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If the total charge stored in the LC cir...

If the total charge stored in the `LC` circuit is `Q_(0)`, then for `tgt= 0`

A

the charge on the capacitor is `Q=Q_(0) cos(pi/2+t/sqrt(LC))`

B

the charge on the capacitor is `Q=Q_(0) cos(pi/2-t/sqrt(LC))`

C

the charge on the capacitor is `Q=-LC(d^(2)Q)/(dt^(2))`

D

the charge on the capacitor is `Q=-1/sqrt(LC)(d^(2)Q)/(dt^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`Q-Q_(0) cosomegat …(1)`
`(dQ)/(dt)=-Q_(0)omegasinomegat implies(d^(2)Q)/(dt^(2))=-Q_(0)omega^(2) cosomegat…(2)`
From `(1)` and `(2)`
`(d^(2)Q)/(dt^(2))=-omega^(2)Q`
`implies Q=-1/omega^(2)(d^(2)Q)/(dt^(2))=-LC(d^(2)Q)/(dt^(2))`
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