Three identical capacitors are given a charge Q each and they are then allowed to discharge through resistance R1, R2 and R3. Their charges, as a function of time shown in the graph below. The smallest of the three resistance is

(1) R3

(2) R2

(3) R1

(4) Cannot be predicted

Concept Videos :-

#21 | Circuit Analysis of Capacitance
#28 | Current Variation with Charging

Concept Questions :-

RC circuit

(3) During the discharge of a capacitor through a resistance, charge at any instant $Q={Q}_{0}{e}^{-t/CR}$

$\frac{{Q}_{0}}{Q}={e}^{-t/CR}$

$t=-CR{\mathrm{log}}_{e}\frac{{Q}_{0}}{Q}$

If Q → constant, then tR

Now, draw a line parallel to the time axis as shown. Suppose this line cut the graphs at points 1, 2 and 3.

Corresponding time are t1, t2 and t3 respectively. Hence from graph t1 < t2 < t3

R1 < R2 < R3

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