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In the given circuit the capacitor (C) m...

In the given circuit the capacitor (C) may be charged through resistance R by a battery V by closing switch `(S_1)`. Also when `(S_1)` is opend and `(S_2)` is closed the capacitor is connected in series with inductor (L).

Given taht the total charge stored in the LC circuit is `(Q_0)`. for `Tge0, the charge on the capacitor is

A

`Q = Q_(0) cos ((pi)/(2) + (t)/(sqrt(LC)))`

B

`Q = Q_(0) cos ((pi)/(2) - (t)/(sqrt(LC)))`

C

`Q =- LC(d^(2)Q)/(dt^(2))`

D

`Q = - (1)/(sqrt(LC)) (d^(2)Q)/(dt^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
Comparing the `LC` oscillation with normal `SHM`, we get
`(d^(2)Q)/(dt^(2)) = - omega^(2)Q`
Here, `omega^(2) = (1)/(LC)`
`Q = - LC(d^(2)Q)/(dt^(2))`
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