Measurement of inductance, capacitance and resistance

MATRUSRI ENGINEERING COLLEGE
DEPARTMENT OF ELECTRICAL AND ELECTRONICS
ENGINEERING
SUBJECT NAME: ELECTRICAL MEASUEMENT & INSTRUMENTATION
FACULTY NAME: Mrs.N.KALPANA
MATRUSRI
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N.Kalpana, Asst.Prof. MECS

SYLLABUS
UNIT I - Instruments
Indicating, Recording and Integrating instruments, Ammeter, Voltmeter, Expression
for torque of moving coil, moving iron, Dynamometer, induction and electrostatic
instruments. Extension of range of instruments, Wattmeter Torque expression for
dynamometer instruments, Reactive power measurement.
UNIT II Meters:
Energy meters, single phase and 3-phase, Driving torque and braking torque
equations, Errors and testing compensation, Maximum demand indicator, Power factor
meters, Frequency meters, Electrical resonance and Weston type of synchro scope.
UNIT III Bridge Methods and transducers:
Measurement of inductance, capacitance and resistance using Bridges, Maxwell’s,
Hay’s. bridge, Anderson, Wein, Desauty’s, Schering’s bridges, Kelvin’s double bridge,
Megger, Loss of charge method, Wagners earthing device, Transducers - Analog and
digital transducers, Strain gauges and Hall effect transducers.
UNIT IV Magnetic Measurements and instrument transformers:
Ballistic galvanometer, Calibration by Hibbert’ s magnetic standard flux meter, Lloyd-
Fischer square for measuring iron loss, Determination of B-H curve and Hysteresis
loop using CRO, Instrument transformers – Current and potential transformers, ratio
and phase angle errors of CT’s and PT’s.
UNIT V Potentiometers:
Crompton’s DC and AC polar and coordinate types, Applications, Measurements of
impedance, Calibration and ammeter voltmeter and wattmeters. Use of oscilloscope in
frequency, phase and amplitude measurements
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Contents:
 Measurement of inductance
 capacitance and resistance using Bridges
 Maxwell’s, Hay’s. bridge, Anderson,
 Wein, Desauty’s, Schering’s bridges
 Kelvin’s double bridge
 Megger, Loss of charge method
 Wagners earthing device,
Course Outcomes: At the end of the Course, the Student will be able to:
CO 1: Apply and Analyze the measurement of various circuit parameters using
bridge methods.
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MEASUREMENT OF RESISTANCE
Resistance is one of the most basic elements encountered in electrical and
electronics engineering. The value of resistance in engineering varies from very
small value like, resistance of a transformer winding, to very high values like,
insulation resistance of that same transformer winding. Although a multimeter
works quite well if we need a rough value of resistance, but for accurate values and
that too at very low and very high values we need specific methods. In this article
we will discuss various methods of resistance measurement. For this purpose we
categories the resistance into three classes-
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MEASUREMENT OF LOW RESISTANCE (<1Ω)
The major problem in measurement of low resistance values is the contact
resistance or lead resistance of the measuring instruments, though being small in
value is comparable to the resistance being measured and hence causes serious
error
The methods employed for measurement of low resistances are:-
1. Kelvin’s Double Bridge Method
2. PotentiometerMethod
3. DucterOhmmeter.
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MEASUREMENT OF MEDIUM RESISTANCE
(1Ω - 100KΩ)
Following are the methods employed for measuring a
resistance whose value is in the range 1Ω -100kΩ
1. Ammeter-VoltmeterMethod
2. Wheatstone BridgeMethod
3. SubstitutionMethod
4. Carey- Foster BridgeMethod
5. OhmmeterMethod
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Ammeter Voltmeter Method
This is the most crude and simplest method of measuring resistance. It uses one ammeter
to measure current, I and one voltmeter to measure voltage, V and we get the value of
resistance as
R=V/I
Now we can have two possible connections of ammeter and voltmeter, shown in the
figure below.
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Now in figure 1, the voltmeter measures voltage drop across
ammeter and the unknown resistance, hence
Hence, the relative error will be,
For connection in figure 2, the ammeter measures the sum of current through voltmeter
and resistance, hence
The relative error will be,
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It can be observed that the relative error is zero for Ra = 0 in
first case and Rv = ∞ in second case. Now the questions stand
that which connection to be used in which case. To find out
this we equate both the errors
Hence for resistances greater than that given
by above equation we use the first method
and for less than that we use second method.
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A voltmeter of 600 Ω resistance and a milliammeter of 0.8 Ω resistance are used to
measure two unknown resistances by voltmeter–ammeter method. If the voltmeter reads
40 V and milliammeter reads 120 mA in both the cases, calculate the percentage error in
the values of measured resistances if (a) in the first case, the voltmeter is put across the
resistance and the milliammeter connected in series with the supply, and (b) in the second
case, the voltmeter is connected in the supply side and milliammeter connected directly in
series with the resistance.
Solution
The connections are shown in the following figure.
Voltmeter reading V = 40 V
Ammeter reading I = 120 mA
measured resistance from voltmeter and I ammeter readings is given by
The ammeter reads the current flowing IR through the resistance Rx and also the current
IV through the voltmeter resistance RV .
Thus,
I = IV + IR
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Now, the voltmeter and the resistance Rx being in parallel,
the voltmeter reading is given by
V = IR × RX = IV × RV
Current through voltmeter
true current throught resistance
IR = I - IV = 120-66.67 = 55.33 mA
true value of resistance =
Thus, percentage error =
The connections are shown in the following figure.
Voltmeter reading V = 40V
Ammeter reading I = 120 mA
measured resistance from voltmeter and ammeter readings is given by
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Voltmeter reads the voltage drop Vr across the
resistance Rx and also the voltage drop
Va across the ammeter resistance Ra .
Thus,
V = Va + Vr
Voltage drop across ammeter
Va = I × Ra = 120 × 10 -3 × 0.8 = 0.096 V
true voltage drop across the resistance
Vr = V - Va = 40 – 0.096 × 39.904 V
true value of resistance=
Percentage error in measurement is =
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The basic circuit of the Wheatstone bridge is shown in the figure below. The bridge
has four arms which consist two unknown resistance, one variable resistance and
the one unknown resistance along with the emf source and galvanometer.
Construction of Wheatstone Bridge
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balance condition, the current through detector iszero.
. .
I1 =I 3
. .
I 2 =I 4
𝐼1
𝐼2
=
𝐼3
𝐼4
--(1)
At balance condition,
Voltage drop across ‘AB’=voltage drop across ‘AD’.
..E1 =E 2
. . . .
I1 Z1 =I 2 Z 2 --------(2)
Similarly, Voltage drop across ‘BC’=voltage drop across
‘DC’
.E 3 =E 4
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The equation (2) shows the balance condition of the Wheatstone bridge.
The value of unknown resistance is determined by the help of the equation (3). The R is
the unknown resistance, and the S is the standard arm of the bridge and the P and Q
are the ratio arm of the bridge.
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The following are the errors in the Wheatstone bridge.
1. The difference between the true and the mark value of the three resistances can cause
the error in measurement.
2. The galvanometer is less sensitive. Thus, inaccuracy occurs in the balance point.
3. The resistance of the bridge changes because of the self-heating which generates an
error.
4. The thermal emf cause serious trouble in the measurement of low-value resistance.
5. The personal error occurs in the galvanometer by taking the reading or by finding the null
point.
The above mention error can be reduced by using the best qualities resistor and
galvanometer. The error because of self-heating of resistance can minimise by measuring the
resistance within the short time. The thermal effect can also be reduced by connecting the
reversing switch between the battery and the bridge.
Errors in Wheatstone Bridge
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The emf supply is attached between point a and b, and the galvanometer is connected
between point c and d. The current through the galvanometer depends on the potential
difference across it.
Working of Galvanometer
The bridge is in balance condition when no current flows through the coil or the potential
difference across the galvanometer is zero. This condition occurs when the potential
difference across the a to b and a to d are equal, and the potential differences across the b
to c and c to d remain same.
The current enters into the galvanometer divides into I1 and I2, and their magnitude remains
same. The following condition exists when the current through the galvanometer is zero.
The bridge in a balanced condition is expressed as
Where E – emf of the battery.
By substituting the value of I1 and 12 in equation (1) we get.
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Limitation of Wheat Stone Bridge
The Wheatstone bridge gives inaccurate readings if it is unbalanced.
The Wheatstone bridge measures resistance from few ohms to megohms.
The upper range of the bridge can be increased with the help of the applied emf,
and the lower range is limited by connecting the lead at the binding post.
Sensitivity of the Wheatstone Bridge
The Wheatstone bridge is more sensitive when all their resistances are equal, or
their ratio is unity. Their sensitivity decreases when their ratio is less than unity. The
reduction in sensitivity reduces the accuracy of the bridge.
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Wheatstone Bridge Method
This is the simplest and the most basic bridge circuit used in measurement studies. It
mainly consists of four arms of resistance P, Q; R and S. R is the unknown resistance under
experiment, while S is a standard resistance. P and Q are known as the ratio arms. An EMF
source is connected between points a and b while a galvanometer is connected between
points c and d.
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A bridge circuit always works on the principle of null detection, i.e. we vary a
parameter until the detector shows zero and then use a mathematical relation to
determine the unknown in terms of varying parameter and other constants. Here also
the standard resistance, S is varied in order to obtain null deflection in the
galvanometer. This null deflection implies no current from point c to d, which implies
that potential of point c and d is same. Hence
Combining the above two equations we get the famous equation –
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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 in a Wheatstone Bridge
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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
minimised 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 minimise 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.
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Four arms of a Wheatstone bridge are as follows: AB = 100 Ω, BC = 10 Ω, CD = 4 Ω, DA =
50 Ω. A galvanometer with internal resistance of 20 Ω is connected between BD, while a
battery of 10-V dc is connected between AC. Find the current through the galvanometer.
Find the value of the resistance to be put on the arm DA so that the bridge is balanced.
PROBLEM
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Substitution Method
The figure below shows the circuit diagram for resistance measurement of an unknown
resistance R. S is a standard variable resistance and r is a regulating resistance.
First the switch is place at position 1 and the ammeter is made to read a certain
amount of current by varying r. The value of ammeter reading is noted. Now the
switch is moved to position 2 and S is varied in order to achieve the same ammeter
reading as it read in the initial case. The value of S for which ammeter reads same as
in position 1, is the value of unknown resistance R, provided the EMF source has
constant value throughout the experiment.
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Ohmmeter Method for Measuring Resistance
Ohmmeters are convenient direct
reading devices for measurement of
approximate resistance of circuit
components without concerning too
much about accuracy. This instrument
is, however, very popular in the sense
that it can give quick and direct
readings for resistance values without
any precise adjustments
requirements from the operator. It is
also useful in measurement
laboratories as an adjunct to a
precision bridge. Value of the
unknown resistance to be measured
is first obtained by the ohmmeter,
and this can save lot of time in bridge
balancing for obtaining the final
precision value using the bridge.
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Before actual readings are taken, the terminals A–B must be shorted together. At this
position with Rx = 0, maximum current flows through the meter. The shunt resistance
R2 is adjusted so that the meter deflects corresponding to its right most full scale
deflection (FSD) position. The FSD position of the pointer is marked ‘zero-resistance’,
i.e., 0 Ω on the scale. On the other hand, when the terminals A–B are kept open
(Rx→∞), no current flows through the meter and the pointer corresponds to the left
most zero current position on the scale. This position of the pointer is marked as ‘∞Ω’
on the scale. Thus, the meter will read infinite resistance at zero current position and
zero resistance at full-scale current position. Series ohmmeters thus have ‘0’ mark at
the extreme right and ‘∞’ mark at the extreme left of scale (opposite to those for
ammeters and voltmeters). The main difficulty is the fact that ohmmeters are usually
powered by batteries, and the battery voltage gradually changes with use and age. The
shunt resistance R2 is used in such cases to counteract this effect and ensure proper
zero setting at all times. For zero setting, Rx = 0, where Rm = internal resistance of the
basic PMMC meter coil
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Following are few methods used for measurement of high resistance
values-
Loss of ChargeMethod
Megger
Megohm bridgeMethod
Direct DeflectionMethod
MEASUREMENT OF HIGH RESISTANCE
(>100KΩ)
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LOSS OF CHARGE METHOD
In this method we utilize the equation of voltage across a discharging capacitorto
find the value of unknown resistance R. Figure below shows the circuit diagram
v=V e-tRC
R=t/(C*loge(V/v)
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Direct Deflection Method for High Resistance
Measurement
For measurement of high resistances, a sensitive galvanometer is used instead of a micro
ammeter
Figure : Measurement of cable insulation resistance
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Figure Meggar for high resistance measurement
Megohmmeter, or Meggar, for High
Resistance Measurement
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1. Armature of the generator rotated by hand driven crank lever
2. The clutch mechanism is designed to slip at a predetermined speed
3. This facilitate the generator to maintain constant speed and constant voltage
while testing
4. Two coils A&B constitutes moving coil Voltmeteand r Ammeter
5. Both or combined to form one instrument
6. Whose insulation to be measured is connected across the X terminal(testing
terminal)
7. Y is connected to ground
8. When crank handle is rotate generator, a voltage is generated in the generator
9. Generated voltage applied across voltage coil (A) through R1
10. When the terminal X&Y are free no current flows through the coil B
11. The torque produced by the coil A rotates moving element(pointer) to show
infinity
12. While testing X &Y terminals are connected across the terminal & body of the
machine for measurement
13. Now the current passes through the deflecting coil B
14. Now the torque produced by the coil B interacts with the torque of A rotates the
moving element to indicate the resistance of coil.
15. Voltage generated by the instrument is around 500 volts.
16. Meggers are available to generate voltages 1000V,2500,5000V also
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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 above Figure 4.20. 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.
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
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. 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 ‘∞ Ω’ as marked in the
scale shown in above 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 ‘∞ Ω’ mark clockwise (according to Figure 4.20) 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 (GR in above Figure ) and the guard wire diverts the surface leakage current from
reaching the main moving system and interfering with its performance.
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Ducter Ohmmeter
It is an electromechanical instrument used for measurement of low resistances. It comprises
of a permanent magnet similar to that of a PMMC instrument and two coils in between the
magnetic field created by the poles of the magnet. The two coils are at right angles to each
other and are free to rotate about the common axis. Figure below shows a Ducter Ohmmeter
and the connections required to measure an unknown resistance R.
One of the coil called current coil, is
connected to current terminals C1 and
C2, while the other coil called, voltage
coil is connected to potential terminals
V1 and V2. Voltage coil carries current
proportional of the voltage drop across
R and so is its torque produced.
Current coil carries current
proportional to the current flowing
through R and so is its torque too. Both
the torque acts in opposite direction
and the indicator come to halt when
the two are equal. This instrument is
useful for resistance in range 100µΩ to
5Ω.
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Megohm Bridge Method
In this method we use the famous Wheatstone bridge philosophy but in a slightly
modified way. A high resistance is represented as in the figure below.
G is the guard terminal. Now we can also
represent the resistor as shown in the
adjoining figure, where RAG and RBG are the
leakage resistances. The circuit for
measurement is shown in the figure below.
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It can be observed that we actually obtain the resistance which is parallel
combination of R and RAG. Although this causes very insignificant error.
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MEASUREMENT OF LOW RESISTANCE (<1Ω)
The major problem in measurement of low resistance values is the contact
resistance or lead resistance of the measuring instruments, though being small in
value is comparable to the resistance being measured and hence causes serious
error
The methods employed for measurement of low resistances are:-
1. Kelvin’s Double Bridge Method
2. PotentiometerMethod
3. DucterOhmmeter.
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Carey-Foster Slide-Wire Bridge
The Carey Foster Bridge is used for
measuring the low resistance or for
the comparison of two nearly equal
resistances. The working principle
of the Carey foster bridge is similar
to the Wheatstone Bridge.
The Carey Foster Bridge is used for measuring the low resistance or for the comparison of
two nearly equal resistances. The working principle of the Carey foster bridge is similar to
the Wheatstone Bridge.
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Let P, Q, R and S are the four resistors used in the bridge. The resistances of P
and Q are known while the R and S are the unknown resistors. The slide wire of
length L is placed between the resistance R and S.
The resistor P and Q are adjusted so that the ratio of P/Q is equivalent to the R/S.
The ratio of the resistance is equivalent by sliding the contact on the sliding
wiring.
Let l1 is the distance from the left at which the balanced is obtained. Now the R
and S are interchanged, and this time the balanced is obtained by sliding the
contact at the distance of l2.
Consider the equation for first balance
The r is the resistance per unit length of the sliding wire.
After interchanging the R and S, the balance equation of the bridge is
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For the first balance equation add 1 on both sides
And for the second balance equation add 1 on both sides
From equation (1) and (2)
The difference between the resistance of S and R is obtained from a distance between
the length of the slide-wire, i.e., l1 – l2 at balance condition. 44

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Calibration of Slide Wire
The calibration of the sliding wire can be done by placing the resistance R or S in parallel
with the slide wire of known resistance. Let S is known and S’ is its values when shunted by
known resistance.
By solving the above equation, we get
By the help of the Carey foster bridge, the direct comparison between the resistance R
and S regarding length can be done. The resistance of other components like the
resistance of P, Q and sliding contact are completely eliminated.
Note: The special switch is used for interchanging the resistor S and R during the test.
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Kelvin Bridge
Definition: The Kelvin bridge or Thompson bridge is used for measuring the unknown
resistances having a value less than 1Ω. It is the modified form of the Wheatstone Bridge.
What is the need of Kelvin Bridge?
Wheatstone bridge use for measuring the resistance from a few ohms to several kilo-
ohms. But error occurs in the result when it is used for measuring the low resistance.
This is the reason because of which the Wheatstone bridge is modified, and the Kelvin
bridge obtains. The Kelvin bridge is suitable for measuring the low resistance.
Modification of Wheatstone Bridge
In Wheatstone Bridge, while measuring the low-value resistance, the resistance of their
lead and contacts increases the resistance of their total measured value. This can easily
be understood with the help of the circuit diagram.
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The r is the resistance of the contacts that connect the unknown resistance R to
the standard resistance S. The ‘m’ and ‘n’ show the range between which
the galvanometer is connected for obtaining a null point.
When the galvanometer is connected to point ‘m’, the lead resistance r is added to
the standard resistance S. Thereby the very low indication obtains for unknown
resistance R. And if the galvanometer is connected to point n then the r adds to the
R, and hence the high value of unknown resistance is obtained. Thus, at point n and
m either very high or very low value of unknown resistance is obtained.
So, instead of connecting the galvanometer from point, m and n we chose any
intermediate point say d where the resistance of lead r is divided into two equal
parts, i.e., r1 and r2
The presence of r1 causes no error in the measurement of unknown resistance.
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From equation (1), we get
as
The above equation shows that if the galvanometer connects at point d then the
resistance of lead will not affect their results.
The above mention process is practically not possible to implement. For obtaining
the desired result, the actual resistance of exact ratio connects between the point m
and n and the galvanometer connects at the junction of the resistor.
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Kelvin Double Bridge Circuit
The ratio of the arms p and q are used to connect the galvanometer at the right place
between the point j and k. The j and k reduce the effect of connecting lead. The P and Q is
the first ratio of the arm and p and q is the second arm ratio.
I2
I1
I2
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The galvanometer is connected
between the arms p and q at a point d.
The point d places at the centre of the
resistance r between the point m and n
for removing the effect of the
connecting lead resistance which is
placed between the unknown
resistance R and standard resistance S.
The ratio of p/q is made equal to the
P/Q. Under balance condition zero
current flows through the
galvanometer. The potential difference
between the point a and b is equivalent
to the voltage drop between the points
Eamd.
Now,
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Eab=Eamd
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The balance equation Eab=Eamd
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The second quantity of the above Eq
can be made very small by making the ratio P/Q as close as possible to p/q. In that case, there
is no effect of the connecting lead resistance ‘r’ on the expression for the unknown resistance.
Thus, the expression for the unknown resistance X can now be simply written as
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The galvanometer is connected between the arms p and q at a point d. The point d
places at the centre of the resistance r between the point m and n for removing the
effect of the connecting lead resistance which is placed between the unknown
resistance R and standard resistance S.
The ratio of p/q is made equal to the P/Q. Under balance condition zero current flows
through the galvanometer. The potential difference between the point a and b is
equivalent to the voltage drop between the points Eamd.
Now,
Eamd = Eam +Emd
Eam=R*I
Emd=p*I2
I2= I* r/(p+q+r)
Eamd = (R*I )+I* r/(p+q+r)
Eac = R*I +[ I*[r(p+q)/(p+q+r)]] +I*S
Eac = I{ R +[r(p+q)/(p+q+r)] +S}
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For zero galvanometer deflection,
As we known, P/Q = p/q then above equation becomes
The above equation is the working equations of the Kelvins bridge. The equation
shows that the result obtains from the Kelvin double bridge is free from the impact of
the connecting lead resistance.
For obtaining the appropriate result, it is very essentials that the ratio of their arms is
equal. The unequal arm ratio causes the error in the result. Also, the value of
resistance r should be kept minimum for obtaining the exact result.
The thermo-electric EMF induces in the bridge during the reading. This effect can be
reduced by measuring the resistance with the reverse battery connection. The real
value of the resistance obtains by takings the means of the two.
Limitations of Kelvins Bridge
1. The sensitive galvanometer is used for detecting the balance condition.
2. The high measurement current is required for obtaining the good sensitivity.
57

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ENGINEERING COLLEGE
A 4-terminal resistor was measured with the help of a Kelvin’s double bridge having the
following components: Standard resistor = 98.02 nW, inner ratio arms = 98.022 Ω Example
4.6 and 202 W, outer ratio arms = 98.025 Ω and 201.96 W, resistance of the link connecting
the standard resistance and the unknown resistance = 600 nW. Calculate the value of the
unknown resistance.
Problem
58

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ENGINEERING COLLEGE
Potentiometer Method for Measuring Low Resistance
Figure :Measurement of low resistance using potentiometer
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ENGINEERING COLLEGE
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
Vx = I * X (1)
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
Vs = I*S (2)
From Eqs (1) and (2), we get
X=(VR/Vs) *S
60

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ENGINEERING COLLEGE
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 stabilised 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.
61

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ENGINEERING COLLEGE
Basis for
Comparison
AC Bridge DC Bridge
Definition The bridge which is
used for measuring the
value of unknown
impedance is known as
the AC bridge.
The DC bridge
measures the
unknown resistance of
the circuit.
Supply AC supply is used DC supply is used
Current Detector AC Detector DC Detector
Components Resistive and Reactive Resistive
Wagner’s Earthing
Device
Required Not required
Types Two Seven
Balancing Time Relatively Less High
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ENGINEERING COLLEGE
Definition: The Wagner earthing device is used for removing the earth capacitance from
the bridges. It is a type of voltage divider circuit used to reduces the error which occurs
because of stray capacitance. The Wagner Earth device provides high accuracy to the
bridge.
At high frequency, stray capacitance is induced between the bridge elements, ground and
between the arms of the bridge. This stray element causes the error in the
measurement. One of the way, of controlling these capacitances is too enclosed the
bridge elements into the shield. Another way of eliminating these stray capacitance is to
places the Wagner Earth device between the elements of the bridge.
Construction of Wagner Earthing Device
The circuit diagram of the Wagner Earth Device is shown in the figure below. Consider the
Z1, Z2, Z3, and Z4 are the impedances arm of the bridge. The Z5 and the Z6 are the two
variable impedances of the Wagner Earth Device. The centre point of the Wagner earth
device is earthed. The impedance of Wagner device arms is similar to the arms of the
bridge. The impedance of the arm consists the resistance and capacitances.
Wagner Earthing Device
63

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64

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ENGINEERING COLLEGE
The Wagner impedance placed in such a way so that they make the bridge
balance with Z1, Z3 and Z2, Z4. The C1, C2 C3 and C4 show the stray
capacitances of the bridges. The D is the detector of the bridge.
The bridge comes in the balance condition by adjusting the impedances of
arms Z1 and Z4. The stray capacitance prevents bridge to comes in the
balanced condition. When the S is not thrown on ‘e’ then the D is connected
between the point p and q. But when S is thrown on ‘e’ then the detector D
is connected between the terminal b and earth.
The impedance Z4 and Z5 are adjusted until the minimum sound is obtained.
The headphones again connected between the point b and d for obtaining
the minimum sound. The headphones are reconnected between the point b
and d, Z4 and Z5 are adjusted for obtaining the minimum sound. The process
is continuously repeated for obtaining the silent sound.
The point b, d, and e all are in the same potential. And the capacitance C1, C2,
C3, C4 all are eliminated from the bridge circuit along with the impedances
Z5 and Z6.
65

MATRUSRI
ENGINEERING COLLEGE
A 4-terminal resistor was measured with the help of a Kelvin’s double bridge having the
following components: Standard resistor = 98.02 nW, inner ratio arms = 98.022 Ω Example
4.6 and 202 W, outer ratio arms = 98.025 Ω and 201.96 W, resistance of the link connecting
the standard resistance and the unknown resistance = 600 nW. Calculate the value of the
unknown resistance.
Problem
66

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ENGINEERING COLLEGE
TRANSDUCERS
Transducer is a device that converts energy in one form of energy to another form
of energy. This converts non-electrical quantity into electrical quantity.
Electrical transducers are defined as the transducers which convert one form of
energy to electrical energy for measurement purposes. The quantities which cannot
be measured directly, such as pressure, displacement, temperature, humidity, fluid
flow, etc., are required to be sensed and changed into electrical signal first for easy
measurement.
The advantages of electrical transducers are the following:
• Power requirement is very low for controlling the electrical or electronic system.
• An amplifier may be used for amplifying the electrical signal according to the
requirement.
• Friction effect is minimised.
• Mass-inertia effect are also minimised, because in case of electrical or electronics
signals the inertia effect is due to the mass of the electrons, which can be negligible.
• The output can be indicated and recorded remotely from the sensing element.
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The main objective of a transducer is to react only for the measurement under specified
limits for which it is designed. It is, therefore, necessary to know the relationship
between the input and output quantities and it should be fixed. A transducer should
have the following basic requirements:
1. Linearity Its input vs output characteristics should be linear and it should produce
these characteristics in balanced way.
2. Ruggedness A transducer should be capable of withstanding overload and some
safety arrangements must be provided with it for overload protection.
3. Repeatability The device should reproduce the same output signal when the same
input signal is applied again and again under unchanged environmental conditions,
e.g., temperature, pressure, humidity, etc.
4. High Reliability and Stability The transducer should give minimum error in
measurement for temperature variations, vibrations and other various changes in
surroundings.
5. High Output Signal Quality The quality of output signal should be good, i.e., the ratio
of the signal to the noise should be high and the amplitude of the output signal
should be enough.
6. No Hysteresis It should not give any hysteresis during measurement while input
signal is varied from its low value to high value and vice versa. 7. Residual
Reformation There should not be any deformation on removal of input signal after
long period of use. 68

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ENGINEERING COLLEGE
Classification of transducers
• Primary and Secondary Transducers
• Analog and Digital Transducers
• Active and Passive Transducers
• Transducers and Inverse Transducers
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Primary and Secondary Transducers
When the input signal is directly sensed by the transducer and physical
phenomenon is converted into the electrical form directly then such a transducer is
called the primary transducer. Example: The thermistor senses the temperature
directly and causes the change in resistance with the change in temperature. When
the input signal is sensed first by some detector or sensor and then its output being
of some form other than input signals is given as input to a transducer for conversion
into electrical form, then such a transducer falls in the category of secondary
transducers. For example, in case of pressure measurement, bourdon tube is a
primary sensor which converts pressure first into displacement, and then the
displacement is converted into an output voltage by an LVDT.
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Analog and Digital Transducers
Analog transducer converts input signal into output signal, which is a continuous
function of time such as thermistor, strain gauge, LVDT, thermo-couple etc. Digital
transducer converts input signal into the output signal of the form of pulse e.g. it gives
discrete output.
• Transducers and Inverse Transducers Transducer, as already defined, is
a device that converts a non-electrical quantity into an electrical quantity. Normally a
transducer and associated circuit has a non-electrical input and an electrical output, for
example a thermo-couple, photoconductive cell, pressure gauge, strain gauge etc. An
inverse transducer is a device that converts an electrical quantity into a non-electrical
quantity. Example: piezoelectric oscillator
Active and Passive Transducers
An active transducer generates an electrical signal directly in response to the physical
parameter and does not require an external power source for its operation. Active
transducers are self generating devices, which operate under energy conversion
principle and generate an equivalent output signal (for example from pressure to
charge or temperature to electrical potential). Typical example of active transducers are
piezo electric sensors (for generation of charge corresponding to pressure) and photo
voltaic cells (for generation of voltage in response to illumination).
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Passive transducer operate under energy controlling principles, which makes it
necessary to use an external electrical source with them. They depend upon the change
in an electrical parameter (R, L and C). Typical example are strain gauges (for resistance
change in response to pressure), and thermistors (for resistance change corresponding
to temperature variations).
Electrical transducer is used mostly to measure non-electrical quantities. For
this purpose a detector or sensing element is used, which converts the physical quantity
into a displacement. This displacement actuates an electric transducer, which acts as a
secondary transducer and gives an output that is electrical in nature. This electrical
quantity is measured by the standard method used for electrical measurement. The
electrical signals may be current, voltage, or frequency; their production is based on R,
L and C effects. A transducer which converts a non-electrical quantity into an analog
electrical signal may be considered as consisting of two parts, the sensing element, and
the transduction element. The sensing or detector element is that part of a transducer
which responds to a physical phenomenon or to a change in a physical phenomenon.
The response of the sensing element must be closely related to the physical
phenomenon. The transduction element transforms the output of a sensing element to
an electrical output. This, in a way, acts as a secondary transducer. Transducers may be
further classified into different categories depending upon the principle employed by
their transduction elements to convert physical phenomena into output electrical
signals. 72

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ENGINEERING COLLEGE
Selecting a Transducer
The transducer or sensor has to be physically compatible with its intended
application.
The following should be considered while selecting a transducer.
1. Operating range: Chosen to maintain range requirements and good
2. Sensitivity: Chosen to allow sufficient output.
3. Frequency response and resonant frequency: Flat over the entire desired
range.
4. Environmental compatibility: Temperature range, corrosive fluids, pressure,
shocks, interaction, size and mounting restrictions.
5. Minimum sensitivity: To expected stimulus, other than the measurand.
6. Accuracy: Repeatability and calibration errors as well as errors expected due to
sensitivity to other stimuli.
7. Usage and ruggedness: Ruggedness, both of mechanical and electrical
intensities versus size and weight.
8. Electrical parameters: Length and type of cable required, signal to noise ratio
when combined with amplifiers, and frequency response limitations.
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ENGINEERING COLLEGE
LINEAR VARIABLE DIFFERENTIAL
TRANSFORMER (LVDT)
The most widely used inductive transducer to translate the linear motion into electrical
signals is the Linear Variable Differential Transformer (LVDT). The basic construction of
LVDT is shown in Figure 11.1. The transformer consists of a single primary winding ‘P’
and two secondary windings S1 and S2 wound on a cylindrical former. A sinusoidal
voltage of amplitude 3 to 15 Volt and frequency 50 to 20000 Hz is used to excite the
primary. The two secondaries have equal number of turns and are identically placed on
either side of the primary winding.
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ENGINEERING COLLEGE
The primary winding is connected to an alternating current source. A movable
soft-iron core is placed inside the former. The displacement to be measured is
applied to the arm attached to the soft iron core. In practice the core is made of
high permeability, nickel iron. This is slotted longitudinally to reduce eddy current
losses. The assembly is placed in a stainless steel housing to provide electrostatic
and electromagnetic shielding. The frequency of ac signal applied to primary
winding may be between 50 Hz to 20 kHz. Since the primary winding is excited by
an alternating current source, it produces an alternating magnetic field which in
turn induces alternating voltages in the two secondary windings. The output
voltage of secondary S1 is ES1 and that of secondary S2 is ES2 . In order to convert
the outputs from S1 and S2 into a single voltage signal, the two secondary S1 and
S2 are connected in series opposition as shown in Figure 11. 2. Differential output
voltage E0 = ES1 − ES2
75

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Figure : Connection of LVDT circuit
76

MATRUSRI
ENGINEERING COLLEGE
When the core is at its normal (NULL) position, the flux linking with both the secondary
windings is equal and hence equal emfs are induced in them. Thus, at null position: ES1
= ES2 . Thus, the output voltage E0 is zero at null position. Now if the core is moved to
the left of the null position, more flux links with S1 and less with winding S2 .
Accordingly, output voltages ES1 is greater than ES2 . The magnitude of output voltage
is thus, E0 = ES1 − ES2 and say it is in phase with primary voltage. Similarly, when the
core is moved to the right of the null position ES2 will be more than ES1 . Thus the
output voltage is E0 = ES1 − ES2 and 180° out of phase with primary voltage. The
amount of voltage change in either secondary winding is proportional to the amount of
movement of the core. Hence, we have an indication of amount of linear motion. By
noticing whether output voltage is increased or decreased, we can determine the
direction of motion. n
Operation
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Advantages
• Linearity is good up to 5 mm of displacement.
• Output is rather high. Therefore, immediate amplification is not necessary.
• Output voltage is stepless and hence the resolution is very good.
• Sensitivity is high (about 40 V/mm).
• It does not load the measurand mechanically.
• It consumes low power and low hysteresis loss also.
Disadvantages
• LVDT has large threshold.
• It is affected by stray electromagnetic fields. Hence proper shielding of the
device is necessary.
• The ac inputs generate noise.
• Its sensitivity is lower at higher temperature.
• Being a first-order instrument, its dynamic response is not instantaneous.
Advantages and Disadvantages of LVDT
78

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