A cylindrical capacitor has charge Q and length L . If both the charge and the length of the capacitor are doubled by keeping the other parameters fixed, then the energy stored in the capacitor

Question

A cylindrical capacitor has charge Q and length L . If both the charge and the length of the capacitor are doubled by keeping the other parameters fixed, then the energy stored in the capacitor, remains same, increases two times, decreases two times, increases four times

MARKS App · Accepted Answer

Energy of a charged capacitor, E = 1 2 Q 2 C For a cylindrical capacitor, C = 2 π ε 0 L log e ⁡ b a E = 1 2 Q 2 2 π ε 0 L log e ⁡ b a ...(i) where L = length of the cylinder a and b = radii of two concentric cylinder C ' = 2 π ε 0 ( 2 L ) log e ⁡ b a E ' = 1 2 2 Q 2 C ' = 1 2 2 Q 2 2 π ε 0 2 L log e b a ...(ii) From Eqs. (i) and (ii), we get E ' = 2 E

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