Q. A cylindrical capacitor has charge $Q$ and length $L.$ If both the charge and length of the capacitor are doubled, by keeping other parameters fixed, the energy stored in the capacitor
A) Remains same
B) Increases two times
C) Decreases two times
D) Increases four times
Explanation
(b) Capacitance of a cylindrical capacitor $= \frac{2\pi\varepsilon_{0}L}{ln\ (b/a)}$
Energy stored in the capacitor
$\frac{1}{2}\frac{Q^{2}}{C} = \frac{1}{2}\frac{Q^{2}\ ln\ (b - a)}{2\pi\varepsilon_{0}L} = \lbrack const\rbrack\frac{Q^{2}}{L}$
If the charge is doubled and length is doubled,
$\lbrack const\rbrack\frac{Q^{'2}}{L^{'}} = \frac{4}{2}\left( \frac{Q^{2}}{L} \right) = 2$ times the energy
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.