When a resistance of 200Ω is connected in series with a galvanometer of resistance ' G ', its range is ' V '. To triple its range, a resistance of 2000Ω is connected in series. The

Question

When a resistance of 200Ω is connected in series with a galvanometer of resistance ' G ', its range is ' V '. To triple its range, a resistance of 2000Ω is connected in series. The value of ' G ' is

TestHub · Accepted Answer

The voltage range of a voltmeter is given by $V = I_{g} (G + R)$ , where $I_{g}$ is the full scale deflection current.

For the first case:

$V = I_{g} (G + 200)$

For the second case, the range is tripled:

$3 V = I_{g} (G + 2000)$

Dividing the second equation by the first equation:

$\frac{3 V}{V} = \frac{I _{g} ( G + 2000 )}{I _{g} ( G + 200 )}$

$3 = \frac{G + 2000}{G + 200}$

$3 (G + 200) = G + 2000$

$3 G + 600 = G + 2000$

$2 G = 1400$

$G = 700Ω$

Answer: $700Ω$

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