In an `LC` circuit shows in Fig. `C = 1 F`, `L = 4 H`. At time `t = 0`, charge in the capacitor is `4 C` and it is decreasing at the rate of `sqrt(5) C s^(-1)`. Choose the corrent statement.

Options

A. Maximum charge in the capacitor can be `6 C`
B. Maximum charge in the capacitor can be `8 C`
C. Charge in the capacitor will be maximum after time `3 sin^(-1) (2//3) s`
D. None of these

Answer

A

Explanation

`i = sqrt(5) A`
`(q_(m)^(2))/(2C) = (q^(2))/(2C) + (1)/(2) Li^(2) rArr q_(max) = 6C`

`q = Q cos(omega t + delta)`, at `t = 0`, `q= 4`
`rArr 4 = 6 cos delta rArr cos delta = (2)/(3) rArr delta = cos^(-1)((2)/(3))`
Change on the capacitor is maximum at `t = t_(1)`
for this `omega t_(1) + delta = pi`
`rArr t_(1) = (1)/(omega) (pi - delta) = sqrt(LC) (pi - delta) = 2 [pi - cos^(-1)((2)/(3))]`