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 $1.75 A, 14.4 V$ and $2.75 A, 22.4 V .$

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Solution

Let the voltmeter reading when, the voltage is $0$ be $V$ .
$\frac{l_{1} R}{l_{2} R} = \frac{V_{1}}{V_{2}}$

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

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

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

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

$\Rightarrow V = 0.4 V$

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Let the voltmeter reading when, the voltage is 0 be V.l1Rl2R=V1V2⇒1.752.75=14.4−V22.4−V⇒0.350.55=14.4−V22.4−V⇒0.070.11=14.4−V22.4−V⇒711=14.4−V22.4−V⇒7(22.4−V)=11(14.4−V)⇒156.8−7V=158.4−11V⇒(7−11)V=156.8−158.4⇒−4V=−1.6⇒V=0.4V