The work done in charging fully both a condensers is
A) \[2C{{V}^{2}}\]
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 :
The two condensers in the 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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