This document discusses various methods for measuring medium resistances between 1-0.1M Ω. It describes four common methods: the voltmeter-ammeter method, substitution method, ohmmeter method, and bridge circuit method. The bridge circuit method operates on the principle of null comparison using a Wheatstone bridge configuration with ratio and standard arms. Sources of error in resistance measurements include thermal EMF and contact resistance. Worked examples are provided to calculate resistance values and measurement uncertainties.

1. Classification of Resistance
Measurements
• Low resistances (0-1) Ω
• Medium resistances (1-0.1M)Ω
• High resistances (≥ 0.1MΩ)
1

2. Medium Resistance Measurement
Methods
(1) Voltmeter-Ammeter (2) Substitution
(3) Ohmmeter (4) Bridge

3. 3
Voltmeter-Ammeter Method
As we know that the
internal resistances of the
voltmeter and ammeter
are large and small,
respectively.

4. 4

5. 5

6. Voltmeter-Ammeter Method
(1) Simple and requires only two meters
(2) Subject to error

7. Substitution Method
• Keep at position 1 and
vary the Rh up to finite
value of current flow
through the circuit.
• Shift to position 2 with the
same value of Rh in
previous case, change
the S value until the
same/previous current
flow through the circuit.
7

8. Ohmmeter Method
(1) Only one meter
(2) Non-linear scale

9. Using Bridge Circuit
9
• Bridge Circuit is a null method, operates on the
principle of comparison
• A known (standard) value is adjusted until it is equal to
the unknown value

10. 10
Wheatstone Bridge
Ratio arms (R1 , R2) & Standard arm (R3 )

11. 11
Wheatstone Bridge Apparatus
The Ratio Control switches the
ratio in decade steps
The remaining four step switches
set the resistance of the standard
arm
R1 , R2 10 Ω, 100 Ω, 1 kΩ 10 kΩ
R3 Min. step 1 Ω, Max value 11110 Ω
Example

12. 12

13. 13

14. 14
Measurement Errors

15. Thermal EMF
15
Creates error in measurement of low resistance

16. 16
Contact Resistance
On the micro scale, surface roughness
limits surface to surface contact
Measurement using four terminals
to avoid contact resistance
Standard resistance model with contact
resistance

17. 17

18. 18

19. 19

20. 20
Figure below show the schematic diagram of a Wheatstone
bridge with the bridge elements. The battery is 5 V and its
internal resistance negligible. The galvanometer has a
current sensitivity of 10 mm/ µA and an internal resistance
of 100 Ω. Calculate the deflection of the galvanometer
caused by the 5 Ω unbalance in arm BC.
Assignment
Ans: 33.2 mm

21. 21
The galvanometer in the previous question is replaced by
one with an internal resistance of 500 Ω and a current
sensitivity of 1 mm/µA. Assuming that the minimum
deflection that can be observed on this galvanometer is 1
mm, determine what is the minimum unbalance in the
resistance that can be detected in arm BC.
Assignment Continued

22. Answers to Assignment-2
1) 2.48 Ω
2) 1.06 %
3) (a) 99.9 Ω, 0.195 Ω, 0.195 %
(b) (i) 80 (ii) 98
(c) (i) 68 (ii) 95
4) (a) 38.3 % (b) 68.3 % (c) 95.5 % (d) 15.7 %
5) For series: For parallel:
6) (a) 8.7 Ω (b) 7.1 Ω (c) 5.6 Ω
Rnσ R
n n
σ