A) \[\frac{3}{4}C{{V}^{2}}\]
B) \[\frac{1}{4}C{{V}^{2}}\]
C) \[2\,C{{V}^{2}}\]
D) \[\frac{1}{2}\,C{{V}^{2}}\]
Correct Answer: A
Solution :
Here capacitors are connected in parallel so potential difference across both capacitors will remain same \[\therefore \,\,\,\,{{Q}_{1}}=CV\,\,and\,\,{{Q}_{2}}\,\,=\,\,\frac{C}{2}\ V\] also \[\operatorname{Q}={{Q}_{1}}+{{Q}_{2}}=CV+\frac{C}{2}V=\frac{3}{2}CV\] Work done in charging capacitor is \[=\,\,\frac{1}{2}\,QV\] \[=\,\,\,\frac{1}{2}\times \left( \frac{3}{2}\,\,CV \right)\times V=\frac{3}{4}C{{V}^{2}}\]You need to login to perform this action.
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