A series combination of n_1 capacitors, each of value C1, is charged by a source of potential difference 4 V. When another parallel combination of n2 capacitors, each of value C2. 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 C2, in terms of C1, is then ?

A series combination of n_1 capacitors, each of value C1, is charged by a source of potential difference 4 V. When another parallel combination of n2 capacitors,  each of value C2. 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 C2, in terms of C1, is then ?

(a) \( \frac{2C_1 n_1}{n_2} \)

(b) \( \frac{16 n_2}{n_1} C_1 \)

(c) \( \frac{2 n_2}{n_1} C_1 \)

(d) \( \frac{16 C_1}{n_1 n_2} \)

Answer :  (d) \( \frac{16 C_1}{n_1 n_2} \)

\( U_1 = U_2 \)

\( \frac{1}{2} \cdot \frac{c_1}{n_1} \cdot (4v)^2 = \frac{1}{2} \cdot n_2 c_2 v^2 \)

\( \frac{c_1 \cdot 16}{n_1 n_2} = c_2 \)