Physics

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 $$2.75\ A, 22.4\ V.$$


SOLUTION
Let the voltmeter reading when, the voltage is $$0$$ be $$V$$.
$$\dfrac{l_1R}{l_2R} = \dfrac{V_1}{V_2}$$

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

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

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

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

$$\Rightarrow V = 0.4V$$
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