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Electric Potential Due to Shell

A capacitor o...

Question

A capacitor of capacitance C is given a charge $q_{0}$ . 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.

\frac{C R}{5}

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\frac{C R}{2}

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\frac{C R}{12}

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\frac{C R}{9}

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Solution

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

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