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 magnitude of zero error in the voltmeter reading be V.
We need to subtract the zero error from the readings obtained under the two given conditions to obtain the true value of potential difference.
Under both the conditions ,the resistance of the wire will not change.
\[\Rightarrow R_1 = R_2 \]
\[ \Rightarrow \frac{V_1}{I_1} = \frac{V_2}{I_2}\]
\[\frac{I_1 R}{I_2 R} = \frac{V_1}{V_2}\]
\[ \Rightarrow \frac{1 . 75}{2 . 75} = \frac{14 . 4 - V}{22 . 4 - V}\]
\[ \Rightarrow \frac{0 . 35}{0 . 55} = \frac{14 . 4 - V}{22 . 4 - V}\]
\[ \Rightarrow \frac{7}{11} = \frac{14 . 4 - V}{22 . 4 - V}\]
\[ \Rightarrow 7 \times \left( 22 . 4 - V \right) = 11\left( 14 . 4 - V \right)\]
\[ \Rightarrow 156 . 8 - 7V = 158 . 4 - 11V\]
\[ \Rightarrow \left( 7 - 11 \right)V = 156 . 8 - 158 . 4\]
\[ \Rightarrow - 4V = - 1 . 6\]
\[ \Rightarrow V = 0 . 4 V\]
Magnitude of zero error, V = 0.4 V, which can either be positive or negative. Positive or negative zero error just indicates that the needle of the voltmeter is to the right or left of the zero marked on the device if zero voltage is applied across the voltmeter.
