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Question

Two plates of a capacitor of capacitance C are given charges q1 and q2. This capacitor is connected across a resistance R as shown. Key is closed at t=0. Find the total charge on each plate after time t


A
(q1q22)+(q1q22)e2tCR (q1+q22)(q1q22)e2tCR
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B
(q1q22)etRC,(q1q22)etCR
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C
(q1+q22)+(q1q22)etCR (q1+q22)(q1q22)etCR
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D
(q1+q22),(q1+q22)
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Solution

The correct option is C (q1+q22)+(q1q22)etCR (q1+q22)(q1q22)etCR
Initially the charges on the plates will be distributed as shown.


Charge on outer surface q1+q22
is constant because q1+q2 is constant.
P.D. across the plates is given by q1q22C
and is independent of the charge on the outer surfaces.
Thus, when capacitor is discharged, the charges on the outer surface do not change. Charge on the inner surface decreases according to the equation.

q=(q1q22)etRC

Total charge on the left plate

q1=q1+q22+[q1q22]etRc

And total charge on the right plate

q2=q1+q22[q1q22]etRC

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