Question

In measuring resistance by voltmeter-ammeter method, the voltmeter can be connected either across supply or across the resistance. If the resistance is low, the voltmeter should be connected
1. across the supply
2. across the resistance
3. either across the supply or across the resistance
4. neither across the supply nor across the resistance

Answer 1

Correct Answer - Option 2 : across the resistance

V–A Method:

In this method, the voltmeter is connected across the supply.

V = Voltmeter reading

A = Ammeter reading

V_L = Voltage across load R.

I_L = Current flowing through load R.

R = Unknown resistance to be measured

R_a = Internal resistance of the ammeter

V_a= voltage drop across ammeter.

V = V_L + V_a

\({R_{meas}} = \frac{V}{A} = \frac{V}{{{I_L}}} = \frac{{{V_L} + {V_a}}}{{{I_L}}}\)

but \({R_{true}} = \frac{{{V_L}}}{{{I_L}}} = R\)

R_meas = R_true + R_a

So, in this method measured value is greater than the true value. This error is due to an ammeter.

Error \( = \frac{{{R_{meas}} - {R_{true}}}}{{{R_{true}}}} = \frac{{{R_a}}}{R}\)

The error is high for very low values of unknown resistance R.

A–V Method:

In this method, the voltmeter is connected across the resistance.

V = Voltmeter reading

A = Ammeter reading

V_L = Voltage across load R.

R = Unknown resistance to be measured

I_L = Current flowing through load R.

I_V = Current flowing through the voltmeter.

\({R_{meas}} = \frac{{{V_L}}}{{\left( {{I_L} + {I_V}} \right)}} = \frac{V}{{\frac{V}{R} + \frac{V}{{{R_V}}}}} = \frac{{R{R_V}}}{{R + {R_V}}}\)

\({R_{true}} = \frac{{{V_L}}}{{{I_L}}} = R\)

The measured value is less than the true value. In this method, the error is due to the voltmeter.

Error \( = \frac{{{R_{meas}} - {R_{true}}}}{{{R_{true}}}} = - \frac{R}{{{R_V}}}\)

The error is low for very low values of unknown resistance R.

Observations:

• In both methods errors due to load side instruments.
• V – A method is best suitable for high resistances in the medium range.
• A – V method is best suitable for low resistances in the medium range.