The presentation describes resistance measurement through Voltmeter & Ammeter methods, DC bridges; Wheatstone bridge and Kelvin double bridge for low resistance.

1. Resistance Measurements & DC
bridges
Unit III: Voltmeter and ammeter methods, Wheatstone bridge, low
resistance measurements, low resistance measuring instruments
AC bridge theory, capacitance bridges, Inductance bridges, Q meter
4/4/2017 1
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad

2. Voltmeter and Ammeter Methods
• Resistance can be measured using Ammeter and Voltmeter and
applying Ohm’s Law,
• Even with accurate instruments. errors has to be taken into account.
4/4/2017 2
NEC 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 across
load then computer resistance R
=E/(I+IV)
• As actual value of R is E/I, presence of
voltmeter current IV introduces error
• Consequently calculated resistance is
less than actual.

3. Voltmeter and Ammeter Methods
When Voltmeter is connected across load, note ammeter reading,
then remove one terminal of voltmeter and again note ammeter
reading. If ammeter reading drops noticeably, then voltmeter current
is not much smaller than resistor current. In the case, voltmeter
should be connected across supply.
4/4/2017 3
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
• When Voltmeter is connected across
supply, then computer resistance
R =(E+EV)/I
• As actual value of R is E/I, presence of
voltage drop across voltmeter EA
introduces error.
• Consequently calculated resistance is
higher than actual.
RSupply
Voltage V
A
V
EA
I
E
Voltmeter connected across supply
+ -

4. 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. Supply
voltage is 10 V, Ammeter impedance is 10 , Voltmeter impedance is
1 M. Voltmeter and ammeter are assumed to be highly accurate,
precise and of high resolution.
What will be calculated resistance & % error in measurement for
setup (a) & (b) if Load resistance is (i) 10  (ii) 100  (iii) 1 K (iv) 10
K (v) 100 K (vi) 1 M (vii) 10 M
4/4/2017 4
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
In the problem, value of load resistance is given for which observed
value from setup (calculated resistance) and % error has to be
obtained.
The load resistance, voltmeter resistance and ammeter resistance can
be used to compute voltmeter and ammeter reading.

5. Voltmeter and Ammeter Methods
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NEC 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
R
V
RA
EA
+ -
 
V
V
V
V
V
V
RR
RR
II
E
E
RR
RRE
II







.
eResistancCalculated
ReadingVoltmeter
.
.
readingAmmeter
A
A
A
A
RR
I
EE
R
RR
EEE
R
E
I








 


eResistancCalculated
.ReadingVoltmeter
readingAmmeter

6. Voltmeter and Ammeter Methods
4/4/2017 6
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
Load
Resistance
value R
(a) Voltmeter is connected across load (b)Voltmeter is connected across supply
Calculated Resistance
R।।Rv
% error in
measurement
Calculated Resistance
R + 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 resistance
measurements
connecting voltmeter across the supply is suitable for high value resistance
measurements

7. 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 equal
Under balanced condition
4/4/2017 7
NEC 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
I2
S
R
Q
P
SIQIVV
RIPIVV
SQ
RP



eq.,twotheDividing
i.eand
i.e,
21
21
Q
P
SR or
Range of accurate measurement by Wheatstone bridge
is 5  -1012 

8. +
Wheatstone Bridge : Thevnin
Equivalent
4/4/2017 8
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
V
S
G
+ VR -
R
QP
r
+ VP -
+ VS -
+ VQ -
V
S
+ VR -
R
QP
+ VP -
+ VS -
+ VQ -
SR
QPG
-
Wheat stone bridge Circuit for VTH across galvanometer
Circuit for RTH across
galvanometer
G r
Thevnin equivalent
across galvanometer
SRQPRTh SQTh VVV 
SQ VV 
SRQP 

9. Wheatstone Bridge
Q. A wheat stone bridge has P=3.5 K, Q= 7 K and S=4 K at
balanced condition. Supply V= 10 V. The galvanometer has a current
sensitivity of 1 A/mm and internal resistance of 2.5 K . Calculate
the change in unknown resistance which can be detected by the
bridge.
4/4/2017 9
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
V
SR
R
VV
VArRIVVV
xx
SRQPR
AI
R
gThgSQTh
Th
g
33333.3
6
2
.10
m17.5K)5.267.3(1)(
K67.3K
42
42
75.3
75.3
1currentergalvanometdetectableMin.
k2k
7
5.3
.4
Q
P
SR














10. Wheatstone Bridge
4/4/2017 10
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad










65.400465.0Thus
0047.2
665375.1
3385.3
A665375.1m
4
3385.310)(
V3385.300517.033333.3
Thusbydecreaseshall&increaseShall
,ergalvanometroughcurrent thdetectablemin.ofcaseIn
'
''
KR
KK
I
VV
RR
mA
S
VVV
II
VV
VVV
R
RR
RR
SR
RR
THRR

11. 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 11
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
potential terminals
Current terminals

12. 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 12
NEC 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

13. Low Resistance Measurements:
Kelvin double bridge
4/4/2017 13
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
 
Q
P
SRPABAif
BII
AII
Q
PR
BII
I
Q
SBISIQIBIVV
AII
I
P
RAIRIPIAIVV
SQ
RP


















 

then
QBQP
Q
P
S
get,weeq.twotheDividing
Q
,and
P
conditionbalancedunder
31
31
31
2
3213
31
2
3213

14. Low Resistance Linear Ohmmeter
A constant current source is connected to the unknown resistance. The
voltage drop across resistance is amplified and measured through a
voltmeter. After calibration it giver resistance on a linear scale
4/4/2017 14
NEC 403 Unit I by Dr Naim R Kidwai,
Professor & Dean, JIT Jahangirabad
VRI Amplifier