Question

A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference 4V. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of $C_2$, in terms of $C_1$, is then:

• A. $\frac{2C_1}{n_1{n}_2}$
• B. $16\frac{n_2}{n_1}{C}_1$
• C. $2\frac{n_2}{n_1}{C}_1$
• D. $\frac{16C_1}{n_1{n}_2}$

Answer 1

The correct option is D $\frac{16C_1}{n_1{n}_2}$


P.D. across each capacitor is $V_1=\frac{4V}{n_1}$
Energy stored across the combination is $U_1=n_1\times \frac{1}{2}{C}_1\frac{16V^2}{n_1^2}=\frac{16C_1{V}^2}{2n_1}$


Energy stored across parallel combination is $U_2=n_2\times \frac{1}{2}{C}_2{V}^2\frac{16C_1{V}^2}{2n_1}=\frac{n_2{C}_1{V}^2}{2}\Rightarrow C_2=\frac{16C_1}{n_1{n}_2}$