In the experiment of calibration of voltmeter, a standard cell of e.m.f. $1.1$ volt is balanced against $440…

In the experiment of calibration of voltmeter, a standard cell of e.m.f. $1.1$ volt is balanced against $440 \mathrm{~cm}$ of potential wire. The potential difference across the ends of resistance is found to balance against $220 \mathrm{~cm}$ of the wire. The corresponding reading of voltmeter is $0.5$ volt. The error in the reading of volmeter will be:
  1. $-0.15$ volt
  2. $0.15$ volt
  3. $0.5$ volt
  4. $-0.05$ volt

Solution

In a voltmeter $ \begin{gathered} \mathrm{V} \propto l \\ \mathrm{~V}=\mathrm{k} l \end{gathered} $ Now, it is given $\mathrm{E}=1.1$ volt for $l_1=440 \mathrm{~cm}$ and $\mathrm{V}=0.5$ volt for $l_2=220 \mathrm{~cm}$ Let the error in reading of voltmeter be $\Delta \mathrm{V}$ then, $ \begin{aligned} &1.1=400 \mathrm{~K} \text { and }(0.5-\Delta \mathrm{V})=220 \mathrm{~K} . \\ &\Rightarrow \frac{1.1}{440}=\frac{0.5-\Delta \mathrm{V}}{220} \\ &\therefore \Delta \mathrm{V}=-0.05 \text { volt } \end{aligned} $

Asked in: JEE Main 2014 (12 Apr Online)

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