A charged capacitor is connected across a 10 $K Ω$ resistor and allowed to discharge. The potential difference across the capacitor drops to 0.37 of its original value after a time of 7.0 s. What is the capacitance of the capacitor?

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0.5 mF

0.6 mF

0.8 mF

0.7 mF

answer is C.

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Detailed Solution

$\begin{array}{l} q = q_{O} e^{- t / R C} \\ {Given at t = 7 s, q = 0.37q}_{O} \\ e^{- 1} = 0.37 \\ ∴ t = RC =7 s \\ \Rightarrow C = \frac{7}{10^{4}} = 0.7 m F \end{array}$

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