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

Options

A. emains same
B. increasestwo times
C. decreases two times
D. increases four times

Answer

B

Explanation

Energy of a charged capacito,
`E = (1)/(2) ( Q ^(2))/( C)`
For a cylindrical capacitor
`C = (2 pi epsi _(0) L )/( log _(e ) ((b)/(a)))`
`E = (1)/(2) (Q ^(2))/( 2 piepsi _(0) L ) log _(e) ((b)/(a)) ...(i)`
where L= length of the cylinder
a and b = radii of two concentric cylinder
`C . = ( 2pi epsi _(0) ( 2 L ))/( log _(e) ((b)/(a)))`
`E . = (1)/(2) (( 2 Q) ^(2))/( C .)`
` = (1)/(2) (( 2Q) ^(2) )/( 2 pi epsi _(0) (2 L ) ) log _(e) ((b)/(a)) ....(ii)`
From Eqs. (i) and (ii), we get
`E . = 2 E`