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Question
How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?
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Solution
The decay of charge across a capacitor,
\[q = Q e^{- \frac{t}{RC}}\]
Here, q = 0.1 % and Q = 1 × 10−3 Q
⇒ 1 × 10−3 Q = \[Q e^{- \frac{t}{RC}}\]
\[\Rightarrow e^{- \frac{t}{RC}}=10^{-3}\]
\[\Rightarrow \frac{t}{rC} = - \left( - 6 . 9 \right) = 6 . 9\]
Let t = nRC
\[\Rightarrow \frac{nRC}{RC} = 6 . 9\]
\[ \Rightarrow n = 6 . 9\]
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