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Series Combination of Cells

A galvanomete...

Question

A galvanometer has resistance G ohms and range v volt. The value of resistance used in series to convert into a voltmeter of range nV is :

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Solution

Given : $V_{i} = V$ $V_{f} = n V$ $R_{g} = G$
Using $V_{i} = I_{g} R_{g}$
$∴$ $V = I_{g} G$ ...........(1)
Using $V_{f} = I_{g} (R_{g} + R)$
$∴$ $n V = I_{g} (G + R)$ ........(2)
Dividing (2) by (1) we get $n = \frac{G + R}{G}$ $⟹ R = (n - 1) G$

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