This document discusses the measurement of electrical components like resistance, inductance, and capacitance. It begins by classifying resistances into low, medium, and high ranges. Methods for measuring medium resistances include the ammeter and voltmeter method, substitution method, and Wheatstone bridge. The Wheatstone bridge provides highly accurate measurements. Kelvin's double bridge is discussed for measuring low resistances. Megaohm bridges and megaohmmeters are described for measuring high resistances. Bridges like Maxwell, Hay's, and Anderson are covered for measuring inductance, while Schering's and Wein's bridges are summarized for measuring capacitance and frequency. Potential sources of error in bridge circuits are also outlined.

1. Electrical and Electronic Measurement
Measurement of Resistance, Inductance and Capacitance
Parveen Malik
Assistant Professor
School of Electronics Engineering
KIIT University
parveen.malikfet@kiit.ac.in
February 6, 2019
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2. Outline
1 Measurement of Resistance
Range of Resistances
Classification of Methods - Low, Medium and High
Medium Resistance measurement
Ammeter & Voltmeter Method
Substitution Method
Wheatstone Bridge
Low Resistance measurement
Kelvin’s double bridge
High Resistance Measurement
Mega-ohm Bridge
Megaohmmeter - Megger
2 A.C. Bridges
Measurement of Inductance
Measurement of Capacitance
3 Errors in Bridge Measurement
4 Wagner’s earthing device
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3. Resistance Measurement
Range of Resistances

4. Range of Resistances1
Low Resistances - Order of 1 Ω or under
Copper , Gold, silver and aluminium.
Resistance series field winding generator, resistance of armature
winding, Earth winding Resistance
Medium Resistances - 1 Ω to 100, 000 Ω
Resistance of field winding of D.C. shunt generator, Resistance of long
transmission line
High Resistances - 100, 000 Ω to upwards
Resistance of cable insulation, resistance of insulator disk of
transmission line
1
This classification is not rigid
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5. Resistance Measurement
Methods of Measurement
Classification

6. Resistance Measurement
Low, Medium and High Resistances
Low resistance
1 Ammeter and Voltmeter Method
2 Kelvin Double Bridge
3 Potentiometer Method
4 Ducter
Medium resistance
1 Ammeter and Voltmeter Method
2 Substitution Method
3 Wheatstone Bridge
4 Ohmmeter method
High resistance
1 Megaohm Bridge
2 Meggar
3 Loss of Charge Method
4 Deflection Method
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7. Measurement of Resistance
Medium Resistance
Ammeter & Voltmeter Method

8. R Measurement (M) - Ammeter & Voltmeter Method
(a)
(b)
Low Resistance values
Fig.(a) - Accurate and most
suitable when R ≪ RV
Rm = R
1+ R
RV
High Resistance values
Fig(b) - Accurate and most
suitable when R ≫ RA
Rm = R
1 + RA
R
Application
Suitable for laboratory
purpose.
Cons
Rough Method
Accuracy depends upon the
accuracy of voltmeter and
ammeter.
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9. Measurement of Resistance
Medium Resistance-Substitution
Method

10. R Measurement (Medium) - Substitution Method
Substitution Method
Pros
More accurate than
ammeter voltmeter.
Cons
Accuracy depends upon
constancy of the battery
emf.
sensitivity of instrument.
accuracy of standard
resistance.
Applications
Used in High frequency a.c.
measurements.
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11. Measurement of Resistance
Medium Resistance
Wheatstone Bridge

12. Resistance Measurement - Wheatstone Bridge
Wheatstone Bridge
Balanced Condition
P
Q = R
S
Pros
Highly Reliable easy to
use
Highly Accurate as reading
is independent of
characteristics of Null
indicating instrument.
Cons
Insufficient sensitivity of null
detector.
Changes in resistance due to
heating effect.
Thermal emf
Error due to resistance of
leads and contacts.
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13. Sensitivity of Wheatstone Bridge

14. Resistance Measurement
Sensitivity of Wheatstone Bridge
Sensitivity is used for
Selecting a galvanometer with which unbalance may be observed.
Determining the minimum unbalance with a given galvanometer
Determining the deflection to be expected for a given unbalance.
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15. Low Resistance Measurement
Problems in Measurement of Low
Resistances

16. Kelvin’s bridge
Problems in Measurement of Mow Resistances
When resistance under
measurement is comparable to
connecting leads resistance.
At Point m,
R =
P(S + r)
Q
At Point n,
R =
PS
Q
− r
At Point d,
R =
PS
Q
P
Q
=
r1
r2
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17. Kelvin’s Double Bridge

18. Kelvin’s double bridge
Balance Equation (2nd ratio arm)
R =
PS
Q
+
qr
p + q + r
P
Q
−
p
q
Accuracies
1000 µΩ to 1 µΩ - 0.05%
100 µΩ to 1000 µΩ - 0.2% to 0.05%
10 µΩ to 100 µΩ - 0.5% to 0.2%
Cons
Accuracy is constrained by
thermoelectric emf.
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19. High Resistance Measurement
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20. Mega-ohm Bridge

21. High Resistance Measurement - Wheatstone Bridge
Resistance in the range -
MΩ
Let us Consider RBG =
RBG = RAB = 100MΩ, the
equivalent resistance
becomes 200/3 = 66.67Ω.
Therefore, Output error is
33.33% ( RAB = 100MΩ)
We need to modify
Wheatstone bridge in order
to get exact RAB value
which is 100MΩ
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22. Megaohm Bridge
Modification to Wheatstone Bridge
Connect b to G point.
When bridge is balanced,the potential difference across RBG is zero
and there is not current flowing through it. We can ignore this branch.
Now RAG comes in parallel to P. Thus, balance equation becomes
(RAG | | P) · S = R · Q and R = (RAG | | P)·S
Q
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23. Megaohmmeter - Megger

24. Megaohmmeter - Megger2
2
Electronic Instrumentation and Measurements- David A. Bell, P 182, Sec
7-7 Parveen Malik () E and EM February 6, 2019 24 / 48

25. Megaohmmeter - Megger3
Controlling Force
τC ∝ FC ∝ I1 ∝
V
R1
Deflecting Force
τd ∝ Fd ∝ I2 ∝
V
Rx + R2
Case 1 - When Rx is open , no current
will flow through the current coil
(Deflecting Coil) and only current that
would flow is through the controlling coil
which brings the pointer to infinity scale.
Case 2 - When Rx is closed, no current
will flow through the voltage Coil (
control coil), only current that would
flow is through the current coil (
Deflecting Coil) which brings the pointer
to 0 scale.
Case 3 - When Rx is put, current start
flowing through the both coils. The
pointer stops when both controlling and
deflecting forces are equal. At this point,
Rx = R1 − R2
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26. A.C. Bridges

27. A.C. Bridges
Balance Equation
Z1 · Z4 = Z2 · Z3
Magnitude Condition
|Z1| · |Z4| = |Z2| · |Z3|
Angle Condition
∠θ1 + ∠θ4 = ∠θ2 + ∠θ3
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28. Measurement of Inductance

29. Maxwell’s bridge

30. Maxwell Inductance Bridge
Balance Equation
L1 = L2R3
R4
, R1 = R2R3
R4
Q = ωL2R2
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31. Maxwell Inductance - Capacitance
Bridge

32. Maxwell Inductance - Capacitance Bridge
Balance Equation
L1 = R2R3C4, R1 =
R2R3
R4
Pros
1 Balance equation independent
of frequency.
2 Scale of resistance can be
calibrate to read inductance
directly.
3 Scale of R4 can be calibrate to
read Q value directly.
Cons
1 Variable Capacitor is very
expensive.
2 Limited to measurement of low
Q coils (1 Q 10).
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33. Hay’s bridge

34. Hay’s Bridge
Balance Equation
L1 = C4R2R3
1+ω2C2
4 R2
4
R1 =
ω2R2R3R4C2
4
1+ω2C2
4 R2
4
Pros
1 Suitable for High Q coils.
2 Q = 1
ωC4R4
expression is simple
and require low value of R4 and
C4.
Cons
Hays bridge is not suitable for
measurement of quality factor
(Q 10).
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35. Anderson Bridge

36. Anderson Bridge
Balance Equation
R1 = R2R3
R4
− r1
L1 = C R3
R4
[r(R4 + R2) + R2R4]
Pros
1 Fixed capacitor is used
2 Accurate determination of
inductance (millimetre range).
3 Accurate result for
determination of capacitance
in terms of inductance.
4 Easy to balance (convergence
point of view -low Q values)
Cons
1 Complicated in terms of the
number of components,
balance equation used.
2 The bridge cannot be easily
shielded.
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37. Owen’s Bridge

38. Owen’s Bridge
Balance Equation
L1 = C4R2R3, R1 = C4
R3
C2
Q = ωC2R2
Pros
1 Balance equation independent
of frequency.
2 Balance equation independent if
R2 and C2 are made variable.
Cons
1 Variable Capacitor is very
expensive.
2 C2 tends to be high while
measuring high Q coils.
Applications
Used in measurement of wide range
of inductances, incremental
inductance and permeability with a
slight modification.
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39. Measurement of Capacitance

40. Schering’s Bridge

41. Schering’s Bridge
Balance Equation
R1 = R3C4
C2
, C1 = R4C2
R3
D = ωR4C4
Pros
1 Balance eq. is independent of
frequency.
Cons
Calibration for dissipation holds only
for one particular frequency.
Applications
Widely used for capacitance, relative
permittivity and D factor
measurement.
It is used for measuring the
insulating properties of electrical
cables and equipment’s.
It can measure small capacitors at
low voltages precisely
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42. Wein’s Bridge
Measurement of Frequency

43. Wein’s Bridge
Frequency Range- 100 Hz
to 100 kHz
Accuracy- 0.1 % to 0.5 %
Balance Equation
R4
R3
= R2
R1
+ C1
C2
f = 1
2π
√
R1R2C1C2
Pros
Can be calibrated by a single control if
R1 = R2 and C1 = C2.
Cons
Difficult to balance if input is not
sinusoidal and contain harmonics.
Applications
Measuring the frequency in audio
range.
Audio and HF oscillators as the
frequency determining device.
Harmonic distortion analyser, as a
notch filter.
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44. Causes of Error in Bridge Measurement
Errors in Bridge Measurement
Stray Conduction effects due to imperfect insulation.
Mutual-Inductance effects, due to magnetic coupling between various
components of the bridge.
Stray-capacitance effects, due to electrostatic fields between
conductor at different potentials.
’Residual’ in components e.g. the existence of small amount of series
inductance or shunt capacitance in nominally non-reactive resistors.
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45. Wagner’s Earthing Device

46. Wagner’s earthing device
To remove earth capacitance from bridge network.
Cab,Cbc,Ccd and Cad - Stray Capacitances
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47. Wagner’s earthing device
Some of disadvantages of
Wagner Earthing devices can be
overcome by using double ratio
A.C. bridge (additional
inductively coupled arms).
First adjust the bridge to get
minimum detection current
by connecting detector at d
point.
Connect the detector at
ground potential and Start
balancing by adjusting Z5 or
Z6. Bring Vb to ground
position (0 V).
Then connect the arms at d
point again and start
balancing to bring detector
at zero current. Repeat the
process again.
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48. Any Questions ?