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Question

A capacitor of capacity 6 μF and initial charge 160 μC in connected with key S and resistance as shown in figure. Point M is earthed. If key is closed at t=0, then the current through resistance (R=1 Ω) at (t=16 μs) is 4n3eA, then find n


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Solution


Initial potential difference across the capacitor = 16060 Volt = 803
When key is closed capacitor starts discharging through a parallel combination of (3+R) = 4Ω and 8Ω both.
Equivalent circuit will be :-
At time t, charge on capacitor will be
q=Qinitial.etτ

current through the circuit is
I=dqdt=Qinitialτ.etτ

As in a parallel circuit, current is divided inversely proportional to resistance
current through R is i=8I4+8
i=23Qinitialτ.etτ
i=13160μC83(6μC).e1616
i=203e
Given that i=4n3e
n=5

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