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A fully charged capacitor C with initial...

A fully charged capacitor C with initial charge `underset(o)(q)` is connected to a coil of self-inductance L at t = 0 . The time at which the energy is stored equally between the electric and the magnetic fields is

A

`pi``sqrt LC`

B

`pi`/4`sqrt LC`

C

`2pi``sqrt LC`

D

`sqrt LC`

Text Solution

Verified by Experts

The correct Answer is:
B
In LC oscillation energy is transferred C to I, I to C, maximum energy in L is = `1/2 LI_max^(2)` . Maximum energy in C is
`q_max^(2)`/2C
Equal energy will be when
1/2L`t^(2)` = 1/2.1/2L`t_max^(2)`
I = 1/`sqrt2` `I_max`
I = `I_max`sin`omega`t = `1/sqrt 2``I_max`
`omega`t = `pi`/4
or 2 `pi`/T t = `pi`/4 or t = T/8 `implies` t = 1/8 `2pi``sqrt LC` = `pi`/4 `sqrt LC`
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