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Physics-

General

Easy

Question

Two condensers, one of capacity $C$ and the other of capacity $fraction numerator C over denominator 2 end fraction$ , are connected to a $V$ volt battery , as shown. The work done in charging fully both the condensers is

$2 C V^{2}$
$\frac{1}{4} C V^{2}$
$\frac{3}{4} C V^{2}$
$\frac{1}{2} C V^{2}$

The correct answer is: $fraction numerator 1 over denominator 2 end fraction C V to the power of 2 end exponent$

The two capacitor the circuit are in parallel order, hence
$C to the power of ´ end exponent equals C plus fraction numerator C over denominator 2 end fraction equals fraction numerator 3 C over denominator 2 end fraction$
The work done in charging the equivalent capacitor is stored in the form of potential energy.
Hence, $W equals U equals fraction numerator 1 over denominator 2 end fraction C to the power of ´ end exponent V to the power of 2 end exponent$
$equals fraction numerator 1 over denominator 2 end fraction open parentheses fraction numerator 3 C over denominator 2 end fraction close parentheses V to the power of 2 end exponent$
$equals fraction numerator 3 over denominator 4 end fraction C V to the power of 2 end exponent$

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