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A capacitor C with a charge Q(0) is conn...

A capacitor C with a charge `Q_(0)` is connected across an inductor through a switch S. If at t=0, the switch is closed, then find the instantaneous charge q on the upper plate of capacitor.

Text Solution

Verified by Experts

The correct Answer is:
`q=Q_(0)sin(sqrt(1/(LC))t+pi/2)`
Applying loop law

`q/C-L(-(di)/(dt))=0`
`q/C+L(d^(2)q)/(dt^(2))=0`
`(d^(2)q)/(dt^(2))+1/(LC)q=0`
This is a equation of `SHM` so `omega=1/sqrt(LC)`
charge will oscillate and at `t=0, q=Q_(0)` so
`q=Q_(0) cos (omegat)=Q_(0) cos(t/sqrt(LC))`
`=Q_(0) sin (t/sqrt(LC)+pi/2)`
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