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Question

The given figure shows a part of a bigger circuit. The rate of change of the capacitor is 6 mF and is decreasing at the constant rate 0.5 mFs1. The potential difference across the capacitor at the shown moment is changing as follows dVdt=2Vs1, d2Vdt2=12Vs2 and the current in the 4Ω resistor is decreasing at the rate of 1mAs1. What is the potential difference (in mV) across the inductor at this moment?

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A
4
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B
3
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C
8
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D
6
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Solution

The correct option is B 4
Charge transferred will be distributed between capacitor Qc=CV
ic=dQcdt=CdVdt+VdCdt
dicdt=Cd2Vdt+2dVdtdCdt+Vd2Cdt=6×122×122×12=1mA/s
dirdt=1mA/s

dildt=dicdt+dirdt=2mA/s
VL=Ldildt=4mV

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