Three identical capacitors are given a charge | vedclass

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(C) During the discharge of a capacitor through a resistance,the charge at any instant $t$ is given by $Q = Q_0 e^{-t/CR}$.Rearranging the equation: $

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$R_1$

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(C) During the discharge of a capacitor through a resistance,the charge at any instant $t$ is given by $Q = Q_0 e^{-t/CR}$.Rearranging the equation: $\frac{Q_0}{Q} = e^{t/CR} \implies t = CR \ln\left(\frac{Q_0}{Q}\right)$.For a constant charge $Q$,the time $t$ is directly proportional to the resistance $R$ $(t \propto R)$.Now,draw a line parallel to the time axis as shown in the graph. Suppose this line intersects the curves at points corresponding to times $t_1, t_2,$ and $t_3$ for resistances $R_1, R_2,$ and $R_3$ respectively.From the graph,it is clear that $t_1 Since $t \propto R$,it follows that $R_1 Therefore,the smallest resistance is $R_1$.

Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistances $R_1, R_2,$ and $R_3$. Their charges,as a function of time,are shown in the graph below. The smallest of the three resistances is

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