Question

A series combination of $N_{1}$ each of capacity $C_{1}$ 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

• A. $\frac{C_{2} N_{1} N_{2}}{9}$
• B. $\frac{C_{2} N_{1}^{2} N_{2}^{2}}{9}$
• C. $\frac{C_{2} N_{1}}{9 N_{2}}$
• D. $\frac{C_{2} N_{2}}{9 N_{1}}$

Answer 1

Answer: (A)

$C_{e q} = \frac{C_{1}}{N_{1}}$
$E = \frac{1}{2} C V^{2}$
$= \frac{1}{2} \frac{C_{1}}{N_{1}} 9 V^{2}$
$= \frac{9}{2} \frac{C_{1}}{N_{1}} V^{2}$
$C_{e q} = N_{2} C_{2}$
$E = \frac{1}{2} C V^{2} = \frac{1}{2} C_{2} N_{2} V^{2}$
$\frac{9}{2} \frac{C_{1}}{N_{1}} \, \, V^{2} = \frac{C_{2} N_{2} V^{2}}{2}$
$C_{1} = C_{2} \frac{N_{2} N_{1}}{9}$