The current in a conductor and the potential difference across it… - Vidyadip

Question

The current in a conductor and the potential difference across its ends are measured by an ammeter and a voltmeter. The meters draw negligible currents. The ammeter is accurate but the voltmeter has a zero error (that is, it does not read zero when no potential difference is applied). Calculate the zero error if the readings for two different conditions are 1.75A, 14.4V and 2.75A, 22.4V.

✓

Answer

Let the voltmeter reading when, the voltage is 0 be X.
$\frac{\text{l}_1\text{R}}{\text{l}_2\text{R}}=\frac{\text{V}_1}{\text{V}_2}$
$\Rightarrow\frac{1.75}{2.75}=\frac{14.4-\text{V}}{22.4-\text{V}}$
$\Rightarrow\frac{0.35}{0.55}=\frac{14.4-\text{V}}{22.4-\text{V}}$
$\Rightarrow\frac{0.07}{0.11}=\frac{14.4-\text{V}}{22.4-\text{V}}$
$\Rightarrow\frac{7}{11}=\frac{14.4-\text{V}}{22.4-\text{V}}$
$\Rightarrow7(22.4-\text{V})=11(14.4-\text{V})$
$\Rightarrow156.8-7\text{V}=158.4-11\text{V}$
$\Rightarrow(7-11)\text{V}=156.8-158.4\Rightarrow-4\text{V}=-1.6$
$\Rightarrow\text{V}=0.4\text{V}.$

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