| Two condensers, one of capacity C and the other of capacity \[\frac{C}{2},\] are connected to a V volt battery, as shown. |
 |
| The work done in charging fully both the condensers is: [AIPMT (S) 2007] |
A) \[2\,C{{V}^{2}}\]
B) \[\frac{1}{4}\,C{{V}^{2}}\]
C) \[\frac{3}{4}\,C{{V}^{2}}\]
D) \[\frac{1}{2}\,C{{V}^{2}}\]
Correct Answer: C
Solution :
| [c] The two condensers in die circuit are in parallel order, hence |
| \[C'=C+\frac{C}{2}=\frac{3C}{2}\] |
| The work done in charging the equivalent capacitor is stored in the form of potential energy. |
| Hence \[W=U=\frac{1}{2}C'\,{{V}^{2}}\] |
| \[=\frac{1}{2}\,\left( \frac{3C}{2} \right){{V}^{2}}\] |
| \[=\frac{3}{4}C{{V}^{2}}\] |
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