Q. If potential difference across a capacitor is changed from 15 V to 30 V, work done is W. The work done when potential difference is changed from 30 V to 60 V, will be:

JIPMERJIPMER 2002Electrostatic Potential and Capacitance Report Error

A

W

6%

B

4 W

18%

C

3 W

3%

D

2 W

74%

Solution:

From relation of work done $ W=\frac{1}{2}C{{V}^{2}}, $ so $ W\propto {{V}^{2}} $ As $ {{V}_{2}}=60-30=30\,V, $ $ {{V}_{1}}=30-15=15\,V $ hence $ \frac{{{W}_{2}}}{{{W}_{1}}}={{\left( \frac{{{V}_{2}}}{V{{ & }_{1}}} \right)}^{2}} $ or $ {{W}_{2}}={{\left( \frac{30}{15} \right)}^{2}}W $ $ {{W}_{1}}=W $ $ {{W}_{2}}=4\,W $

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