First slide

voltmeter

Question

A voltmeter has a range $0 - V$ with a series resistance R. With a series resistance 2R, the range is $0 - V' .$ The correct relation between V and V' is

Moderate

A

$V^{'} = 2 V$
B

$V^{'} > 2 V$
C

$V^{'} > > 2 V$
D

$V^{'} < 2 V$

Solution

For conversion of galvanometer (of resistances) into voltmeter, a resistance is connected in series.
$\begin{array}{l} ∴ i_{g} = \frac{V}{R + G} and i_{g} = \frac{V^{'}}{2 R + G} \\ \Rightarrow \frac{V}{R + G} = \frac{V^{'}}{2 R + G} \\ \Rightarrow \frac{V^{'}}{V} = \frac{2 R + G}{R + G} = \frac{2 (R + G) - G}{(R + G)} \\ = 2 - \frac{G}{(R + G)} \Rightarrow V^{'} = 2 V - \frac{VG}{(R + G)} \Rightarrow V^{'} < 2 V \end{array}$

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