CLASS NOTES ON ELECTRICAL MEASUREMENTS & INSTRUMENTATION 2015

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

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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.

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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 = Tc (1.1)

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 θ .

TC ∝ θ (1.2)

The deflecting torque produced Td proportional to ‘I’. When TC = Td , the pointer will come to a
steady position. Therefore
θ∝I (1.3)

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Fig. 1.5

Since, θ 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.

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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.

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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
θ = 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
F = BIL sin θ (1.4)
°
When θ = 90
For N turns, F = NBIL (1.5)
Torque produced Td = F × ⊥ r distance (1.6)

Td = NBIL × b = BINA (1.7)

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

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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

I m = Current through meter

I sh =current through shunt

I= current to be measure
∴Vm = Vsh (1.10)

I m Rm = I sh Rsh

I m Rsh
= (1.11)
I sh Rm

Apply KCL at ‘P’ I = I m + I sh (1.12)

Eqn (1.12) ÷ by I m

I I
= 1 + sh (1.13)
Im Im

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I R
=1+ m (1.14)
Im Rsh

 R 
∴ I = I m 1 + m  (1.15)
 Rsh 
 R 
1 + m  is called multiplication factor
 Rsh 
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
Let Rm =resistance of meter

Rse =resistance of multiplier

Vm =Voltage across meter

Vse = Voltage across series resistance

V= voltage to be measured
I m = I se (1.16)

Vm Vse
= (1.17)
Rm Rse

V R
∴ se = se (1.18)
Vm Rm

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Apply KVL, V = Vm + Vse (1.19)

Eqn (1.19) ÷ Vm

V V  R 
= 1 + se = 1 + se  (1.20)
Vm Vm  Rm 

 R 
∴V = Vm 1 + se  (1.21)
 Rm 

 Rse 
1 +  → Multiplication factor
 Rm 

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

Let ‘ θ ’ be the deflection corresponding to a current of ‘i’ amp
Let the current increases by di, the corresponding deflection is ‘ θ + dθ ’

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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 dL
e= ( Li ) = L + i (1.22)
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 + i 2 dL (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.

Fig. 1.11

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