A voltmeter has a resistance ‘G’ and range ‘V’. What resistance should be connected in series with it to increase its range to ‘nV’ ?

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$(n - 1) G$

$(n + 1) G$

$\frac{G}{(n - 1)}$

$\frac{G}{(n + 1)}$

answer is A.

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Detailed Solution

When a voltmeter is connected in parallel with a circuit, it draws a small current from the circuit, which can affect the voltage being measured. To minimize this effect, a high resistance is used in the voltmeter. However, this also limits the range of the voltmeter. To increase the range of the voltmeter, a resistance is connected in series with it. Let R be the resistance to be connected in series with the voltmeter. Then, the total resistance of the circuit becomes G+R. Let I be the current flowing through the circuit and V be the voltage being measured. By Ohm's law, we have
$V = I R$
When the range of the voltmeter is V, it gives full-scale deflection for a voltage of V. Thus, the current through the voltmeter is

$I = \frac{V}{G}$

When the range of the voltmeter is increased to nv, the current flowing through the voltmeter is still the same, but the voltage being measured is nv. Therefore, we have

$\frac{n v}{G + R} = \frac{V}{G}$

$R = (n - 1) G$

Hence the correct answer is $(n - 1) G .$

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