Question

A series combination of $N_1$ each of capacity $C_1$ is charged to a potential difference $3V$ . 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. $\frac{C_2{N}_1}{9N_2}$
• D. $\frac{C_2{N}_2}{9N_1}$

Answer 1

Answer: (A)

$C_{eq}=\frac{C_1}{N_1}$
$E=\frac{1}{2}C{V}^2$
$=\frac{1}{2}\frac{C_1}{N_1}9V^2$
$=\frac{9}{2}\frac{C_1}{N_1}{V}^2$
$C_{eq}=N_2{C}_2$
$E=\frac{1}{2}C{V}^2=\frac{1}{2}{C}_2{N}_2{V}^2$
$\frac{9}{2}\frac{C_1}{N_1}{V}^2=\frac{C_2{N}_2{V}^2}{2}$
$C_1=C_2\frac{N_2{N}_1}{9}$