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]

Question

Smart Achievers · Accepted Answer

(2)

Current in RC circuit, $\ln I$

or $\ln I = \ln I_{0} - \frac{t}{R C}$ or $\ln I = (- \frac{t}{R C}) + \ln I_{0}$

$\ln I = (- \frac{t}{R C}) + l n (\frac{E_{0}}{R})$

Comparing with $y = m x + C$

Intercept $= \ln (\frac{E_{0}}{R})$ and slope $= - \frac{1}{R C}$

So, when $x$ is changed to $2 x$ , then slope increases and current becomes less. Hence New graph is Q.

Solution

Q.
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]

1 $P$

2 $Q$

3 $R$

4 $S$

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