The amount of work done is increasing the voltage across the plates of a capacitor from $5 V$ to $10 V$ is $W$ . The work done in increasing it from $10 V$ to $15 V$ will be :

0.6 W

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1 W

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1.25 W

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1.67 W

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Solution

The correct option is C $1.67 W$
As we know that work done
$= U_{f i n a l} - U_{i n i t i a l} = \frac{1}{2} C (V_{2}^{2} - V_{1}^{2})$
When potential difference increases from $5 V$ to $10 V$ then
$W = \frac{1}{2} C (10^{2} - 5^{2}) . . . (i)$
when potential difference increases from $10 V$ to $15 V$ , then
$W = \frac{1}{2} C (15^{2} - 10^{2}) . . . (i i)$
On solving Eq (i) and (ii) we get
$W^{'} = 1.67 W$

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