Q. 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) $\frac{16C_{1}}{n_{1}n_{2}}$
B) $\frac{2C_{1}}{n_{1}n_{2}}$
C) $16\frac{n_{2}}{n_{1}}C_{1}$
D) $2\frac{n_{2}}{n_{1}}C_{1}$
Explanation
(a) $\frac{1}{2}\left( \frac{C_{1}}{n_{1}} \right)(4V)^{2} = \frac{1}{2}\left( n_{2}C_{2} \right)V^{2} \Rightarrow C_{2} = \frac{16C_{1}}{n_{1}n_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.