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 1

Let the voltmeter reading when, the voltage is $0$ be $V$.

$\frac{l_{1}R}{l_{2}R}=\frac{V_1}{V_2}$

$\Rightarrow \frac{1.75}{2.75}=\frac{14.4-V}{22.4-V}\Rightarrow \frac{0.35}{0.55}=\frac{14.4-V}{22.4-V}$

$\Rightarrow \frac{0.07}{0.11}=\frac{14.4-V}{22.4-V}\Rightarrow \frac{7}{11}=\frac{14.4-V}{22.4-V}$

$\Rightarrow 7(22.4-V)=11(14.4-V)\Rightarrow 156.8-7V=158.4-11V$

$\Rightarrow (7-11)V=156.8-158.4\Rightarrow -4V=-1.6$

$\Rightarrow V=0.4V$