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A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one eighth of its initial value. The ratio t₁/t₂ will be

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1/2

1/3

1/4

1/6

answer is D.

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Detailed Solution

In t₁ time energy becomes half so charge will

$become \frac{1}{\sqrt{2}} time$

$q = Q_{0} e^{\frac{t_{1}}{RC}} = \frac{Q_{0}}{\sqrt{2}}$

$and q' = Q_{0} e^{- \frac{t_{2}}{RC}} = \frac{Q_{0}}{8} = {(\frac{Q_{0}}{\sqrt{2}})}^{6}$

$\begin{aligned} \Rightarrow t_{2} = 6 t_{1} \\ \Rightarrow \frac{t_{1}}{t_{2}} = \frac{1}{6} \end{aligned}$

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