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Discharging of Capacitors

How many time...

Question

How many time constants will elapse before the charge on a capacitor falls to 0.1 $%$ of its maximum value in a discharging RC circuit ?

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Solution

$q = Q^{e - \frac{t}{r c}}$

$q = 0.1 % Q = 1 \times 10^{- 3} Q$

$So, 1 \times 10^{- 3} Q = Q \times e^{\frac{- t}{r c}}$

$\Rightarrow e^{\frac{- t}{r c}} = 10^{- 3}$

$\Rightarrow \frac{t}{r C} = - (- 6.9) = 6.9$

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