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Question

An LC circuit initially oscillates with frequency 'f' and the maximum current in the circuit is imax. If the total energy of the circuit is increased to twice of its initial value, then

A
the period of oscillation will become double its initial value.
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B
the maximum charge on the capacitor will become 2 times its initial value
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C
the maximum current that will appear in the circuit will be 2 times its initial value imax.
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D
at the moment energy stored in capacitor and inductor becomes equal , the charge on the capacitor will be equal to the initial maximum charge on it.
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Solution

The correct options are
B the maximum charge on the capacitor will become 2 times its initial value
C the maximum current that will appear in the circuit will be 2 times its initial value imax.
D at the moment energy stored in capacitor and inductor becomes equal , the charge on the capacitor will be equal to the initial maximum charge on it.
As there will be no change in either L or C by changing energy of the oscillations

f=(12πLC) will not change.

Thus, the period of oscillation will remain constant.

Total energy 2E=(2Qm)22C

Therefore maximum charge on the capacitor has become 2 times of the initial maximum charge Qm
Also,

12Li2m2×12Li2mim=2im

Thus, the maximum current that will appear in the circuit will be 2 times of its initial value im
Total energy is equally divided between capacitor and inductor.

Charge on capacitor =12[2Q2m2C]=Q2m2C

i.e. it is equal to initial maximum charge on the capacitor.

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