Vidyavardhini’s College of Engineering & Technology,

vasai-Road

Branch: Instrumentation Engineering

Subject: Electrical Networks and Measurement

Chapter 6: Measurement of R, L, C

(Revised 2019)

1

Syllabus

• Measurement of medium, low and high resistance,

• Megger,

• AC bridges,

• measurement of self and mutual inductances (Maxwell and Hay Bridges),

• Measurement of capacitance (Schering Bridge),

• Derivations & numerical related to all bridges.

2

Classification Of Resistance

• High resistance: under this category resistance is greater than 0.1 M ohm/100 K ohm.

• Medium resistance: under this category resistance is ranging from 1 ohm to 0.1M ohm/100 K ohm.

• Low resistance: under this category resistance value is lower than 1 ohm.

3

Method of Measurement of Low Resistance

• Voltmeter and Ammeter Method

• Ohmmeter

• Kelvin Bridge Method

• Kelvin’s Double Bridge Method

4

Voltmeter and Ammeter Method

• There are two methods of connecting voltmeter and ammeter for measurement of resistance as shown in figure.

• In both cases measured value of unknown resistance is equal to the reading of voltmeter divided by reading of ammeter.

5

0

ammeter resistance

measured value of resistance

when

If the value of resistance is large compared to ammeter resistan

R a

X X X a

a

X X a

m

X

m

m X a

X m a

X m a

V V V

V I R I R

where

R

I R RVR

I I

where

R

R R R

R R R

R R R

ce ( )

then the effect of ammeter resistance becomes negligible.

Hence the circuit is used to measure the resistance in medium range and is not suitable

for the low resisatnce measurement.

X aR R

6

1

1

voltmeter resistance

measured value of resistance

when

If the valu

t X V

t

X V

V

m

X V

m

X Vm

X V

X VX V

m

VX V

m

V m mX

mm V

V

X m

V

I I I

V VI

R R

where

R

V VR

V VI

R R

where

R

R RR

R R

R RR R

R

RR R

R

R R RR

RR R

R

R R

R

e of resistance to be measured is very small ascompared to voltmeter resistance ( )

then the effect of becomes negligible.

Hence the circuit is used to measure the resistance in low range.

X V

m

V

R R

R

R

7

Ohmmeter

• The purpose of an ohmmeter, is to measure the resistance placed

between its leads. This resistance reading is indicated through a mechanical meter movement which operates on electric current.

• Types of ohmmeter

Shunt type ohmmeter

Series type ohmmeter

8

SERIES TYPE OHMMETER

1. In this Figure,

R1 is the current limiting resistor, R2 is the zero adjust resistor,RX is the unknown resistor,E is the internal battery voltage and Rm is the internal resistance of the d’Arsonval movement.

A and B are the output terminals of the ohmmeter acrosswhich an unknown resistor is connected. 9

2. When RX = 0 (short circuit), R2 is adjusted to get full-scale current through the movement. Then, I = Ifsd. The pointer will be deflected to its maximum position on the scale. Therefore, this full-scale current reading is marked 0 ohms.

3. When RX = ∞ (open circuit), I = 0. The pointer will read zero. Therefore, the zero current reading is marked ∞ ohms.

10

1. Figure shows the basic circuit of the shunt-type ohmmeter where

movement mechanism is connected parallel to the unknown resistance. In this circuit it is necessary to use a switch, otherwise current will always flow in the movement mechanism.

2. Resistor ‘Rsh’ is used to bypass excess current.

Shunt type ohmmeter

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3. Let the switch be closed. When RX = 0 (short circuit), the pointer reads zero because full current flows through Rx and no current flows through the meter and Rsh. Therefore, zero current reading is marked 0 ohms.

4. When RX = ∞ (open circuit), no current flows through RX. Resistor R1 is adjusted so that full-scale current flows through the meter. Therefore, maximum current reading is marked ∞ ohms.

12

The Wheatstone bridge consists of two parallel resistance branches with

each branch containing two series resistor elements.

A DC voltage source is connected across the resistance network to

provide a source of current through the resistance network.

A null detector is the galvanometer which is connected between the

parallel branches to detect the balance condition.

The Wheatstone Bridge

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Operation

(i) We want to know the value of R4, vary one of the remaining resistor until the current through the null detector decreases to zero.

(ii) the bridge is in balance condition, the voltage across resistor R3 is equal to the voltage drop across R4.

1 3

1 2

2 4

3 4

1 1 2 4

1 4

1 2 3 4

1 3 4 4

As current through galvanometer is zero,

For zero current through galvanometer

the points B and D must be at the same

potential.

i.e.

( ) (

EI I

R R

and

EI I

R R

I R I R

E ER R

R R R R

R R R R1 2

1 3 1 4 4 1 4 2

14 3

2

)R R

R R R R R R R R

RR R

R

14

Kelvin Bridge

The Kelvin Bridge is the modified version of the Wheatstone Bridge.

The modification is done to eliminate the effect of contact and lead

resistance when measuring unknown low resistance.

15

16

17

Kelvin’s Double Bridge

18

19

20

21

22

Methods for Measurement of High Resistances

1) Direct deflection method

2) Loss of charge method

3) Megohm bridge

4) Megger

23

• The figure shows the measurement of high resistance using direct deflection method. For measurement of high resistance such as insulation resistance of cables, a sensitive galvanometer of d’Arsonval type is used in place of the microammeter.

Direct deflection method

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• The galvanometer G shows the current between the conductor and the metallic sheath. The leakage current is carried by the guard wire wound on the insulation and therefore does not flow through the galvanometer as shown in figure.

• The insulation resistance of the cable is given by,

R

VR

I

25

• A very high value resistance to be measured is shunted by a known value capacitor.

• The voltage across parallel combination is measured using electrostatic voltmeter.

• Initially switch is kept open. When the switch is closed, capacitor starts charging. The voltage across capacitor is given by

Loss of Charge Method

V v 1t

RC

Ce

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• When switch is opened.

• Then capacitor starts discharging through R.

• Then voltage is given by

V ve

V e

v

Simplifying,

0.4343 tR = =

v v ln log

V V

t

RC

C

t

RCC

C C

t

C C

27

28

Megger

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• MEGGER is used for measuring resistance of conductor insulation.

• The megger is a portable instrument consisting of two primary elements

• 1) a hand-driven DC generator, G, which supplies the necessary voltage for making the measurement, and

• 2) The instrument portion, which indicates the value of the resistance being measured.

• When the generator is not operated, the pointer floats freely and may come to rest at any position on the scale.

• If the test leads are open-circuited, the pointer moves to infinity, which indicates a resistance too large to measure.

• When a resistance such as Rx is connected between the test leads, the pointer indicates the value of resistance Rx.

• The instrument is not injured under the circumstances because the current is limited by R3.

Bridges

• To measure parameters R, L, C, f, Q (Quality factor of a coil) and ‘D’ (Dissipation factor of a capacitor) of electronic circuits, bridge circuits are employed.

• DC bridges can measure resistance R accurately

over wide ranges.

• AC bridges can be used to determine the unknown values of inductor L and capacitor C and even R and frequency f also.

30

Types of Bridges

DC Bridges

1. Wheatstone and

2. Kelvin

AC Bridges

1. Maxwell

2. Anderson

3. Schering

4. Wien bridge

Balancing of AC bridges is more difficult than DC bridgesbecause both magnitude and phase angle conditions haveto be satisfied for balance. The detector must respond to

imbalance AC current. Headphones are used as new detectors. No sound signal is heard if the bridge is in balance.

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• Therefore, for the balance of AC bridges,

1. The products of magnitudes of the opposite arms must be equal.

2. The sum of the phase angles of the opposite arms must be equal.

32

MAXWELL BRIDGE

This bridge is used to determine the value of an unknown inductance L in terms of the known capacitance. The bridge circuit is shown in figure

33

ADVANTAGES:1) The balance equation is independent of frequency of measurement.2) The balance equation is independent of losses associated with inductances.3) The scale of resistance can be calibrated to read the inductance.4) The scale of R1 can be calibrated to read the Q value directly.

DISADVANTAGES:1)It cannot be used for measurement of high Q values, it is limited to measure low Q value (1<Q<10)2) It cannot be used for measurement of very low Q values, less than one, because of balance converge problem.

(Derivation Remain)

34

HAY BRIDGE(opposite angle bridge)

This bridge circuit is developed to overcome the limitations of the Maxwell bridge. R1 is in series with a standard capacitor C1 unlike the Maxwell bridge, where it is in parallel. This bridge circuit can be used for high Q coils with a Q factor > 10.

35

• The Hay bridge is known as an opposite angle bridge since C and L elements are involved, one is a leading angle element and the other a lagging angle element.

36

ADVANTAGES:1) It is best suitable for the measurement of inductance with high Q, typically greater than 10.2) It gives very simple expression for Q factor in terms of elements in the bridge.3) It requires very low value resister R1 to measure high Q inductance.DISADVANTAGES:1) It is only suitable for measurement of high Q inductance. Consider expression for unknown inductance.(Derivation Remain)

37

SCHERING BRIDGE

The Schering bridge is used extensively for the measurement of capacitance, particularly for insulators with a phase angle of nearly 90°. In the standard arm of the bridge, a high-quality mica capacitor for general measurements and an air capacitor for insulator measurements are used. The circuit is shown in figure

38

(Derivation Remain)