Q140 / 180 · JIPMER 2017 · Physics

Two condensers, one of capacity $C$ and the other of capacity $\frac{C}{2}$, are connected to a $V$-volt battery, as shown. Figure The work done in charging fully both the condensers is

  • A
    $C V^2$
  • B
    $\frac{1}{4} C V^2$
  • Correct answer
    C
    $\frac{3}{4} C V^2$
  • D
    $\frac{1}{2} C V^2$

Solution

The two condensers in the circuit are in parallel order, hence $C^{\prime}=C+\frac{C}{2}=\frac{3 C}{2}$ The work done in charging the equivalent capacitor is stored in the form of potential energy. Hence, $W=U=\frac{1}{2} C^{\prime} V^2=\frac{1}{2}\left(\frac{3 C}{2}\right) V^2=\frac{3}{4} C V^2$

Hence, the correct answer is option: 'C'.

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