
If A.C. is supplied, a reversing torque is produced. This cannot produce a continuous deflection.
Therefore this instrument cannot be used in A.C.

Torque developed by PMMC

Let Td =deflecting torque

TC = controlling torque
= angle of
deflection K=spring
constant b=width of
the coil

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 l=height of the coil or length of coil
N=No. of turns
I=current
B=Flux density
A=area of the coil
The force produced in the coil is given by
(1.4)
F BIL sin

When 90

For N turns, F NBIL (1.5)

Torque produced F distance (1.6)

Td r

Td NBIL b (1.7)
BINA

Td BANI (1.8)
Td I (1.9)
Advantages
✓ Torque/weight is high
✓ Power consumption is less
✓ Scale is uniform
✓ Damping is very effective
✓ Since operating field is very strong, the effect of stray field is negligible
✓ Range of instrument can be extended
Disadvantages
✓ Use only for D.C.
✓ Cost is high
✓ Error is produced due to ageing effect of PMMC
✓ Friction and temperature error are present

14
1.7.1 Extension of range of PMMC instrument
Case-I: Shunt
A low shunt resistance connected in parrel with the ammeter to extent the range of current. Large
current can be measured using low current rated ammeter by using a shunt.

Fig. 1.8

Let Rm =Resistance of meter

Rsh =Resistance of shunt

Im = Current through meter

Ish =current through shunt

I= current to be measure
Vm Vsh (1.10)

ImRm IshRsh

I
(1.11)
m
R
Is sh
R
h
m

Apply KCL at ‘P’ I Im (1.12)

Ish

Eqn (1.12) ÷ by Im
15
I Ish
1 (1.13)
Im Im

16
 I
1 (1.14)
Rm

Im Rsh

Rm

I Im 1 R (1.15)
sh
Rm

1 R is called multiplication factor

sh
Shunt resistance is made of manganin. This has least thermoelectric emf. The change is
resistance, due to change in temperature is negligible.

Case (II): Multiplier

A large resistance is connected in series with voltmeter is called multiplier (Fig. 1.9). A large
voltage can be measured using a voltmeter of small rating with a multiplier.

Fig. 1.9
Rm =resistance of meter
Let
Rse =resistance of multiplier

Vm =Voltage across meter

Vse = Voltage across series

resistance V= voltage to be measured

Im (1.16)
Ise

17
Vm (1.17)
Vse Rm
Rs
e

Vs (1.18)
e Rse
V Rm
m

18
 (1.19)
Apply KVL, V Vm
Vse

Eqn (1.19) ÷Vm

V Vse Rse

V 1 V 1R (1.20)
m m m
Rse

V Vm 1 R (1.21)
m
Rse

1 R Multiplication factor
m

1.8 Moving Iron (MI) instruments

One of the most accurate instrument used for both AC and DC measurement is moving iron
instrument. There are two types of moving iron instrument.
• Attraction type
• Repulsion type
1.8.1 Attraction type M.I. instrument
Construction:The moving iron fixed to the spindle is kept near the hollow fixed coil (Fig. 1.10).
The pointer and balance weight are attached to the spindle, which is supported with jeweled
bearing. Here air friction damping is used.

Principle of operation
The current to be measured is passed through the fixed coil. As the current is flow through the
fixed coil, a magnetic field is produced. By magnetic induction the moving iron gets magnetized.
The north pole of moving coil is attracted by the south pole of fixed coil. Thus the deflecting force
is produced due to force of attraction. Since the moving iron is attached with the spindle, the
spindle rotates and the pointer moves over the calibrated scale. But the force of attraction depends
on the current flowing through the coil.

Torque developed by M.I

19
Let ‘ ’ be the deflection corresponding to a current of ‘i’ amp
Let the current increases by di, the corresponding deflection is ‘ d ’

20
 Fig. 1.10
There is change in inductance since the position of moving iron change w.r.t the fixed
electromagnets.
Let the new inductance value be ‘L+dL’. The current change by ‘di’ is dt seconds.
Let the emf induced in the coil be ‘e’ volt.
d di
e (Li) L i (1.22)
dL

dt dt dt
Multiplying by ‘idt’ in equation (1.22)
di dL
e idt L idt i idt (1.23)

dt dt

e idt Lidi i2dL (1.24)

Eqn (1.24) gives the energy is used in to two forms. Part of energy is stored in the inductance.
Remaining energy is converted in to mechanical energy which produces deflection.

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 Fig. 1.11

22
Change in energy stored=Final energy-initial energy stored
1 1 2
(L dL)(i di)2 Li
2 2
1
{(L dL)(i2 di2 2idi)
Li2} 2
1
{(L dL)(i2 2idi)
Li 2} 2
1
{Li2 2Lidi i 2dL 2ididL
Li 2} 2
1
{2Lidi
2
i dL} 2 (1.25)
1 2
Lidi i dL
2 (1.26)
Mechanical work to move the pointer by d
Td d
By law of conservation of energy,
Electrical energy supplied=Increase in stored energy+ mechanical work done.
(1.27)
Input energy= Energy stored + Mechanical energy
1 2
Lidi i2dL Lidi i dL Td d
2 (1.28)
1 2
i dL Td d
2

1 2 dL (1.29)
T i
d
2 d
At steady state condition
Td TC
1 2 dL (1.30)
i K
2
d
1 2 dL (1.31)
i
2K d

23
 i2 (1.32)

When the instruments measure AC, i2rms

Scale of the instrument is non uniform.

24
Advantages
✓ MI can be used in AC and DC
✓ It is cheap
✓ Supply is given to a fixed coil, not in moving coil.
✓ Simple construction
✓ Less friction error.
Disadvantages
✓ It suffers from eddy current and hysteresis error
✓ Scale is not uniform
✓ It consumed more power
✓ Calibration is different for AC and DC operation
1.8.2 Repulsion type moving iron instrument
Construction:The repulsion type instrument has a hollow fixed iron attached to it (Fig. 1.12). The
moving iron is connected to the spindle. The pointer is also attached to the spindle in supported
with jeweled bearing.
Principle of operation: When the current flows through the coil, a magnetic field is produced by
it. So both fixed iron and moving iron are magnetized with the same polarity, since they are kept
in the same magnetic field. Similar poles of fixed and moving iron get repelled. Thus the deflecting
torque is produced due to magnetic repulsion. Since moving iron is attached to spindle, the spindle
will move. So that pointer moves over the calibrated scale.
Damping: Air friction damping is used to reduce the oscillation.
Control: Spring control is used.

25
 Fig. 1.12

1.9 Dynamometer (or) Electromagnetic moving coil instrument (EMMC)

Fig. 1.13

26
This instrument can be used for the measurement of voltage, current and power. The difference
between the PMMC and dynamometer type instrument is that the permanent magnet is replaced
by an electromagnet.

Construction:A fixed coil is divided in to two equal half. The moving coil is placed between the
two half of the fixed coil. Both the fixed and moving coils are air cored. So that the hysteresis
effect will be zero. The pointer is attached with the spindle. In a non metallic former the moving
coil is wounded.
Control: Spring control is used.
Damping: Air friction damping is used.
Principle of operation:

When the current flows through the fixed coil, it produced a magnetic field, whose flux density is
proportional to the current through the fixed coil. The moving coil is kept in between the fixed
coil. When the current passes through the moving coil, a magnetic field is produced by this coil.

The magnetic poles are produced in such a way that the torque produced on the moving coil
deflects the pointer over the calibrated scale. This instrument works on AC and DC. When AC
voltage is applied, alternating current flows through the fixed coil and moving coil. When the
current in the fixed coil reverses, the current in the moving coil also reverses. Torque remains in
the same direction. Since the current i1 and i2 reverse simultaneously. This is because the fixed and
moving coils are either connected in series or parallel.

Torque developed by EMMC

Fig. 1.14

27
Let
L1=Self inductance of fixed coil
L2= Self inductance of moving coil
M=mutual inductance between fixed coil and moving coil
i1=current through fixed coil
i2=current through moving coil
Total inductance of system,

Hence the deflection of pointer is proportional to the current passing through fixed coil and
moving coil.

28
1.9.1 Extension of EMMC instrument
Case-I Ammeter connection
Fixed coil and moving coil are connected in parallel for ammeter connection. The coils are
designed such that the resistance of each branch is same.
Therefore
I1 I2 I

Fig. 1.15

To extend the range of current a shunt may be connected in parallel with the meter. The value
Rsh is designed such that equal current flows through moving coil and fixed coil.

Td I1I2 (1.41)
dM
d

Or Td I2 (1.42)
dM
d
TC (1.43)
K

I2 (1.44)
dM

Kd

I 2 (Scale is not uniform) (1.45)

29
Case-II Voltmeter connection

Fixed coil and moving coil are connected in series for voltmeter connection. A multiplier may be
connected in series to extent the range of voltmeter.

30
 Fig.1.16

Case-III As wattmeter

When the two coils are connected to parallel, the instrument can be used as a wattmeter. Fixed coil
is connected in series with the load. Moving coil is connected in parallel with the load. The moving
coil is known as voltage coil or pressure coil and fixed coil is known as current coil.

Fig. 1.17

31
Assume that the supply voltage is sinusoidal. If the impedance of the coil is neglected in
comparison with the resistance ‘R’. The current,

32
 (1.66)
(Td )avg KVI cos

TC (1.67)

KVI cos (1.68)

VI cos (1.69)
Advantages
✓ It can be used for voltmeter, ammeter and wattmeter
✓ Hysteresis error is nill
✓ Eddy current error is nill
✓ Damping is effective
✓ It can be measure correctively and accurately the rms value of the voltage

Disadvantages
✓ Scale is not uniform
✓ Power consumption is high(because of high resistance )
✓ Cost is more
✓ Error is produced due to frequency, temperature and stray field.
✓ Torque/weight is low.(Because field strength is very low)

Errors in PMMC
✓ The permanent magnet produced error due to ageing effect. By heat treatment, this error
can be eliminated.
✓ The spring produces error due to ageing effect. By heat treating the spring the error can be
eliminated.
✓ When the temperature changes, the resistance of the coil vary and the spring also produces
error in deflection. This error can be minimized by using a spring whose temperature co-
efficient is very low.
1.10 Difference between attraction and repulsion type instrument
An attraction type instrument will usually have a lower inductance, compare to repulsion type
instrument. But in other hand, repulsion type instruments are more suitable for economical
production in manufacture and nearly uniform scale is more easily obtained. They are therefore
much more common than attraction type.

33
INDUCTION TYPE INSTRUMENTS

11.1 Working Principle of Induction Type Instruments

Consider an aluminum disc placed the between the pole of an electromagnet, as shown in fig. 11.1. Let
the flux produced by flow of current of I Amperes through the coil be F and this flux will lag behind I,
by a small angle β as shown in vector diagram.

Fig. 11.1 Working principle of induction type instruments

Fig. 11.2 Vector diagram

Since the aluminum disc act as a short circuited secondary of the transformer, therefore, an e.m.f., (say
e volts) lagging behind the flux F by �radians will be induced in it. As a result of this induced e.m.f.,
the eddy current (I�) starts flowing in the disc. Since the disk is purely resistive therefore the eddy
current will be in phase with induced e.m.f. (e) will lag behind the main flux F by � radians. As the
component of eddy current (I�) along flux F is zero, therefore torque produced is zero. It can be proved
as follows.

Let the instantaneous values of flux and eddy current be given by F = Fmax Sin θ and i = Imax Sin (θ �
α). Where α is the phase angle between the induced eddy current and flux (F).
Instantaneous torque α F i

����������

34
����������

����������

����������
���������� α Fi Cos α

Where F and i are r.m.s. values.

Since in single phase induction type instruments the angle α between main flux F and eddy current I�
is �and Cos �is zero, therefore torque produced is zero. Hence to obtain the resultant torque it is
necessary to produce an eddy current which is either appreciable less than or appreciable more than
�radians, out of phase with the flux which it reacts. Several arrangements are possible but here we will
discuss about the descriptions of the two of these.

11.2 Pole Shaded Method

As shown in Fig. 11.3, in this method, the working current is passed through the coil of an electromagnet
which has an air gap in one limb. Permanent magnet is used for providing damping torque. The
aluminum disc is mounted on pivots and jewel bearings.

Fig. 11.3 Pole shaded method

Fig. 11.4 Vector diagram

35
Two spiral springs are employed to provide controlling torque, wounded in direction opposite to each
other if the instrument is used as Voltmeter, Ammeter and Wattmeter etc. One half of the pole face is
surrounded by a copper band in order to split the working flux into two different paths. The copper
shading band acts as a single turn short circuited secondary winding of the transformer. The spiral
springs, pointer and scale etc. have been omitted for simplicity.

11.2.1 Theory

Let the total flux produced in the magnetic core be F Weber. Due to shading of pole, this flux will split
up into two fluxes i.e. flux through un-shaded portion and other through the shaded portion. Suppose
the flux F1 be the flux of the shaded portion of the pole. This flux F1 will induce an e.m.f. in the copper
ring, which will lag the flux F1 by 90�, as shown in Fig. 11.4. The induced e.m.f. will force a current
say i to flow in the copper ring which will be lagging behind the flux F1 by 900. The current flowing in
the copper ring will produce its own magnetic field say F�2 in phase with current i. The flux given by
the shaded portion of the pole will be the vector sum of F1 and F�2 which is equal to F2 lagging behind
flux F1 by an angle θ and its value should be 400 to 600 for producing effective deflecting torque.

Let the flux F1 and F2 are the fluxes passing through the shaded and un-shaded portions of the pole
respectively induce e.m.fs. e1 and e2 in the disc, each of which is 900 in phase behind the fluxes
responsible for inducing it. These induced e.m.fs; will induce eddy currents (say i1 and i2) in the disc
lagging by a small angle (say α) behind its voltage due to the inductance of the path in the disc.

Fig. 11.5 Vector diagram

From Fig. 11.5, it is obvious that each of the current i1 and i2 has a component in phase with the other
flux such i1′ and i2′. Hence two torques are acting in a directions having angle θ are produced in the
instrument. Resultant of these two torques, provides an operating or deflecting torque.

11.3 Two Pole Method

This method is also known as split phase method. In this method, two laminated magnets A and B are
placed near to each other with aluminum (Al) disc in between and a non inductive resistance R is
connected in series with the magnetizing coil of magnet A and an inductive coil L is connected in series
with the magnetizing coil of magnet B, as shown in Fig. 11.6.

36
 Fig. 11.6 Two pole method (split phase)

Hence there will be two fluxes having phase difference of less than 90� with each other, acting on the
disc which will produce a resultant torque in the aluminium disc.

Let the flux produced by the magnet A and B is F1 and F2 respectively. F2 is lagging F1 by an angle θ as
shown in Fig. 11.5. Hence an operating or deflecting torque will be produced as explained above in case
of shaded pole method.

INDUCTION TYPE VOLTMETER AND AMMETER

12.1 Shaded Pole Type Voltmeter

A volt meter is an instrument used to measure the potential difference between the two points in an
electric circuit. In analog voltmeters, the pointer moves over a calibrated scale in proportion to potential
difference across the points where as in case of digital voltmeters, it displays numerical values with the
help of analog to digital converter. The induction type voltmeter operates on the either shaded pole
method or on two pole method�s working principle as explained in Lesson 11.

Fig. 12.1 Shaded pole type voltmeter

A non inductive high resistance is also inserted in series with the shunt coil and is connected across the
supply, whose potential difference has to be measured. Since the voltmeters are connected across the
supply, so the current flowing through coil is very small of the order of 5 to 10 mA. The spindle of
37
aluminum disc is provided with a pointer moving over a calibrated scale in terms of voltage. Spiral
springs are provided on both the ends of spindle for providing controlling torque. Permanent magnet (C-
magnet) is used to provide damping torque on the spindle. As the instrument is provided with spiral
springs, to provide controlling torque, the scale of the instrument is uniform because in such instrument
this torque is directly proportional to angle of deflection of the pointer. Spiral springs, pointer and
damping magnets are omitted for clear understanding of the figure. For detail working of the instrument,
please refer to working principle of induction type instruments described in Lesson 11.

12.2 Split Phase Ammeter

An ammeter is always connected in series with load current directly or through CT (Current
Transformer). As shown in Fig. 12.2, both the windings on the two laminated electromagnets A and B
are connected in series but winding is shunted by a resistance R with the result of which, the current in
this winding lags with respect to the total current (I). Hence the necessary phase angle (α) required
between two fluxes is produced by the laminated electromagnets A and B.

Fig. 12.2 Split phase induction type ammeter

The operating principle of the induction type instrument is based on the two pole method as discussed
in Lesson 11. Two fluxes produced by laminated magnet A and B are focused upon the aluminum disc,
having a phase angle between them required for producing a resultant torque in the spindle of the moving
system. Being a spring control based controlling torque, the scale is uniform and the deflecting torque is
directly proportional to square the load current. Eddy current damping is used to provide necessary
damping torque by a permanent magnet. Spiral springs, pointer and damping magnets are omitted for
clear understanding of the Fig. 12.2.

12.3 Advantages and Disadvantages of Induction Type Instruments

Advantages
(a) Damping is very much effective and efficient.
(b) Full scale deflection more than 200� can be obtained.
Disadvantages

(a) Power consumption is large and hence not recommended where continuous monitoring of ac
quantities is required.
38
(b) Variation in temperature and frequency may cause serious errors if necessary compensations
are not provided.
(c) As these instruments are based on principle of induction, they can be used on AC supply
only.

12.4 Compensation for Frequency and Temperature Errors

12.4.1 Compensation for variation in frequency

Variation in frequency causes serious errors because deflecting torque is directly proportional to
frequency and also the value of impedance (Z) and Cos α depends upon the supply frequency. The error
is compensated by use of non inductive shunt in case of an Ammeter, when the frequency increases, the
increase in impedance of the winding cause a greater proportion of the total current to flow in the non
inductive shunt (whose impedance remains constant for all frequency) and lesser proportion of the total
current in flow in the winding and to an extent thus compensate the increase in torque (since T α. f).

In case of voltmeter, the impedance of the winding increases with the increase in frequency, hence
smaller current is drawn by the winding, which tends to compensate the increase in torque due to increase
in frequency.

12.4.2 Compensation for variation in temperature

Variation in temperature changes the resistance of the eddy current paths, therefore, may result in serious
errors. The error is compensated in case of an ammeter, employing a shunt of material having a high
temperature coefficient of resistance than the material of the disc. This shunt may be the same one as
used for frequency compensation. When the temperature increases, the resistance of the shunt increases,
hence the greater portion of the current flows through the coil and decreases in torque due to smaller
eddy current in the disc owing to increase in resistance at high temperature is compensated. The
combination of shunt and swapping resistance in series with the instrument is often employed to
compensate the temperature error in case of voltmeters. Since the frequency errors in induction type
instruments are so serious that cannot be compensated satisfactorily. Hence these instruments are used
for only constant frequency supplies or where the fluctuation in frequency is very small.
INDUCTION TYPE WATTMETER, WATT-HOUR METER, AND DYNAMOMETER TYPE
POWER FACTOR METER

13.1 Induction Type Wattmeter

These types of watt-meters operate on the same working principle on which the induction type ammeter
and voltmeter operates. These instruments can only be used on ac supply while dynamo-meter type watt
meters can be used on either ac or dc supply system. Induction type watt-meters are useful only when
the supply and frequency remains constant. Since both the coils i.e. current coil and pressure coils are
necessary in such instrument, it is not essential to use shaded pole principle. Because for producing a

39
deflecting torque, two fluxes are essential with suitable phase angle and it would be available from these
two coils.

13.1.1 Construction

A watt-meter has two laminated electromagnet, one of which is excited by load current or definite
fraction of it, and is connected in series with the circuit, known as series magnet and the other is excited
by the current proportional to the applied voltage or fraction of it and is always connected across the
supply, known as shunt magnet. An aluminum disc is so mounted so that it cuts the fluxes produced by
both the magnets. As a result of which, two e.m.f�s are produced which induces two eddy currents in
the disc. C - Magnet is used to provide necessary damping torque to the pointer, to damp out the
oscillations. Deflecting torque is produced due to interaction of these eddy currents and the inducing
flux. Copper shading bands are provided either on central limb or on the outer limb of the shunt magnet,
and can be so adjusted as to make the resultant flux in the shunt magnet lag behind the applied voltage
by 90�. Both the watt-meters are provided with spiral springs A and B, for producing controlling torque
to counter balance the deflecting torque. In Fig. 13.2 the spiral spring and damping magnet is omitted
for simplicity. The scale of such type instruments is quite uniform and extends over an angle of 300�.
Currents up to 100 A can be handled by these watt-meters directly where as beyond this current
transformers are used. Two types of induction type watt meters are available. Line diagrams of both of
the types are detailed in Fig. 13.1 and 13.2.

Fig. 13.1 Induction type wattmeter

In the form of the instrument shown in Fig. 13.1, two pressure coils are connected in series in such a way
that both of them send flux through the central limb. The series magnet also carries two small current
coils connected in series and wound so that they magnetized their respective cores in the same direction.
Correct phase displacement between the fluxes produced by series and shunt magnet is obtained by the
adjustment of copper shading band on the central limb.

40
 Fig. 13.2 Induction type wattmeter

In Fig. 13.2, there is only one pressure and one current coil. Two projecting poles of shunt magnet are
surrounded by a copper shading band whose position can be adjusted for correcting the phase of the flux
of this magnet with the applied voltage. The pressure coil circuit of induction type instrument is made
as inductive as possible so that the flux of the shunt magnet may lag nearly by 90 degree behind the
applied voltage.

13.1.2 Advantages

The advantages of induction watt meters are the same as those of induction ammeters long scale,
freedom from effects of stray field, and have effective damping torque.

13.1.3 Disadvantages

Following are the disadvantage of the induction type instruments:

a) Change in temperature causes variation in the resistance of the moving element, affects the eddy
currents therein, and so the operating torque. The error due to this is in part offset by a balancing
effect due to change in temperature of the windings.
b) Change in frequency from that of the calibration value causes variations in both the reactance of
the voltage coil circuit, which is highly inductive, and also in the amount of compensation from the
phase compensating circuit. Within the limits of frequency variation met within practice on the
mains, this last error in not important.

13.2 Induction Type Single Phase Watt Hour Meter

A watt hour meter is used to sum up the total energy consumed by a consumer during a period so that it
can be charged for the actual energy consumed. The working principle, theory and advantage /
disadvantages are almost similar to single phase watt meter. The construction of single phase watt hour
meter is also almost similar to single phase induction type watt meter as discussed above. The pointer

41
and spiral springs are replaced by wheel-train mechanism for summing up of total energy consumed
where as the damping magnet is replaced by braking magnet. The construction of this type of watt hour
meter is shown in Fig.

Fig. Induction type energy meter

The brake magnet and recording wheel-train being omitted for clear understanding of the diagram. The
description of registering mechanism and braking system is detailed below.

13.2.1 Registering or counting system

The registering or counting system essentially consists of gear train, driven either by worm or pinion
gear on the disc shaft, which turns pointers that indicate on dials the number of times the disc has turned.
The energy meter thus determines and adds together or integrates all the instantaneous power values so
that total energy used over a period is thus known. Therefore, this type of meter is also called
an integrating meter.

13.2.2 Braking system

Braking of the disk is provided by a small permanent magnet, located diametrically opposite to the
alternating current magnets. The disk moves between the magnets gaps. The movement of rotating disc
through the magnetic field crossing the air gap sets up eddy currents in the disc that reacts with the
magnetic field and exerts a braking torque. By changing the position of the brake magnet or diverting
some of the flux therefore, the speed of the rotating disc can be controlled. Creep error can be rectified
by drilling a small hole in the aluminum disc passing through the magnetic flux of braking magnet.

13.3 Errors and Adjustment in Induction Type Instruments

13.3.1 Phase and speed error

It is necessary that the energy meter should give correct reading on all power factors, which is only
possible when the field set up by shunt magnet flux lags behind the applied voltage by 90 degree.
42
Ordinarily the flux set up by shunt magnet does not lag behind the applied voltage exactly by 90 degree
because of winding resistance and iron losses. The flux due to shunt magnet is made to lag behind applied
voltage by 90 degree with the help of copper shading band provided on the central limb. An error due to
incorrect adjustment of shading band will be evident when the meter is tested on a load of power factor
less than unity.

An error on the fast side under these conditions can be eliminated by bringing the shading band nearer
to the disc and vice versa. An error in the speed of the meter when tested on non inductive load can be
eliminated by adjustment of the position of the brake magnet. Movement of the brake magnet in the
direction of the spindle will reduce the braking torque and vice versa. Speed of disc is directly
proportional to the distance between the disc and brake magnet.

13.3.2 Friction compensation

The two shading bands embrace the flux contained in the two outer limbs of the shunt electromagnet,
and thus eddy current are induced in them which cause a phase displacement between the enclosed flux
and main gap flux. As a result, a small driving torque is exerted on the disc, this torque being adjusted,
by variation of the position of these bands, to compensate for frictional torque in the instrument.

In some energy meter, it is observed that the disc continue to rotate even when the load on the energy
meter is zero and potential coil is in excited condition. This defect is known as creeping and is prevented
by cutting two holes or slots in the disc on opposite sides of the spindle. The disc tends to remain
stationary when one of the holes comes under one of pole of the shunt magnet. In some cases, a small
piece of iron wire is attached to the edge of the disc. The force of attraction of the brake magnet upon
this wire is sufficient to prevent continuous rotation of the disc under no load condition.

13.3.3 Temperature and frequency errors

The error due to variation in temperature is very small. Since the various effects due to change in
temperature tends to neutralize each other on unity power factor if not on low power factor (lagging).
Since the meters are used normally on fixed frequency and hence these can be adjusted to have a
minimum error at declared supply frequency which is normally 50 cycles / second.

13.4 Single Phase Dynamo-meter Type Power Factor Meter

The power factor meter is used to indicate the instantaneous power factor of the consumer. It consist of
two fixed coils CC connected in series carrying the load current (or a definite fraction of it) and two
identical moving coils P1 & P2 wound with a fine copper wire, fixed at right angle to each other and
pivoted on the same spindle. The pressure coils P1 and P2 move together and carry a pointer, which
indicates the power factor of the circuit directly on the scale.

43
 Fig. Dynamometer type power factor meter

The pressure coil P1 is connected across the supply through a non inductive resistance R and pressure
P2 is connected across the supply through a highly inductive choke coil of inductance L. The value of
non inductive resistance R and inductance L are so chosen that for the normal frequency, the current in
the two pressure coil P1 and P2 is same. Thus these coils P1 and P2 produce equally strong magnetic field
displaced by 900 in space as well as in the phase. For measurement of power factor on high voltage
system, the current and pressure coils of the instrument may be connected to the main circuit through
current and potential transformer respectively.

13.4.1 Theory

While measuring power factor of an installation, there may be three possibilities of installations power
factor, which are described here:

(a) Power Factor is Unity: When the circuit is switched on, the current in the potential coil P1 will
be in phase with current in coils CC, where as the current in pressure coil P2 will lag 900 behind the
voltage or behind the current in the circuit coli CC. Thus pressure coil P1 will experience a turning
moment so its plane will come in a position parallel to a plane of a current coil CC. The average
torque on coil P2 will be zero but being mechanically coupled to coil P1, it will follow the rotation
of coil P1. Hence the pointer will in the centre of the calibrated scale and it will show the power
factor as unity. The position of coil P1 is shown in Fig. and it will maintain the reading till the load
current is in phase with the voltage.
(b) When Power Factor is Zero (lagging): In this situation, the current flowing in the pressure coil
P2 will be in phase with load current flowing in the fixed current coil CC, both lagging behind the
applied circuit voltage by 900 and current in pressure coil P1 will lead the load current in current coil
CC by 900. Thus only pressure coil P2 will experience a turning moment so its plane will come in a
position parallel to the plane of current coils CC. At this instant, the pointer will indicate zero power
factor lagging.
(c) When Power Factor Zero (leading): When the current flowing in fixed coils CC leads the
applied voltage by 90 degree and, therefore, the field of pressure coils P1 by 90 degree and that of
coil P2 by 180 degree. Hence the polarity of field in current coils is the reverse of that considered
44
 above. At this instant, the pointer will indicates the power factor as zero leading on the other half of
the scale.

For an intermediate power factor, the moving system takes up intermediate position and the pointer
makes an angle of (90 degree - F) with the axis of the fixed coils where F the phase angle between load
current is and applied voltage of the load circuit.
Errors in wattmeter and energy meter and their compensation and adjustment

Errors in Wattmeter Compensation method

To overcome this error, wattmeter’s are provided

with additional compensating winding which is
connected in series with pressure coil but
positioned in such a manner that it produces a
field in opposition to that produced by current in
current coil.

Error
due to connection method
A suitable value capacitor connected in parallel
Error due to pressure coil inductance
with pressure coil.
This error can be reduced by designing pressure
coil circuit such that inductive reactance of the
Error due to Pressure Coil Capacitance
circuit matches exactly with the capacitance
reactance of the circuit i.e. XL=XC.
This error can be reduced by proper design of
pressure coil and current coil system so that they
Error due to mutual inductance effect
always remain in a zero position of mutual
inductance.
To avoid this error, magnetic shield is placed over
Error due to stray magnetic fields
CC & PC.
These are minimized by avoiding solid metal
Error due to eddy currents
parts and using laminated core.
Using zero temperature coefficient materials for
Temperature error
coils and components, this can be minimized.
It is avoided by designing the moving system
Error due to vibration of moving system such that its natural freq is greater than 2 times
the freq of deflecting torque of the wattmeter.
The weight of moving system be reduced to
Error due to friction
minimum possible.

Phantom Loading
45
Definition: Phantom loading is the phenomena in which the appliances consume electricity even
when they turn off. The disc of the energy meter rotates which increases the reading of the meter, but
the devices do not consume power. This type of loading is also known as the vampire or virtual
loading. The phantom loading mainly occurs in the “electronic” appliances.

The phantom loading is used for examining the current rating ability of the energy meter. The actual
loading arrangement will waste a lot of power. The phantom loading consumes very less power as
compared to real loading, and because of this reason, it is used for testing the meter.

In phantom loading, the pressure coil and the current coil are separately excited by the supply source.
The pressure coil is energised from the small supply voltage, and the current energises the current coil
at very small voltages.

The pressure and current coil circuit have low impedance (less obstruction of movement of the
electron) because of which highly rated current is passed through it. The total current supplied for the
phantom loading is the sum of the pressure coil current which is supplied at normal voltage and the
current of the current coil supply at low voltages.

Example of Phantom Loading

Consider the DC energy meter having rating voltage 220V and current 9 Ampere. The resistance of the
pressure coil and the current coil is 4400Ω and 0.1Ω respectively. The power consumption of the load
by direct and indirect phantom is explained below.

Direct Loading Arrangement

The circuit for direct loading is shown in the figure

below.

The power consumption of the pressure coil circuit is calculated as

Power = (220)2/ 4400 = 48400/4400 = 11watt

The power consumption of the current circuit is expressed as

Power = 220 Χ 9 = 1980watt

46
The total power consumed by the pressure and current circuit

Power = 11watt + 1980watt = 1991watt

Phantom Loading Arrangement

The circuit of the phantom loading is shown in the figure below.

The power consumption of the pressure coil is given below.

P = (220)2/4400 = 11watt

The current coil of the phantom loading arrangement is separately excited by the battery of the 9V. The
power of the current coil is measured as

Power = 9 Χ 9 = 81watt

The total power consumed by the phantom loading is expressed as

Total Power = 11watt + 81watt = 92watt

The above example shows that in phantom loading the pressure and the current coil is separately
excited by the meter. Hence the power loss is less in phantom loading as compared to direct loading.

47
 Unit -2
Polyphase Metering
Blondel’s Theorem

Blondel's theorem tells about the number of watt-meters required to measure three-phase power.

It states that, in order to measure power in a network with n number of lines. The total number of
watt-meters required is equal to n, and total power is the sum of all the watt-meters readings. It is in
such condition that, if current coils of each wattmeter are connected in each line and corresponding
voltage coils are connected such that, one end to their respective line and other ends of all the voltage
coils are connected together forming a common point.

Suppose, if the common point is to be taken on any one of the lines. Then the other end of the voltage
coils is connected to that common line (i.e., common point). In such conditions, the power can be
measured by (n-1) watt-meters. Thus for measuring 3-phase power, only 2 watt-meters are required,
this is called Two Wattmeter Method.

The pressure coil of all the three wattmeters namely W1, W2 and W3 are connected to a common
terminal known as the neutral point. The product of the phase current and line voltage represents
phase power and is recorded by an individual wattmeter.

The total power in a three wattmeter method of power measurement is given by the algebraic sum
of the readings of three wattmeters. i.e.
Where,

W1 = V1I1

W2 = V2I2

W3 = V3I3

Except for 3 phase, 4 wire unbalanced load, 3 phase power can be measured by using only Two
Wattmeter Method.

Measurement of Three Phase Power

Various methods are used for measurement of three phase power in three phase circuits on the
basis of number of wattmeters used. We have three methods to discuss:
1. Three wattmeters method
2. Two wattmeters method
3. Single wattmeter method.
Let us discuss one by one each method in detail.

Measurement of Three Phase Power by Three Wattmeters Method

The circuit diagram is shown below-

Here, it is applied to three phase four wire systems, current coil of all the three wattmeters marked
as 1, 2 and 3 are connected to respective phases marked as 1, 2 and 3. Pressure coils of all the three
wattmeters are connected to a common point at neutral line. Clearly each wattmeter will give reading
as product of phase current and line voltage which is phase power. The resultant sum of all the
readings of wattmeter will give the total power of the circuit. Mathematically we can write

Measurement of Three Phase Power by Two Wattmeters Method

In this method we have two types of connections

1. Star connection of loads

2. Delta connection of loads.
When the load is star connected load, the diagram is shown in below-

Phasor diagram for real power measurements

For star connected load clearly the reading of wattmeter one is product of phase current and
voltage difference (V2-V3). Similarly the reading of wattmeter two is the product of phase
current and the voltage difference (V2-V3). Thus the total power of the circuit is sum of the
reading of both the wattmeters. Mathematically we can write

but we have , hence putting the value of .

We get total power as .

When delta connected load, the diagram is shown in below
The reading of wattmeter one can be written as

and reading of wattmeter two is

but , hence expression for total power will reduce to .

Measurement of Three Phase Power by One Wattmeter Method

Limitation of this method is that it cannot be applied on unbalanced load. So under this condition we

have .
Diagram is shown below:
Two switches are given which are marked as 1-3 and 1-2, by closing the switch 1-3 we get reading
of wattmeter as

Similarly the reading of wattmeter when switch 1-2 is closed is

Variation of wattmeter readings with load PF (lag)

PF PF W1 W2 W3ph=W1+ Remarks
angle W2
φ (lag) cos φ VLILcos(30- VLILcos(30+ √3VLILcosφ Gen. Case (always
φ) φ) W1≥W2)
00 UPF √3/2 VLIL √3/2 VLIL 2W1 or 2W2 W1=W2
300 0.86 VLIL VLIL/2 1.5W1 or W2=W1/2
6 3W2
600 0.5 √3/2 VLIL ZERO W1 alone W2 reads zero
For taking readings, the PC
or
>600 W1 W2 reads W1+(-W2)
<0.5 CC connection of W2
should
negative be reversed) (LPF case)
Instrument Transformers:

Instrument Transformers Basics

Why instrument transformers?
In power systems, currents and voltages handled are very large.
Direct measurements are not possible with the existing equipments.
Hence it is required to step down currents and voltages with the help of instrument
transformers so that they can be measured with instruments of moderate sizes

Instrument Transformers
Transformers used in conjunction with measuring instruments for measurement purposes
are called “Instrument Transformers”.
The instrument used for the measurement of current is called a “Current Transformer” or
simply “CT”.
The transformers used for the measurement of voltage are called “Voltage transformer”
or “Potential transformer” or simply “PT”.

Fig 1. Current Transformer Fig 2. Potential Transformer

Fig 1. indicates the current measurement by a C.T. The current being measured passes
through the primary winding and the secondary winding is connected to an ammeter.
The C.T. steps down the current to the level of ammeter.
Fig 2. shows the connection of P.T. for voltage measurement. The primary winding is
connected to the voltage being measured and the secondary winding to a voltmeter.
The P.T. steps down the voltage to the level of voltmeter.
Merits of Instrument Transformers:
1. Instruments of moderate size are used for metering i.e. 5A for current and 100
to 120 volts for voltage measurements.
2. Instrument and meters can be standardized so that there is saving in costs.
Replacement of damaged instruments is easy.
3. Single range instruments can be used to cover large current or voltage ranges,
when used with suitable multi range instrument transformers.
4. The metering circuit is isolated from the high voltage power circuits. Hence
isolation is not a problem and the safety is assured for the operators
5. There is low power consumption in metering circuit.
6. Several instruments can be operated from a single instrument
Nominal Ratio: It is the ratio of rated primary winding current (voltage) to the rated
secondary winding current (voltage).

Turns ratio: This is defined as below

Burden of an Instrument Transformer:

The rated burden is the volt ampere loading which is permissible without errors
exceeding the particular class of accuracy.
2.2. Current Transformer equivalent circuit:

X1 = Primary leakage reactance

R1 = Primary winding resistance
X2 = Secondary leakage reactance
Z0 = Magnetizing impedance
R2 = Secondary winding resistance
Zb = Secondary load
Note: Normally the leakage fluxes X1 and X2 can be neglected

2.3. Current transformer, simplified equivalent circuit:

 2.4. Current transformer: Phase displacement and current ratio error :

2.5. Construction of CT
Construction of Current Transformer:
Current transformers are constructed in various ways. In one method there are two
separate windings on a magnetic steel core. The primary winding consists of a few turns
of heavy wire capable of carrying the full load current while the secondary winding
consist of many turns of smaller wire with a current carrying capacity of between 5/20
amperes, dependent on the design. This is called the wound type due to its wound primary
coil.

2.6. Wound Type

Phasor Diagram

Angle by which the reversed I2 differs in phase from the I1vector

Ideally the I2should lag the I1by 1800and hence the phase angle is ZERO
In practice this angle is < 1800due to magnetizing and loss component of the I1

Potential Transformer Basics

Potential transformers are normally connected across two lines of the circuit in which the
voltage is to be measured. Normally they will be connected L-L (line-to-line) or L-G (line-
to-ground). A typical connection is as follows:
2.8. Phasor Diagram of Potential Transformer:
The theory of a potential transformer is the same as that of a power transformer. The
main difference is that the power loading of a P.T. is very small and consequently the
exciting current is of the same order as the secondary winding current while in a power
transformer the exciting current is a very small fraction of secondary winding load
current.
 Unit 3
Potentiometers
A potentiometer is an instrument designed to measure an unknown voltage by comparing it
with a known voltage. The known voltage may be supplied by a standard cell or any known
voltage. At null condition, no current flows, so no power consumed. So the measurement is
independent of source resistance.
It can also measure current by measuring voltage drop across a standard resistor.
It is used extensively for calibration of voltmeters & ammeters.
Measurements using comparison methods are capable of a high degree of accuracy because the
result obtained does not depend upon the actual deflection of a pointer, as is the case in
deflection methods, but only upon the accuracy with which the voltage of the reference source
is known.

Procedure to Calibrate Volt-meter

1. In this circuit, the ends of a uniform resistance wire R1 are connected to a regulated DC
supply VS for use as a voltage divider.
2. A standard electrochemical cell is used whose emf is known (e.g. 1.0183 volts)
CALIBRATION/STANDARDISATION OF POTENTIOMETER
3. Switch ‘S’ is placed at calibrate position
4. Sliding position k is positioned at a point corresponding to standard cell voltage (1.0183
volts)
5. The potentiometer is first calibrated by positioning the wiper (arrow) at the spot on the R1
wire that corresponds to the voltage of a standard cell
𝑅 Cell Voltage
so that 𝑅2 =
1 𝑉𝑆
𝑅
Cell Voltage=𝑅2 𝑉𝑆 =Working current * AX
1
6. The supply voltage VS is then adjusted until the galvanometer shows zero, indicating the
voltage on R2 is equal to the standard cell voltage.
7. As resistance of wire is uniform & proportional to length, working current i.e. volts/cm is
measured.
MEASUREMENT OF UNKNOWN VOLTAGE SOURCE
8. Now Rheostat will not be varied.
9. Now switch ‘S’ is placed at operate position
10. An unknown DC voltage, in series with the galvanometer, is then connected to the sliding
wiper, across a variable-length section R3 of the resistance wire. The wiper is moved until no
current flows into or out of the source of unknown voltage, as indicated by the galvanometer
in series with the unknown voltage. The voltage across the selected R3 section of wire is then
equal to the unknown voltage. The final step is to calculate the unknown voltage from the
fraction of the length of the resistance wire that was connected to the unknown voltage.
11. If the length of the R1 resistance wire is AB, where A is the (-) end and B is the (+) end,
and the movable wiper is at point Y at a distance AY on the R3 portion of the resistance wire
when the galvanometer gives a zero reading for an unknown voltage, the distance AY is
measured or read from a pre-printed scale next to the resistance wire. The unknown voltage
can then be calculated as VU= working cur * AY
CROMPTON-LABORATORY D.C. POTENTIOMATER:-

CONSTRUCTION:-
Modern Lab Potentiometers use calibrated dial resistors and a small circular wire of one or
more turns (instead of previously used long slide wire), thus reducing the size of instrument.
In the figure, there is one dial resistor with 15 steps, each having a precision resistor of 10 Ω.
Total 150 Ω & 1.5 volt.
Slide-Wire:- is of single turn having resistance of 10 Ω & 0.1 Volt. The working current is 10
mA.
So each step of dial-resistor correspond to 10*10* 10-3 =0.1 volt
The slide wire is provided with 200 scale divisions with a total voltage range of 0.1 volt.
So each division=0.1/200=0.005 volt
The Potentiometer is provided with a double throw switch to make connection to either the
standard cell or un-known emf. To operate the Galvanometer at its
maximum sensitivity, provision is made to short the protective resistance near balance
condition.
STEPS TO FOLLOW TO MAKE MEASUREMENT:-
1. The combination of dial-resistor & Slide-wire is set to standard cell voltage (1.0186 volt).
Dial-resistor set at 1 volt, slide- wire set at 0.0186 V.
2. Galvanometer is calibrated with switch S, connected to standard cell. Rheostat is adjusted
foe zero Galvanometer deflection.
3. As the null point is approached, protective resistance is shorted to increase Galvanometer
sensitivity. This completes the process of ‘Standardization’ of Galvanometer.
4. Now switch S is thrown to operate position to find out un-known emf. Now the potentiometer
is balanced using dial- switch & slide-wire.
5. At null, the value of emf is read directly from setting of dial adjust & slide-wire.
6. Standardization is checked again.
VERNIER POTENTIOMETER: -

CONSTRUCTION:-
There are 3 measuring dials.
1 st Dial Measures upto 1.5 v in step of 0.1 v
2 nd Dial has 102 studs & read upto 0.1 V in steps of 0.001 V.
3 rd Dial has 102 studs & reads from -0.0001 v to + 0.0001 v in steps of 0.00001 v (i.e. 10 µv).
There is no Slide-wire.
The 2nd Dial shunts two of the coils of 1st Dial. The moving arm of 2nd -dial carries two arms
spaced two-studs apart.
In practice, the resistance of 2nd -dial is greater than that between two studs in the main dial,
so that voltage drop across 2nd -dial is greater than 0.1 v. If this is not done, voltage drop in
contact resistances & leads would cause 2nd -dial voltage less than 0.1 v.
3 rd -dial is obtained from a shunt ckt which permits a true zero & a small –ve setting is
obtained.
OPERATION:-
The limitations imposed on performance of ordinary potentiometers by slide-wire are
eliminated in a vernier potentiometer. This instrument has two ranges.
1. Normal range of 1.6 v down to 10 µv
2. Lower range of 0.16 v to 1 µv.
The Vernier potentiometer reads to increment of 0.00001 v (10 µv) & has a readability of 1 µv
on 0.1 range. If a 3rd range of * 0.01 is provided, readability becomes 0.1 µv
AC Potentiometer: A potentiometer is an instrument which measures unknown voltage by
balancing it with a known voltage. The known source may be DC or AC. The working
phenomenon of DC potentiometer and AC potentiometer is same. But there is one major
difference between their measurements, DC potentiometer only measures the magnitude of the
unknown voltage. Whereas an AC potentiometer measures both the magnitude and phase of
unknown voltage by comparing it with a known reference.
There are two types of AC potentiometers:
1. Drysdale-Tinsley Potentiometer/ Polar type potentiometer
2. Gall-Tinsley Potentiometer / Coordinate type potentiometer.
Polar type Potentiometer : In such type of instruments, two separate scales are used to
measure magnitude and phase angle on some reference of the unknown e.m.f. There is a
provision on the scale that it could read phase angle up to 3600. It has electrodynamometer
type ammeter along with DC potentiometer and phase-shifting transformer which is operated
by single phase supply.
In a phase-shifting transformer, there is a combination of two ring-shaped laminated steel
stators connected perpendicularly to each other as shown in the figure. One is directly
connected to power supply and the other one is connected in series with variable resistance and
capacitor. The function of the series components is to maintain constant AC supply in the
potentiometer by doing small adjustments in it.
Between the stators, there is laminated rotor having slots and winding which supplies voltage
to the slide-wire circuit of the potentiometer. When current start flowing from stators, the
rotating field is developed around the rotor which induces an e.m.f. in the rotor winding.

Figure Poler Type potentiometer

The phase displacement of the rotor emf is equal to rotor movement angle from its original
position and it is related to the stator supply voltage. The whole arrangement of the winding is
done in such a way that the magnitude of the induced emf in the rotor may change but it does
not affect the phase angle and it can be read on the scale fixed on the top of the instrument.
The induced emf in rotor winding by stator winding 1 can be expressed as

The induced emf in the rotor winding by the stator winding 2,

From equation (1) and (2), we get

Therefore, resultant induced emf in the rotor winding due to two stator winding

Where, Ø gives the phase angle.

Coordinate type Potentiometer : In coordinate AC potentiometer, two separate
potentiometers are caged in one circuit as shown in the figure. The first one is named as the in-
phase potentiometer which is used to measure the in-phase factor of an unknown e.m.f. and the
other one is named as quadrature potentiometer which measures quadrature part of the
unknown e.m.f. the sliding contact AA’ in the in-phase potentiometer and BB’ in quadrature
potentiometer are used for obtaining the desired current in the circuit. By adjusting rheostat R
and R’ and sliding contacts, the current in the quadrature potentiometer becomes equal to the
current in the in-phase potentiometer and a variable galvanometer shows the null value. S1 and
S2 are signs changing switches which are used to change the polarity of the test voltage if it is
required for balancing the potentiometer. There are two step-down transformers T1 and T2
which isolate potentiometer from the line and give an earthed screens protection between the
winding. It also supplies 6 volts to potentiometers.

Figure Coordinate AC potentiometer

Now to measure unknown e.m.f. its terminals are connected across sliding contacts AA’ using
selector switch S3. By doing some adjustments in sliding contacts and rheostat, the whole
circuit gets balanced and galvanometer reads zero at the balanced condition. Now the in-phase
component VA of the unknown e.m.f. is obtained from the in-phase potentiometer and
quadrature component VB is obtained from quadrature potentiometer.
Thus, the resultant voltage of the coordinate AC potentiometer is

And the phase angle is given by

 Unit 4 notes
Measurement of Resistances
CLASSIFICATION OF RESISTANCES
For the purposes of measurements, the resistances are classified into three major groups based
on their numerical range of values as under:
• Low resistance (0 to 1 ohm)
• Medium resistance (1 to 100 kilo-ohm) and
• High resistance (>100 kilo-ohm)
Accordingly, the resistances can be measured by various ways, depending on their range of
values, as under:
1. Low resistance (0 to 1 ohm): AV Method, Kelvin Double Bridge, potentiometer, doctor
ohmmeter, etc.
2. Medium resistance (1 to 100 kilo-ohm): AV method, wheat stone’s bridge, substitution
method, etc.
3. High resistance (>100 kilo-ohm): AV method, Fall of potential method, Megger, loss of
charge method, substitution method, bridge method, etc.
4.1 Measurement of medium resistances
In this section, we will discuss the method of measurement of Medium Resistance. The
different methods used for Medium resistance are as follows:
· Ammeter Voltmeter method
· Substitution Method
· Wheatstone Bridge Method
· Ohmmeter Method
4.1.1 Ammeter Voltmeter Method:
There are two possible connections for the measurement of Medium Resistance using Ammeter
Voltmeter Method as shown in figure below:

In both the cases, the reading of Voltmeter and Ammeter is taken. If the Voltmeter reading is
V and Ammeter reading is I then the measured Resistance will be
Rm = V/I

This measured Resistance Rm will be the true value of the Resistance if and only if the
Resistance of Ammeter is zero and that of Voltmeter is infinite. But actually this is not possible
to achieve zero resistance Ammeter and infinite Resistance Voltmeter. Therefore measured
value of resistance Rm will deviate from the true value R (Say).
So we will discuss both the circuit individually and will calculate the percentage error in the
measurement.
Case1:

We consider first kind of connection as shown in figure 1 above. It is clear from the figure that
Voltmeter is measuring the Voltage drop across the Ammeter as well as resistor.
So V = Va + Vr
Let current measured by Ammeter = I
Therefore, measured Resistance Rm = V/I
So, Rm = (Va+Vr) / I =(IRa+IR) / I = Ra+R
Therefore, the measured Resistance is the sum of Resistance of Ammeter and true Resistance.
Therefore measured value will only represent true value if Ammeter Resistance Ra is Zero.
True value of Resistance R = Rm –Ra
= Rm(1-Ra/Rm)
Relative Error = (Rm-R)/R = Ra/R
Therefore, Relative Error will be less if the true value of Resistance to be measured is high as
compared to the internal Resistance of Ammeter. That’s why this method should be adopted
when measuring high Resistance but it should be under Medium Resistance category.
Case2:
We will consider second connection in which Voltmeter is connected in which Voltmeter is
connected toward Resistance R whose value is to be measured.

It is obvious from figure that Ammeter will read the current flowing through the Voltmeter and
Resistance R. Therefore current measured by Ammeter Ia = Iv+Ir
So, Ia = Iv+Ir
= V/Rv+V/R where Rv is Resistance of Voltmeter and V is Voltmeter reading.
Measured Resistance Rm = V/Ia
= V/(V/Rv+V/R)
= RvR/(R+Rv)
= R/(1+R/Rv) ….Dividing Numerator and Denominator by Rv
Therefore, true value of Resistance R = RmRv/(Rv-Rm)
= Rm(1-Rm/Rv)
Therefore, true value of Resistance will only be equal to measured value if the value
of Voltmeter Resistance Rv is infinite.
If we assume that the value of Voltmeter Resistance Rv is large as compared to the Resistance
to be measured R, then Rv>>>Rm
So, True value R = Rm(1+Rm/Rv)
Thus from the above equation it is clear that the measured value of Resistance is smaller than
the true value.
Relative Error = (Rm-R)/R
= -R/Rv
Therefore, it is clear from the expression of Relative Error that, error in measurement will be
low if the value of Resistance under measurement is very less as compared to the internal
Resistance of Voltmeter.
This is the reason; this method is used for the Contact Resistance Measurement. As the value
of Contact Resistance is of the order of 20 micro Ohm which is very less as compared to the
internal Resistance of Voltmeter.
The Voltmeter Ammeter Method for Cases1 and Case2 are simple method but it is not accurate
method. The error in the value of Resistance depends on the accuracy of Ammeter as well as
Voltmeter. If the accuracy of both the instrument are supposed 0.5% then when both the
instrument read near full scale, the error in measurement of Resistance may vary from 0 to 1%
while if both the instrument read near half scale then error may double and so on.
However this method is very useful where high accuracy is not required. The suitability of
Case1 or Case2 depends on the value of Resistance to be measured. The division point between
the two methods is at the Resistance for which both the method give same Relative Error.
So, Ra/R = R/Rv
R=
4.1.2 Measurement of Medium Resistance by Substitution Method

In Substitution Method, the Resistance whose value is to be measured is compared with the
Standard Resistance by some technique which is described in this section. The connection
diagram for Substitution Method is given below.

Here, R is the unknown Resistance, S the Standard variable Resistance, A is Ammeter and r is
Regulating Resistance.
When we put the Switch at position 1 then R is connected in the circuit. The Regulating
Resistance r is adjusted till the reading of Ammeter is at a chosen scale mark. Now the Switch
is thrown to position 2 putting the Standard variable Resistance S in the circuit. Now the
variable Resistor S is adjusted till the reading of Ammeter is same as when R was in the circuit.
The setting of dial of S is read. Since the substitution of one resistance for another has left
current unaltered, and provided that EMF of battery and position of Regulating Resistance r
remain unaltered, the two Resistance R and S must be equal. Thus the value of unknown
Resistance R is equal to the dial setting of Standard Resistance S.
This method of measurement is more accurate as compared to the Ammeter Voltmeter Method
as in this method measurement is not affected by the accuracy of Ammeter. However, the
accuracy of this method is greatly affected if there is any change in the Battery EMF during
the time when the reading in two settings is taken. Therefore to avoid the error because of
change of EMF of Battery, a Battery of enough capacity is used so that it remains constant
during the entire period of testing.
The accuracy of this method also depend on resistance of circuit excluding R and S, upon the
sensitivity of instrument and upon the accuracy with which the Standard Resistance S is known.
This method is not widely used for simple Resistance measurement and is used in modified
form for the measurement of High Resistance. The Substitution Method is however very
important as it finds its use in application of bridge method and in high accuracy A.C
measurement.
4.1.3 WHEATSTONE BRIDGE
For measuring accurately any electrical resistance Wheatstone bridge is widely used. There are
two known resistors, one variable resistor and one unknown resistor connected in bridge form
as shown below. By adjusting the variable resistor the current through the Galvanometer is
made zero. When the current through the galvanometer becomes zero, the ratio of two known
resistors is exactly equal to the ratio of adjusted value of variable resistance and the value of
unknown resistance. In this way the value of unknown electrical resistance can easily be
measured by using a Wheatstone Bridge. THEORY The general arrangement of Wheatstone
bridge circuit is shown in the figure below. It is a four arms bridge circuit where arm AB, BC,
CD and AD are consisting of electrical resistances P, Q, S and R respectively. Among these
resistances P and Q are known fixed electrical resistances and these two arms are referred as
ratio arms. An accurate and sensitive Galvanometer is connected between the terminals B and
D through a switch S2. The voltage source of this Wheatstone bridge is connected to the
terminals A and C via a switch S1 as shown. A variable resistor S is connected between point
C and D.
The potential at point D can be varied by adjusting the value of variable resistor. Suppose
current I1 and current I2 are flowing through the paths ABC and ADC respectively. If we vary
the electrical resistance value of arm CD the value of current I2 will also be varied as the
voltage across A and C is fixed. If we continue to adjust the variable resistance one situation
may comes when voltage drop across the resistor S that is I2.S is becomes exactly equal to
voltage drop across resistor Q that is I1.Q. Thus the potential at point B becomes equal to the
potential at point D hence potential difference between these two points is zero hence current
through galvanometer is nil. Then the deflection in the galvanometer is nil when the switch S2
is closed.
Now, from Wheatstone bridge circuit

And

Now potential of point B in respect of point C is nothing but the voltage drop across the resistor
Q and this is

Again potential of point D in respect of point C is nothing but the voltage drop across the
resistor S and this is

Equating, equations (i) and (ii) we get,

Errors in a Wheatstone Bridge

A Wheatstone bridge is a fairly convenient and accurate method for measuring resistance.

However, it is not free from errors as listed below:

1. Discrepancies between the true and marked values of resistances of the three known arms
can introduce errors in measurement.

2. Inaccuracy of the balance point due to insufficient sensitivity of the galvanometer may result
in false null points.

3. Bridge resistances may change due to self-heating (I 2R) resulting in error in measurement
calculations.

4. Thermal emfs generated in the bridge circuit or in the galvanometer in the connection points
may lead to error in measurement.

5. Errors may creep into measurement due to resistances of leads and contacts. This effect is
however, negligible unless the unknown resistance is of very low value.

6. There may also be personal errors in finding the proper null point, taking readings, or during
calculations.

Errors due to inaccuracies in values of standard resistors and insufficient sensitivity of

galvanometer can be eliminated by using good quality resistors and galvanometer.

Temperature dependent change of resistance due to self-heating can be minimized by

performing the measurement within as short time as possible.

Thermal emfs in the bridge arms may cause serious trouble, particularly while measuring low
resistances. Thermal emf in galvanometer circuit may be serious in some cases, so care must
be taken to minimize those effects for precision measurements. Some sensitive galvanometers
employ all-copper systems (i.e., copper coils as well as copper suspensions), so that there is no
junction of dissimilar metals to produce thermal emf. The effect of thermal emf can be balanced
out in practice by adding a reversing switch in the circuit between the battery and the bridge,
then making the bridge balance for each polarity and averaging the two results.

4.2 MEASUREMENT OF LOW RESISTANCES

The methods used for measurement of medium resistances are not suitable for measurement of
low resistances. This is due to the fact that resistances of leads and contacts, though small, are
appreciable in comparison to the low resistances under measurement. For example, a contact
resistance of 0.001 Ω causes a negligible error when a medium resistance of value say, 100 Ω
is being measured, but the same contact resistance would cause an error of 10% while
measuring a low resistance of value 0.01 Ω.
Hence special type of construction and techniques need to be used for measurement of low
resistances to avoid errors due to leads and contacts. The different methods used for
measurement of low range resistances are
(i) Voltmeter-ammeter method,
(ii) Kelvin's double-bridge method, and
(iii) Potentiometer method.
4.2.1 Voltmeter-ammeter method for low resistance measurement:
In principle, the voltmeter-ammeter method for measurement of low resistance is very similar
to the one used for measurement of medium resistances, as described in Section 4.1.1 This
method, due to its simplicity, is very commonly used for measurement of low resistances when
accuracy of the order of 1% is sufficient. The resistance elements, to be used for such
measurements, however, need to of special construction. Low resistances are constructed with
four terminals as show in figure below.

Figure Voltmeter-ammeter method for measuring

One pair of terminals CC', called the current terminals, is used to lead current to and from the
resistor. The voltage drop across the resistance is measured between the other pair of terminals
PP', called the potential terminals. The voltage indicated by the voltmeter is thus simply the
voltage drop of the resistor across the potential terminals PP' and does not include any contact
resistance drop that may be present at the current terminals CC’.
Contact drop at the potential terminals PP' are, however, less itself, since the currents passing
through these contacts are extremely small (even zero under 'null' balance condition) owing to
high resistance involved in the potential circuit. In addition to that, since the potential circuit
has a high resistance voltmeter in it, any contact resistance drop in the potential terminals PP'
will be negligible with respect to the high resistances involved in the potential Circuit.
Value of the unknown resistance RX in this case is given by Precise measurement in this
method requires that the voltmeter resistance to be appreciably high, otherwise the voltmeter
current will be an appreciable fraction of the current actually flowing through the ammeter, and
a serious error may be introduced in this account.
4.2.2 Kelvin's Double-Bridge Method for Measuring Low Resistance:
Kelvin's double-bridge method is one of the best available methods for measurement of low
resistances. It is actually a modification of the Wheatstone bridge in which the errors due to
contacts and lead resistances can be eliminated. The connections of the bridge are shown in
Figure.

Figure Kelvin' s double bridge Kelvin's double bridge

incorporates the idea of a second set of ratio arms, namely, p and q, and hence the name 'double
bridge'.
X is the unknown low resistance to be measured, and S is a known value standard low
resistance. 'r' is a very low resistance connecting lead used connect the unknown resistance X
to the standard resistance S. All other resistances P, Q, p, and q are of medium range. Balance
in the bridge is achieved by adjusting S.
Under balanced condition, potentials at the nodes a and b must be equal in order that the
galvanometer G gives "null" deflection. Since at balance, no current flows through the
galvanometer, it can be considered to be open circuited and the circuit can be represented as
shown in Figure below.
FIG. 12 Kelvin' s double-bridge under balanced condition
Since under balanced condition, potentials at the nodes a and b are equal, the we must have ...
the balance equation Vcb = Vcda can now be re-written as.
4.2.3 Potentiometer Method for Measuring Low Resistance
The circuit for measurement of low value resistance with a potentiometer is shown in Figure
below.

Figure Measurement of low resistance using potentiometer

The unknown resistance X is connected in series with a standard known resistance S.

Current through the ammeter in the circuit is controlled by a rheostat. A two-pole double throw
switch is used. When the switch is in the position 1-1', the unknown resistance X gets connected
to the potentiometer, whereas when the switch is at position 2-2', the standard resistance S gets
connected to the potentiometer.
Potentiometers are believed to give reasonably accurate values of potentials.
Thus, with the switch in position 1-1', the potentiometer reading is the voltage drop across the
unknown resistance, given by Without changing any of the circuit parameters, now if the switch
is thrown to position 2-2', potentiometer now reads the voltage drop across the standard
resistance, given by From Eqs (21) and (22), we get Knowledge of accurate value of the
standard resistance S can thus give reasonably accurate values of the unknown resistance X.
Accuracy of this method however, depends on the assumption that the value of current remains
absolutely constant during the two sets of measurements. Therefore, an extremely stabilized dc
power supply is required in this method.
Value of the standard resistor S should be of the same order as the unknown resistance X. The
ammeter inserted in the circuit has no other function rather than simply indicating whether
there is any current is flowing in the circuit is not. Exact value of the current is not required for
final calculations. It is however, desired that the current flowing through the circuit be so
adjusted that the voltage drop across each resistor is of the order of 1 V to be suitable for
accurate measurement by commercially available potentiometers.
4.3 MEASUREMENT OF HIGH RESISTANCES
High resistances of the order of several hundreds and thousands of megohms (MW) are often
encountered in electrical equipment’s in the form of insulation resistance of machines and
cables, leakage resistance of capacitors, volume and surface resistivity of different insulation
materials and structures.
4.1 Difficulties in Measurement of High Resistance
1. Since the resistance under measurement has very high value, very small currents are
encountered in the measurement circuit. Adequate precautions and care need to be taken to
measure such low value currents.
2. Surface leakage is the main difficulty encountered while measurement of high resistances.
The resistivity of the resistance under measurement may be high enough to impede flow of
current through it, but due to moisture, dust, etc., the surface of the resistor may provide a lower
resistance path for the current to pass between the two measuring electrodes. In other words,
there may thus be a leakage through the surface. Leakage paths not only pollute the test results,
but also are generally variable from day to day, depending on temperature and humidity
conditions.
The effect of leakage paths on measurements can be eliminated by the use of guard circuits as
described by Figure.
Figure (a) shows a high resistance RX being mounted on a piece of insulation block. A battery
along with a voltmeter and a micro-ammeter are used to measure the resistance by voltmeter-
ammeter method. The resistance RX under measurement is fitted on the insulating block at the
two binding posts A and B. IX is the actual current flowing through the high resistance and IL
is the surface leakage current flowing over the body of the insulating block. The micro-
ammeter, in this case, thus reads the actual current through the resistor, and also the leakage
current (I = IX + IL.).
Measured value of the resistance, thus computed from the ratio E/I, will not be the true value
of RX, but will involve some error. To avoid this error, a guard arrangement has been added in
FIG. 14(b). The guard arrangement, at one end is connected to the battery side of the micro-
ammeter, and the other end is wrapped over the insulating body and surrounds the resistance
terminal A. The surface leakage current now, flows through this guard and bypasses the micro-
ammeter. The micro-ammeter thus reads the true of current IX through the resistance RX. This
arrangement thus allows correct determination of the resistance value from the readings of
voltmeter and micro-ammeter.

Figure Guard circuit for measurement of high resistance: (a) Circuit without guard (b) Circuit
with guard
3. Due to electrostatic effects, stray charges may be induced in the measuring circuit.
Flow of these stray charges can constitute a current that can be comparable in magnitude with
the low value current under measurement in high resistance circuits.
This may thus, cause errors in measurement. External alternating electromagnetic fields can
also affect the measurement considerably. Therefore, the measuring circuit needs to be
carefully screened to protect it against such external electrostatic or electromagnetic effects.
4. While measuring insulation resistance, the test object often has considerable amount of
capacitance as well. On switching on the dc power supply, a large charging current may flow
initially through the circuit, which gradually decays down. This initial transient current may
introduce errors in measurement unless considerable time is provided between application of
the voltage supply and reading the measurement, so that the charging current gets sufficient
time to die down.
5. High resistance measurement results are also affected by changes in temperature, humidity
and applied voltage inaccuracies.
6. Reasonably high voltages are used for measurement of high resistances in order to raise the
current to substantial values in order to be measured, which are otherwise extremely low. So,
the associated sensitive galvanometers and micro-ammeters need to be adequately protected
against such high voltages.
Taking these factors into account, the most well-known methods of high resistance
measurements are (i) direct deflection method, (ii) loss of charge method, and (iii)
megohmmeter or meggar.
4.3.2 Direct Deflection Method for High Resistance Measurement
The direct deflection method for measuring high resistances is based on the circuit described
in Figure, which in effect is the voltmeter-ammeter method. For measurement of high
resistances, a sensitive galvanometer is used instead of a micro ammeter as shown in Figure.
A schematic diagram for describing the direct deflection method for measurement of insulation
resistance of a metal sheathed cable is given in Figure.

Figure: Measurement of cable insulation resistance

The test specimen, cable in this case, is connected across a high voltage stable dc source; one
end of the source being connected to the inner conductor of the cable, and the other end, to the
outer metal sheath of the cable. The galvanometer G, connected in series as shown in FIG. 15,
is intended to measure the current IX flowing through the volume of the insulation between the
central conductor and the outer metal sheath. Any leakage current IL flowing over the surface
of the insulating material is bypassed through a guard wire wound on the insulation, and
therefore does not flow through the galvanometer.
A more detailed scheme for measurement of insulation resistance of a specimen sheet of solid
insulation is shown in Figure.
Figure: Measurement of high resistance by direct deflection method
A metal disk covering almost the entire surface is used as electrode on one side of the insulation
sheet under measurement. On the other side of the insulating sheet, the second electrode is
made of a smaller size disk. A guard ring is placed around the second electrode with a small
spacing in between them. This guarding arrangement bypasses any surface leakage current on
the insulator or any other parts of the circuit from entering the actual measuring circuit. The
galvanometer thus reads specifically the volume resistance of the insulation specimen,
independent of any surface leakage.
A calibrated Ayrton shunt is usually included along with the galvanometer to provide various
scale ranges and also to protect it.
The galvanometer scale is graduated directly in terms of resistance. After one set of
measurement is over, the galvanometer is calibrated with the help of a high value (˜ 1 MΩ)
calibrating resistor and the shunts.
In case the insulation under measurement has high inherent capacitance values (like in a cable),
there will be an initial inrush of high capacitive charging current when the dc source is first
switched on. This charging current will, however, decay down to a steady dc value with time.
To protect the galvanometer from such initial rush of high current, the Ayrton shunt connected
across the galvanometer should be placed at the highest resistance position . Thus, initially the
galvanometer is bypassed from the high charging current.
After the test is complete, it is required that the test specimen should be discharged, especially
if it is of capacitive in nature. The 'test-short' switch is placed in the 'short' position so that any
charge remaining in the insulation specimen is discharged through the short circuited path.
The change-over switch across the battery enables tests at different polarities. The switch
across the galvanometer enables reversal of the galvanometer connections.
A special technique, Price's guard-wire method is employed for measurement of insulation
resistance of cables which do not have metal sheath outside. The schematic diagram of such a
measurement system is provided in Figure.
Figure: Measurement of high resistance by Price' s guard-wire method.
The unsheathed cable, except at the two ends where connections are made, is immersed in
water in a tank. For testing of the cable insulation, the cable core conductor acts as one electrode
and in the absence of the metal sheath outside, the water and the tank act as the other electrode
for measurement. The cable is immersed in slightly saline water for about a day and at nearly
constant ambient temperature.
The two ends of the cables are trimmed as shown in Figure, thus exposing the core conductor
as well as some portion of the insulation. The core conductors are connected together to form
one electrode of the measuring system. A guard circuit is formed by twisting a bare wire around
the exposed portion of the insulation at the two stripped ends of the cable. This guard wire is
connected to the negative terminal of the supply battery.
The positive terminal of the battery is connected to the metal tank. This enables any surface
leakage current to bypass the galvanometer and pass directly to the battery. Thus, the
galvanometer will read only true value of the current flowing through volume of the insulation,
and not the additional surface leakage current.
The D'Arsonval galvanometer to be used is normally of very high resistance and very sensitive
to record the normally extremely low insulation currents. An Ayrton universal shunt is usually
included along with the galvanometer to provide various scale ranges and also to protect it. The
galvanometer scale is graduated directly in terms of resistance. After one set of measurement
is over, the galvanometer is calibrated with the help of the high value (˜ 1 MΩ) calibrating
resistor R and the shunt. The resistance R and the shunt also serve the purpose of protecting
the galvanometer from accidental short circuit current surges. The 4-terminal commutator C,
as shown in Figure is used for reversal of galvanometer connections.
Since the cable will invariably have high capacitance value, there will be an initial inrush of
high capacitive charging current when the dc source is first switched on. This charging current
will, however, decay down to a steady dc value with time. To protect the galvanometer from
such initial rush of high current, the switch S2 is placed on position a so that initially the
galvanometer is bypassed from the high charging current. Once the capacitor charging period
is over and the current settles down, the switch S2 is pushed over to position b to bring the
galvanometer back in the measurement circuit. The contacts a and b are sufficiently close
enough to prevent the circuit from breaking while the switch S2 is moved over.
After the test is complete, it is required that the test specimen should be discharged. The switch
S1 is used for this purpose, so that any charge remaining in the insulation specimen is
discharged through itself.
4.3.3 Loss of Charge Method for High Resistance Measurement
In this method, the resistance to be measured is connected directly across a dc voltage source
in parallel with a capacitor. The capacitor is charged up to a certain voltage and then discharged
through the resistance to be measured. The terminal voltage across the resistance-capacitance
parallel combination is recorded for a pre-defined period of time with a help of a high-
resistance voltmeter (electrostatic voltmeter or digital electrometers).
Value of the unknown resistance is calculated from the discharge time constant of the circuit.
Operation of the loss of charge method can be described by the schematic circuit diagram of

Figure.
Figure: Loss of charge method for measurement of high resistance
In Above Figure, the unknown resistance R to be measured is connected across the capacitor
C and their parallel combination is connected to the dc voltage source.
Let the capacitor is initially charged up to a voltage of V while the switch is kept ON.
Once the switch is turned OFF, the capacitor starts to discharge through the resistance R.
During the discharge process, the voltage v across the capacitor at any instant of time t is given
by Thus, the insulation resistance can be calculated as With known value of C and recorded
values of t, V and v, the unknown resistance R can be estimated using (24).
The pattern of variation of voltage v with time is shown in Figure.
Capacitor discharge pattern Great care must be taken to record the voltages V and v and also
the time t very precisely, otherwise large errors may creep in to the calculation results.
This method, though simple in principle, require careful choice of the capacitor. The capacitor
C itself must have sufficiently high value of its own leakage resistance, at least in the same
range as the unknown resistance under measurement. The resistance of the voltmeter also needs
to be very high to have more accurate results.
4.3.4 Megohmmeter, or Meggar, for High Resistance Measurement
One of the most popular portable type insulation resistance measuring instruments is the
megohmmeter or in short, meggar. The meggar is used very commonly for measurement of
insulation resistance of electrical machines, insulators, bushings, etc. Internal diagram of a
meggar is shown in Figure.
The traditional analog deflecting-type meggar is essentially a permanent magnet crossed-coil
shunt type ohmmeter.
The instrument has a small permanent magnet dc generator developing 500 V dc (some other
models also have 100 V, 250 V, 1000 or 2500 V generators). The generator is hand driven,
through gear arrangements, and through a centrifugally controlled clutch switch which slips at
a predefined speed so that a constant voltage can be developed. Some meggars also have
rectified ac as power supply.

Figure: Meggar for high resistance measurement

The moving system in such instruments consists of two coils, the control coil CC and the
deflecting coil CD. Both the coils are mounted rigidly on a shaft that carries the pointer as well.
The two coils move in the air gap of a permanent magnet. The two coils are arranged with such
numbers of turns, radii of action, and connected across the generator with such polarities that,
for external magnetic fields of uniform intensity, the torque produced by the individual coils
are in opposition thus giving an astatic combination. The deflecting coil is connected in series
with the unknown resistance RX under measurement, a fixed resistor RD and then the
generator. The current coil or the compensating coil, along with the fixed resistance RC is
connected directly across the generator. For any value of the unknown, the coils and the pointer
take up a final steady position such that the torques of the two coils are equal and balanced
against each other. For example, when the resistance RX under measurement is removed, i.e.,
the test terminals are open-circuited, no current flows through the deflecting coil CD, but
maximum current will flow through the control coil CC. The control coil CC thus sets itself
perpendicular to the magnetic axis with the pointer indicating '8 Ω' as marked in the scale
shown in Figure. As the value of RX is brought down from open circuit condition, more and
more current flows through the deflecting coil CD, and the pointer moves away from the '8 Ω'
mark clockwise on the scale, and ultimately reaches the '0 Ω' mark when the two test terminals
are short circuited.
The surface leakage problem is taken care of by the guard-wire arrangement. The guard ring
and the guard wire diverts the surface leakage current from reaching the main moving system
and interfering with its performance.
Photographs of some commercially available meggars are shown in Figure.
Figure: Commercial meggars: (a) Analog type ( WACO) (b) Digital type (Yokogawa)
 Unit 5
AC Bridges
INTRODUCTION: Alternating current bridges are most popular, convenient and accurate instruments
for measurement of unknown inductance, capacitance and some other related quantities. In its simplest
form, ac bridges can be thought of to be derived from the conventional dc Wheatstone bridge. An ac
bridge, in its basic form, consists of four arms, an alternating power supply, and a balance detector.
SOURCES AND DETECTORS IN AC BRIDGES: For measurements at low frequencies, bridge power
supply can be obtained from the power line itself. Higher frequency requirements for power supplies are
normally met by electronic oscillators. Electronic oscillators have highly stable, accurate yet adjustable
frequencies. Their output waveforms are very close to sinusoidal and output power level sufficient for
most bridge measurements.
When working at a single frequency, a tuned detector is preferred, since it gives maximum sensitivity at
the selected frequency and discrimination against harmonic frequencies. Vibration galvanometers are
most commonly used as tuned detectors in the power frequency and low audio-frequency ranges. Though
vibration galvanometers can be designed to work as detectors over the frequency range of 5 Hz to 1000
Hz, they have highest sensitivity when operated for frequencies below 200 Hz.
Head phones or audio amplifiers are popularly used as balance detectors in ac bridges at frequencies of
250 Hz and above, up to 3 to 4 kHz.
Transistor amplifier with frequency tuning facilities can be very effectively used as balance detectors
with ac bridges. With proper tuning, these can be used to operate at a selective band of frequencies with
high sensitivity. Such detectors can be designed to operate over a frequency range of 10 Hz to 100 kHz.
General form of A.C. bridge: AC bridge are similar to D.C. bridge in topology(way of connecting).It
consists of four arm AB,BC,CD and DA .Generally the impedance to be measured is connected
between ‘A’ and ‘B’. A detector is connected between ‘B’ and ’D’. The detector is used as null
deflection instrument. Some of the arms are variable element. By varying these elements, the potential
values at ‘B’ and‘D’ can be made equal. This is called balancing of the bridge.
 Fig. General form of A.C. bridgeAt
the balance condition, the current through detector is zero.
I1=I3
I2=I4
I1 I3
=
I2 I4

At balance condition,

Voltage drop across ‘AB’=voltage drop across ‘AD’.

E1 = E 2
I1 Z1 = I 2 Z 2
Similarly, Voltage drop across ‘BC’=voltage drop across ‘DC’
E3 = E4
I 3 Z 3 = I4 Z 4
Form above equation

I1 z2
=
I2 z1
 I3 z4
=
I4 z3

From above equation we can write

  For balance condition, magnitude on either side must be equal.

 Angle on either side must be equal.

Summary
For balance condition,

5.1 Measurements of inductance

5.1.1 Maxwell’s inductance bridge

The choke for which R1 and L1 have to measure connected between the points ‘A’ and ‘B’.
In this method the unknown inductance is measured by comparing it with the standard inductance.

Fig. Maxwell’s inductance bridge

L2 is adjusted, until the detector indicates zero current.
Let R1= unknown resistance
L1= unknown inductance of the choke.
L2= known standard inductance
R1,R2,R4= known resistances.

Fig Phasor diagram of Maxwell’s inductance bridge

 Advantages

✓ Expression for R1 and L1 are simple.

✓ Equations area simple
✓ They do not depend on the frequency (as w is cancelled)
✓ R1 and L1 are independent of each other.

Disadvantages

✓ Variable inductor is costly.

✓ Variable inductor is bulky.

5.1.2 Maxwell’s inductance capacitance bridge

Unknown inductance is measured by comparing it with standard capacitance. In this bridge,

balance condition is achieved by varying ‘C4’.

Fig Maxwell’s inductance capacitance bridge

Substituting the value of Z4 from Above equation and we get

Fig Phasor diagram of Maxwell’s inductance capacitance bridge

Comparing real parts, R1R4 = R2R3

 Advantages

✓ Equation of L1 and R1 are simple.

✓ They are independent of frequency.
✓ They are independent of each other.
✓ Standard capacitor is much smaller in size than standard inductor.

Disadvantages

✓ Standard variable capacitance is costly.

✓ It can be used for measurements of Q-factor in the ranges of 1 to 10.
✓ It cannot be used for measurements of choke with Q-factors more than 10.
We know that Q =wC4R4

For measuring chokes with higher value of Q-factor, the value of C4 and R4 should be
higher. Higher values of standard resistance are very expensive. Therefore this bridge cannot be
used for higher value of Q-factor measurements.
5.1.2 Hay’s bridge

Fig Hay’s bridge

 Fig Phasor diagram of Hay’s bridgeAt

balance condition, Z1Z4=Z3Z2

Substituting the value of R1 from eqn. we have,

Substituting the value of L1 in above eqn., we have

Advantages

✓ Fixed capacitor is cheaper than variable capacitor.

✓ This bridge is best suitable for measuring high value of Q-factor.

Disadvantages

✓ Equations of L1and R1 are complicated.

✓ Measurements of R1 and L1 require the value of frequency.
✓ This bridge cannot be used for measuring low Q- factor.
5.1.3 Anderson’s bridge

Fig Anderson’s bridge

.

Fig Phasor diagram of Anderson’s bridge

Fig Equivalent delta to star conversion for the loop MO
Fig Simplified diagram of Anderson’s bridge
Advantages

✓ Variable capacitor is not required.

✓ Inductance can be measured accurately.
✓ R1 and L1 are independent of frequency.
✓ Accuracy is better than other bridges.
Disadvantages
✓ Expression for R1 and L1 are complicated.
✓ This is not in the standard form A.C. bridge.
Heaviside's bridge for mutual inductance measurement
Before we introduce this bridge let us know more about the uses of mutual inductor in bridge circuits.
Now one question must arise in our mind that why we are so much interested in mutual inductance,
answer to this question is very simple we will use this mutual inductor in Heaviside bridge circuit. We
use standard mutual inductor in finding out the the value of unknown mutual inductor in various circuits.
Mutual inductor is used in various circuits as main component in determining the value of self
inductance, capacitance and frequency etc.
But in many industries the use of mutual inductor in finding out the value of known self inductor is not
practices because we have various other accurate methods for finding out self inductor and capacitance
and these other methods may include the use of standard capacitor which are available at cheaper rate.
However there may be some merits of use mutual inductor in some cases but this field is very vast.
Many researches are going on the application of mutual inductor in bridge circuits. In order to understand
the mathematical part of Heaviside bridge, we need to derive the mathematical relation between self
inductor and mutual inductor in two coils connected in series combination. Here we interested in finding
out the expression for mutual inductor in terms of self inductance.
Let us consider two coils connected in series as shown in figure given below.

Such that the magnetic fields are additive, the resultant inductor of these two can be calculated as

Where, L1 is the self inductor of first coil,

L2 is the self inductor of second coil,

M is the mutual inductor of these two coils.

Now if the connections of any one of the coils is reversed then we have

On solving these two equations we have

Thus the mutual inductor of the two coils connected in series is given by one-fourth of the difference
between the measured value of self inductor when taking the direction of field in the same direction and
value of self inductor when the direction of field is reversed.
However, one needs to have the two series coils on the same axis in order to get most accurate result.
Let us consider the circuit of Heaviside mutual inductor bridge, given below,

Main application of this bridge in industries is to measure the mutual inductor in terms of self inductance.
Circuit of this bridge consists of four non inductive resistors r1, r2, r3 and r4 connected on arms 1-2, 2-3,
3-4 and 4-1 respectively. In series of this bridge circuit an unknown mutual inductor is connected. A
voltage is applied to across terminals 1 and 3. At balance point electric current flows through 2-4 is zero
hence the voltage drop across 2-3 is equal to voltage drop across 4-3. So by equating the voltage drops
of 2-4 and 4-3 we have,

Also we have,

and mutual inductor is given by,

Let us consider some special case,

In this case the mutual inductor is reduced to

Now let us consider the circuit of Campbell’s Heaviside bridge given below:

This is the modified Heaviside bridge. This bridge is used to measure the unknown value of self inductor
in terms of mutual inductance.The modification is due to addition of balancing coil l, and R in arm 1 –
4 and also electrical resistance r is included in arm 1-2. Short circuit switching is connected across r2 and
l2 in order to have two sets of readings one while short circuiting r2 and l2 and other while open circuiting
r2 and l2.
Now let us derive the expression for self inductor for this modified Heaviside bridge. Also let us assume
that the value of M and r with switch open be M1 and r1, M2 and r2 with switch closed.
For open switch, we have at balance point,

and with closed switch we can write

Thus we final expression for self inductor

De Sauty Bridge for capacitance measurement

This bridge provide us the most suitable method for comparing the two values of capacitor if we
neglect dielectric losses in the bridge circuit. The circuit of De Sauty’s bridge is shown below.

Battery is applied between terminals marked as 1 and 4. The arm 1-2 consists of capacitor c1 (whose
value is unknown) which carries current i1 as shown, arm 2-4 consists of pure resistor (here pure
resistor means we assuming it non inductive in nature), arm 3-4 also consists of pure resistor and arm
4-1 consists of standard capacitor whose value is already known to us.
Let us derive the expression for capacitor c1 in terms of standard capacitor and resistors.
At balance condition we have,

It implies that the value of capacitor is given by the expression

In order to obtain the balance point we must adjust the values of either r3 or r4 without disturbing any
other element of the bridge. This is the most efficient method of comparing the two values of capacitor
if all the dielectric losses are neglected from the circuit.
Now let us draw and study the phasor diagram of this bridge. Phasor diagram of De Sauty bridge is
shown below:

Let us mark the current drop across unknown capacitor as e1, voltage drop across the resistor r3 be e3,
voltage drop across arm 3-4 be e4 and voltage drop across arm 4-1 be e2. At balance condition the
current flows through 2-4 path will be zero and also voltage drops e1 and e3 be equal to voltage drops
e2 and e4 respectively.
In order to draw the phasor diagram we have taken e3 (or e4) reference axis, e1 and e2 are shown at
right angle to e1 (or e2). Why they are at right angle to each other? Answer to this question is very
simple as capacitor is connected there, therefore phase difference angle obtained is 90o.
Now instead of some advantages like bridge is quite simple and provides easy calculations, there are
some disadvantages of this bridge because this bridge give inaccurate results for imperfect capacitor
(here imperfect means capacitors which not free from dielectric losses). Hence we can use this bridge
only for comparing perfect capacitors.
Here we interested in modify the De Sauty’s bridge, we want to have such a kind of bridge that will
gives us accurate results for imperfect capacitors also. This modification is done by Grover. The
modified circuit diagram is shown below:

Here Grover has introduced electrical resistances r1 and r2 as shown in above on arms 1-2 and 4-1
respectively, in order to include the dielectric losses. Also he has connected resistances R1 and R2
respectively in the arms 1-2 and 4-1. Let us derive the expression capacitor c1 whose value is unknown
to us. Again we connected standard capacitor on the same arm 1-4 as we have done in De Sauty’s
bridge. At balance point on equating the voltage drops we have:

On solving above equation we get:

This the required equation.

By making the phasor diagram we can calculate dissipation factor. Phasor diagram for the above
circuit is shown below

Let us mark δ1 and δ2 be phase angles of the capacitors c1 and c2 capacitors respectively. From the
phasor diagram we have tan(δ1) = dissipation factor = ωc1r1 and similarly we have tan(δ2) = ωc2r2.
From equation (1) we have

on multiplying ω both sides we have

Therefore the final expression for the dissipation factor is written as

Hence if dissipation factor for one capacitor is known. However this method is gives quite inaccurate
results for dissipation factor.
2.5.1 Wein’s bridge

Wein’s bridge is popularly used for measurements of frequency of frequency. In this bridge, the
value of all parameters are known. The source whose frequency has to measure is connected as
shown in the figure.
 Fig Wein’s bridge

Fig Phasor diagram of Wein’s bridge

NOTE The above bridge can be used for measurements of capacitance. In such case, r1 and C1 are
unknown and frequency is known. By equating real terms, we will get R1 and C1. Similarly by
equating imaginary term, we will get another equation in terms of r1 and C1. It is only used for
measurements of Audio frequency.
A.F=20 HZ to 20 KHZ
R.F=>> 20 KHZ
Comparing imaginary term,
High Voltage Schering Bridge

Fig High Voltage Schering bridge

 (1) The high voltage supply is obtained from a transformer usually at 50 HZ.

Wagner earthing device:

Fig Wagner Earthing device

Wagner earthing consists of ‘R’ and ‘C’ in series. The stray capacitance at node ‘B’ and ‘D’ are
CB, CD respectively. These Stray capacitances produced error in the measurements of ‘L’ and ‘C’.
These error will predominant at high frequency. The error due to this capacitance can be eliminated
using wagner earthing arm.

Close the change over switch to the position (1) and obtained balanced. Now change the switch to
position (2) and obtained balance. This process has to repeat until balance is achievedin both the
position. In this condition the potential difference across each capacitor is zero. Current drawn by
this is zero. Therefore they do not have any effect on the measurements.

What are the sources of error in the bridge measurements?

✓ Error due to stray capacitance and inductance.

✓ Due to external field.
✓ Leakage error: poor insulation between various parts of bridge can produced this error.
✓ Eddy current error.
✓ Frequency error.
 ✓ Waveform error (due to harmonics)
✓ Residual error: small inductance and small capacitance of the resistor produce this error.

Precaution

✓ The load inductance is eliminated by twisting the connecting the connecting lead.
AÎ0Î r
✓ In the case of capacitive bridge, the connecting lead are kept apart.(QC = )
d
✓ In the case of inductive bridge, the various arm are magnetically screen.
✓ In the case of capacitive bridge, the various arm are electro statically screen to reduced
the stray capacitance between various arm.
✓ To avoid the problem of spike, an inter bridge transformer is used in between the source
and bridge.
✓ The stray capacitance between the ends of detector to the ground, cause difficulty in
balancing as well as error in measurements. To avoid this problem, we use wagner earthing
device.