Resistance Measurement Methods

(1) Voltmeter-Ammeter (2) Substitution

(3) Ohmmeter (4) Bridge

Voltmeter-Ammeter Method

(1) Simple and requires only two meters

(2) Subject to error

Ohmmeter Method

(1) Only one meter(2) Non-linear scale

Using Bridge Circuit

4

• 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

5

Wheatstone Bridge

Ratio arms (R1 , R2) & Standard arm (R3 )

6

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 kΩR3 Min. step 1 Ω, Max value 11110 Ω

Example

7

Measurement Errors

Thermal EMF

8

Creates error in measurement of low resistance

9

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

10

11

12

13

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

14

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

Answers to Assignment-2

1) 2.48 Ω2) 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

Rn R

n n