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Q.

A capacitor is charged from a battery through a resistance of 1 M Ω. If it takes 1 sec for the charge to reach one-half of its final value then capacity of capacitor is

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a

0.69µF

b

$\frac{1}{0 .36} μF$

c

$\frac{1}{0 .696} μF$

d

0.36µF

answer is D.

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Detailed Solution

$\begin{array}{l} q = q_{0} (1 - e^{\frac{t}{CR}}); \frac{q_{0}}{2} = q_{0} (1 - e^{- \frac{t}{CR}}) \\ - e^{- \frac{t}{CR}} = - \frac{1}{2}; \frac{t}{CR} = \log_{e} 2 \Rightarrow 1 = (0 .693) \times 10^{6} \times C \\ C = \frac{1}{0 .693} μF \end{array}$

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A capacitor is charged from a battery through a resistance of 1 M Ω. If it takes 1 sec for the charge to reach one-half of its final value then capacity of capacitor is