Q.
Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistance $R_{1},R_{2}$ and $R_{3}.$ Their charges, as a function of time shown in the graph below. The smallest of the three resistance is
A) $R_{3}$
B) $R_{2}$
C) $R_{1}$
D) Cannot be predicted
Explanation
(c) During the discharge of a capacitor through a resistance charge at any instant $Q = Q_{0}e^{- t/CR}$
$\Rightarrow \frac{Q_{0}}{Q} = e^{t/CR} \Rightarrow t = CR\log_{e}\frac{Q_{0}}{Q}$
If $Q \rightarrow$ constant, then $t \propto R$
Now, draw a line parallel to the time axis as shown. Suppose this line cut the graphs at points 1, 2 and 3. Corresponding times are $t_{1},t_{2}$ and $t_{3}$ respectively. Hence from graph $t_{1} < t_{2} < t_{3}$
$\Rightarrow R_{1} < R_{2} < R_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.