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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Answer:

Correct Answer: 4. (b)

Solution:

  1. 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).



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