Resistance Measurements & DC bridges

Unit III: Voltmeter and ammeter methods, Wheatstone bridge, lowresistance measurements, low resistance measuring instrumentsAC bridge theory, capacitance bridges, Inductance bridges, Q meter

4/4/2017 1NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

Voltmeter and Ammeter Methods

• Resistance can be measured using Ammeter and Voltmeter andapplying Ohm’s Law,

• Even with accurate instruments. errors has to be taken into account.

4/4/2017 2NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

RSupply Voltage V

A

V

IV

I+IV

I

E

Voltmeter connected across load

• When Voltmeter is connected acrossload then computer resistance R=E/(I+IV)

• As actual value of R is E/I, presence ofvoltmeter current IV introduces error

• Consequently calculated resistance isless than actual.

Voltmeter and Ammeter Methods

When Voltmeter is connected across load, note ammeter reading,then remove one terminal of voltmeter and again note ammeterreading. If ammeter reading drops noticeably, then voltmeter currentis not much smaller than resistor current. In the case, voltmetershould be connected across supply.

4/4/2017 3NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

• When Voltmeter is connected acrosssupply, then computer resistanceR =(E+EV)/I

• As actual value of R is E/I, presence ofvoltage drop across voltmeter EA

introduces error.

• Consequently calculated resistance ishigher than actual.

RSupply Voltage V

A

V

EA

I

E

Voltmeter connected across supply

+ -

Voltmeter and Ammeter Methods

Q. In order to measure resistance using voltmeter and ammeter,Voltmeter is placed (a) across the load (b) across the supply. Supplyvoltage is 10 V, Ammeter impedance is 10 , Voltmeter impedance is1 M. Voltmeter and ammeter are assumed to be highly accurate,precise and of high resolution.What will be calculated resistance & % error in measurement forsetup (a) & (b) if Load resistance is (i) 10 (ii) 100 (iii) 1 K (iv) 10K (v) 100 K (vi) 1 M (vii) 10 M

4/4/2017 4NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

In the problem, value of load resistance is given for which observedvalue from setup (calculated resistance) and % error has to beobtained.

The load resistance, voltmeter resistance and ammeter resistance canbe used to compute voltmeter and ammeter reading.

Voltmeter and Ammeter Methods

4/4/2017 5NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

RV IV

I+IV I

E

(a) Voltmeter connected across load

RV

RA

RV IV

I

E

(b)Voltmeter connected across supply

RV

RA

EA

+ -

V

V

V

V

VV

RR

RR

II

E

E

RR

RREII

.e ResistancCalculated

ReadingVoltmeter

.

.readingAmmeter

AA

AA

RRI

EE

R

RREEE

R

EI

e ResistancCalculated

.ReadingVoltmeter

readingAmmeter

Voltmeter and Ammeter Methods

4/4/2017 6NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

LoadResistance

value R

(a) Voltmeter is connected across load (b)Voltmeter is connected across supply

Calculated ResistanceR।।Rv

% error in measurement

Calculated ResistanceR + Ra

% error in measurement

10 9.9999 -0.001 20 100

100 99.99 -0.01 110 10

1 K 0.999001 K -0.0999 1.01K 1

10 K 9.90099 K -0.9901 10.01 K 0.1

100 K 90.90909 K -9.0909 100.01 K 0.01

1 M 0.5 M -50 1.00001 M 0.001

10 M 0.9090909 M -90.9091 10.00001 M 0.0001

It can be noted that

connecting voltmeter across the load is suitable for low value resistancemeasurements

connecting voltmeter across the supply is suitable for high value resistancemeasurements

Wheatstone Bridge• Accurate resistance measurement is done using Wheatstone bridge.• When galvanometer deflects, the bridge is said to be unbalanced.• Under balanced condition, null deflection is achieved.• null deflection occurs when, potential across its terminals are equalUnder balanced condition

4/4/2017 7NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

R

V

Q

S

P

G

Precision resistor

Precision resistor

Unknown resistor

Adjustable Precision resistor

I1

I2S

R

Q

P

SIQIVV

RIPIVV

SQ

RP

eq., two theDividing

i.e and

i.e ,

21

21

Q

PSR or

Range of accurate measurement by Wheatstone bridge

is 5 -1012

+

Wheatstone Bridge : Thevnin Equivalent

4/4/2017 8NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

V

SG

+ VR -

R

QPr

+ VP -

+ VS -

+ VQ -

V

S

+ VR -

R

QP

+ VP -

+ VS -

+ VQ -

SR

QPG-

Wheat stone bridge Circuit for VTH across galvanometerCircuit for RTH across

galvanometer

G r

Thevnin equivalent across galvanometer

SRQPRTh SQTh VVV

SQ VV

SRQP

Wheatstone BridgeQ. A wheat stone bridge has P=3.5 K, Q= 7 K and S=4 K atbalanced condition. Supply V= 10 V. The galvanometer has a currentsensitivity of 1 A/mm and internal resistance of 2.5 K . Calculatethe change in unknown resistance which can be detected by thebridge.

4/4/2017 9NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

VSR

RVV

VArRIVVV

xxSRQPR

AI

R

gThgSQTh

Th

g

33333.36

2.10

m 17.5 K)5.2 67.3( 1)(

K67.3 K42

4 2

75.3

7 5.3

1current er galvanomet detectable Min.

k 2k 7

5.3.4

Q

PSR

Wheatstone Bridge

4/4/2017 10NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

65.400465.0 Thus

0047.2665375.1

3385.3

A 665375.1 m 4

3385.310)(

V 3385.300517.033333.3

Thus by decrease shall & increase Shall

,er galvanomet roughcurrent th detectable min. of case In

'

''

KR

KKI

VVRR

mAS

VVVII

VV

VVV

R

RR

RRSR

RR

THRR

Low Resistance Measurements: Four terminal resistance

• Connecting leads introduce error for low resistance measurement

• Error occurs due to voltage drop at contact where heavy current flow.

To avoid errors introduced by contacts, in very low resistances. two sets

of contact) are provided; current terminal & Potential terminal.

• Current terminals are outermost and handle large currents.

• Potential terminals are situated in between current terminals and

those handle current in A or mA

• Resistance is defined as between voltage terminals so voltage drop at

current terminal do not introduce error.

4/4/2017 11NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

potential terminals

Current terminals

Low Resistance Measurements: Kelvin double bridge

• Modification of Wheatstone bridge For vey low resistance measurement

• It uses two additional resistances, to avoid effect of contact resistances

4/4/2017 12NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

V

I2

Q

S

P

G

Four terminal resistor

I1

+ VS -

R

A B

+ VR -

I3

I2-I3

Low Resistance Measurements: Kelvin double bridge

4/4/2017 13NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

Q

PSRPABAif

B II

A II

Q

PR

B III

QS BI SI QI BIVV

A II I

PR AI RI PI AIVV

SQ

RP

thenQB

QP

Q

P

S get, weeq. two theDividing

Q

, and

P

condition balancedunder

31

31

31

2

3213

31

2

3213

Low Resistance Linear OhmmeterA constant current source is connected to the unknown resistance. Thevoltage drop across resistance is amplified and measured through avoltmeter. After calibration it giver resistance on a linear scale

4/4/2017 14NEC 403 Unit I by Dr Naim R Kidwai, Professor & Dean, JIT Jahangirabad

VRI Amplifier