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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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Knowledge Check

  • A capacitor is charged to a potential of V_(0) . It is connected with an inductor through a switch S. The switch is closed at time t=0. Which of the following statement(s) is/are correct?

    A
    The maximum current in the circuit is `V_(0)sqrt((C)/(L))`
    B
    Potential across capacitor becomes zero for the first time at `t=pisqrt(LC)`
    C
    Energy stored in the inductor at time `t=(pi)/(2)sqrt(LC)` is `(1)/(4)CV_(0)^(2)`
    D
    Maximum energy stored in the inductor `(1)/(2)CV_(0)^(2)`

  • In the circuit shown in figure, the capacitor is charged with a cell of 5V .If the switch is closed at t=0 , then at t=12s , charge on the capacitor is

    A
    `(0.37)10muC`
    B
    `(0.37)^(2)10muC`
    C
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    D
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  • The charge on each of the capacitors 0.16 ms after the switch S is closed in figure is :

    A
    `24 mu C`
    B
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    C
    `25.2 mu C`
    D
    `40 mu C`

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