Electrostatics 6 Question 4
4. A capacitor is charged using an external battery with a resistance $x$ in series. The dashed line shows the variation of $\ln I$ with respect to time. If the resistance is changed to $2 x$, the new graph will be
(2004, 2M)
(a) $P$
(b) $Q$
(c) $R$
(d) $S$
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Solution:
- Charging current, $I=\frac{E}{R} e^{-\frac{t}{R C}}$
Taking $\log$ on both sides, $\log I=\log \frac{E}{R}-\frac{t}{R C}$
When $R$ is doubled, slope of curve decreases. Also at $t=0$, the current will be less. Graph $Q$ represents the best. Hence, the correct option is (b).
