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Question

A capacitor of capacitance C is given a charge q0. At time t=0 it is connected to an uncharged capacitor of equal capacitance through a resistance R. Find the charge on the first capacitor and the second capacitor as a function of time t. Also, plot the corresponding q-t graphs.

A
CR5
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B
CR2
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C
CR12
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D
CR9
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Solution

The correct option is B CR2
Both capacitors have equal capacitance. Hence half-half charge distribute over both the capacitors.
q1=q2=q0/2q1=q2=q02
q1q1 decreases exponentially from q0q0 to q0/2q02. While q2q2 increases exponentially from 0 to q0/2q02. Corresponding graphs and equation are given in the answer.
The time constant of the two exponential equations will be
τC=(Cnet)τC=(Cnet)
R=(C/2); R=CR/2
888728_213461_ans_2374c0332bae49fcbd6fd657a3cc0252.JPG

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