Q139 / 150 · MHT CET 2018 · Physics

A series combination of $N_{1}$ is charged to a potential difference $3 V$ . Another parallel combination of $N_{2}$ (each of capacity $C_{2}$ is charged to a potential difference $V$ . The total energy stored in both the combination is the same. The value of $C_{1}$ in terms of $C_{2}$ is

Solution

C_{e q} = \frac{C_{1}}{N_{1}}

E = \frac{1}{2} C V^{2}

= \frac{1}{2} \frac{C_{1}}{N_{1}} 9 V^{2}

= \frac{9}{2} \frac{C_{1}}{N_{1}} V^{2}

C_{e q} = N_{2} C_{2}

E = \frac{1}{2} C V^{2} = \frac{1}{2} C_{2} N_{2} V^{2}

\frac{9}{2} \frac{C_{1}}{N_{1}} V^{2} = \frac{C_{2} N_{2} V^{2}}{2}

C_{1} = C_{2} \frac{N_{2} N_{1}}{9}

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