Resistance Measurement instruments

Classification of Resistance Measurements

• Low resistances (0-1) Ω

• Medium resistances (1-0.1M)Ω

• High resistances (≥ 0.1MΩ)

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Medium Resistance Measurement Methods

(1) Voltmeter-Ammeter (2) Substitution(3) Ohmmeter (4) Bridge

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Voltmeter-Ammeter Method

As we know that the internal resistances of the voltmeter and ammeter are large and small, respectively.

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

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.

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

Using Bridge Circuit

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• 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

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Wheatstone Bridge

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

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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

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Measurement Errors

Thermal EMF

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Creates error in measurement of low resistance

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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

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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

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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

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