PE ZC213 / TA ZC233

Engineering Measurements

BITS Pilani Swapna Kulkarni

Pilani|Dubai|Goa|Hyderabad WILP Division, BITS-Pilani,Pilani

1
Types of Instrument

2 BITS pilani, Deemed to be University under Section 3, UGC Act

Problem

The coil of a PMMC instrument has 60 turns, on a former that is 18 mm wide,

the effective length of the conductor being 25 mm. It moves in a uniform field
of flux density 0.5 Tesla. The control spring constant is 1.5 × 10-6 Nm/degree.
Calculate the current required to produce a deflection of 100 degree.

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 Solution:
Total deflecting torque exerted on the coil,
Td = Bilnb (N-m) = 0.5 × i × 25 × 10-3 × 60 × 18 × 10-3
The control torque of the springs is TC = ks × θ =1.5 × 10-6 × 100

At equilibrium, Td = TC
0.5 × i x 18 × 10^-3 × 25 × 10^-3 × 60 = 1.5 × 10^-6 × 100

BITS pilani, Deemed to be University under Section 3, UGC Act

 Problem

A PMMC instrument has a coil of dimensions 15 mm × 12 mm. The flux

density in the air gap is 1.8 × 10^-3 wb/m2 and the spring constant is 0.14
× 10 ^-6 N-m/rad. Determine the number of turns required to produce an
angular deflection of 90° when a current of 5 mA is flowing through the
coil.
Solution
Total deflecting torque exerted on the coil, Td = Bilnb (N-m)
= 1.8 × 10-3 × 5 × 10-3 × 15 × 10 -3 × 12 × 10 -3 × n
The control torque of the springs is TC = ks × θ
= 0.14 × 10 -6 × 90 ×π/180
At equilibrium, Td = TC
1.8 × 10-3 × 5 × 10-3 × 15 × 10 -3 × 12 × 10 -3 × n
= 0.14 × 10 -6 × 90 × π/180

BITS pilani, Deemed to be University under Section 3, UGC Act

BITS pilani, Deemed to be University under Section 3, UGC Act
 MI instruments

Moving-iron instruments are generally

used to measure alternating voltages and
currents. In moving-iron instruments the
movable system consists of one or more
pieces of specially-shaped soft iron,
which are so pivoted as to be acted upon
by the magnetic field produced by the
current in coil.
There are two general types of moving-
iron instruments namely:
1. Repulsion (or double iron) type
2. Attraction (or single-iron) type

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MI instruments

BITS pilani, Deemed to be University under Section 3, UGC Act

Elements of MI
instruments

• Moving element: a small piece of soft iron in the form of a

vane or rod.
• Coil: to produce the magnetic field due to current flowing
through it and also to magnetize the iron pieces.
• In repulsion type, a fixed vane or rod is also used and
magnetized with the same polarity.
• Control torque is provided by spring or weight (gravity).
• Deflecting torque produces a movement on an aluminum
pointer over a graduated scale.

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Attraction Type

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Repulsion Type

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Working

• The deflecting torque in any moving-iron instrument is due

to forces on a small piece of magnetically ‘soft’ iron that is
magnetized by a coil carrying the operating current. In
repulsion type moving–iron instrument consists of two
cylindrical soft iron vanes mounted within a fixed current-
carrying coil. One iron vane is held fixed to the coil frame
and other is free to rotate, carrying with it the pointer shaft.
Two irons lie in the magnetic field produced by the coil that
consists of only few turns if the instrument is an ammeter
or of many turns if the instrument is a voltmeter.

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 Working

•Current in the coil induces both vanes to become

magnetized and repulsion between the similarly magnetized
vanes produces a proportional rotation. The deflecting torque
is proportional to the square of the current in the coil, making
the instrument reading is a true ‘RMS’ quantity Rotation is
opposed by a hairspring that produces the restoring torque.
Only the fixed coil carries load current, and it is constructed
so as to withstand high transient current.
•Moving iron instruments having scales that are nonlinear and
somewhat crowded in the lower range of calibration

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Applications

Measurement of Electric Voltage and Current

• Moving iron instruments are used as Voltmeter and
Ammeter only.
• Both can work on AC as well as on DC.
Ammeter:
• Instrument used to measure current in the circuit.
• Always connected in series with the circuit and carries the
current to be measured.
• This current flowing through the coil produces the desired
deflecting torque.
• It should have low resistance as it is to be connected in
series.

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Applications

Voltmeter
• Instrument used to measure voltage between two points in
a circuit.
• Always connected in parallel.
• Current flowing through the operating coil of the meter
produces deflecting torque.
• It should have high resistance. Thus a high resistance of
order of kilo ohms is connected in series with the coil of
the instrument

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Advantages

• The instruments are suitable for use in AC and DC circuits.

• The instruments are robust, owing to the simple
construction of the moving parts.
• The stationary parts of the instruments are also simple.
• Instrument is low cost compared to moving coil
instrument.
• Torque/weight ratio is high, thus less frictional error.

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 BITS Pilani
Pilani|Dubai|Goa|Hyderabad

Measurements of Resistance
WHY resistance of material is measured ?

Cable manufacturers
Electric motor & generator manufacturers
Installation & maintenance of power cables, switchgear &
voltage tap changers

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Classification of Resistances. The classification of resistances, from the point of
view of measurement,:
(1) Low Resistance. All resistances of the order of 1 ohm and under may be
classified as low resistances.
(ii) Medium Resistances. This class includes resistances from l ohm upwards to
about 100,000 ohm. ·
(iii) High Resistances. Resistances of the order of 100,000 ohm and upwards
are classified as high resistances.

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MEASUREMENT OF MEDIUM
RESISTANCES
Methods of Measurement of medium resistances are :
(i) Ammeter· Voltmeter method.
(iii) Wheatstone bridge method.
(ii Substitution method.
(iv) Ohmmeter method.

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Ammeter· Voltmeter method.

Let Ra be the resistance of the

ammeter. Therefore Va=IRa
Now the measured value of resistance
Rm1=V/I=(Va+VR)/I= (IR+IRa)/I=R+Ra
True value of resistance, R=Rm1-
Ra=Rm1(1- R1/Rm1)
Relative error= (Rm1-R)/R=Ra/R

Thus measured value is higher than true value. True value

is equal to measured value only if the ammeter resistance
Ra is zero.

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In figure b, let Rv be the resistance of
the voltmeter
Current through the voltmeter, Iv=V/Rv
Measured value of resistance,
Rm2=V/I=V/(Ir+Iv)=V/(V/R+V/Rv)

True value of resistance, R=Rm2 Rv/(Rv-

Rm2)
Relative error, ε r = (Rm2-R) / R =Ra/R
If the value of resistance under measurement is
large as compared to internal resistance of
ammeter, the error in measurement would be
small.

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Ammeter-voltmeter method

Advantage
Easy, simple, rough method.
Disadvantage
At full scale error may be around 0-1%.
Errors sometimes considerably high.

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Example

• The resistance of ammeter is 0·01 ohm and that of voltmeter, 2000 ohm. In
case of (b) the current measured is 2 A and the voltage 180 V. Find the
percentage error in calculating resistance R as a quotient of the readings and
the true value of R. Also find the reading of the voltmeter in case of (a) if the
current indicated by the ammeter is 2 A.

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solution

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Bridge circuits

▪ The equivalent electric circuit of some transducers can be

represented as an impedance, and, as a consequence, the
capability of measuring such electrical quantities
accurately is important.
▪ Bridge circuits are used for the measurement of
resistance, inductance, and capacitance accurately.
Wheatstone bridge
▪ The Wheatstone bridge is normally used for the
comparison and measurement of resistances in the range
of 1Ώ to 1 MΏ

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Current I1=V/(P+Q) and Current I2=V/(R+S)
Now potential of point B in respect of point C is nothing but
the voltage drop across the resistor Q and this is
I1*Q=VQ/(P+Q)
Again, potential of point D in respect of point C is nothing but
the voltage drop across the resistor S and this is
I2*S=VS/(R+S)

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956
BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956
Wheatstone Bridge

Wheatstone Bridge Application

• The Wheatstone bridge is used for the precise measurement of low resistance.
• Wheatstone bridge and an operational amplifier are used to measure physical parameters such as
temperature, light, and strain.
• Quantities such as impedance, inductance, and capacitance can be measured using variations on the
Wheatstone bridge.

Wheatstone Bridge Limitations

• For low resistance measurement, the resistance of the leads and contacts becomes significant and
introduces an error.
• For high resistance measurement, the measurement presented by the bridge is so large that the
galvanometer is insensitive to imbalance.
• The other drawback is the resistance change due to the current’s heating effect through the resistance.
Excessive current may even cause a permanent change in the value of resistance.

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956

Contd..
Hay Bridge

Maxwell Bridge

BITS Pilani, Deemed to be University under Section 3 of UGC Act, 1956