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Question
How many time constants will elapse before the power delivered by a battery drops to half of its maximum value in an RC circuit?
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Solution
Power = CV2 = q × V
Now,
\[\frac{qV}{2} = qV \times e^{- t/rc} \]
\[ \Rightarrow \frac{1}{2} = e^{- t/rc} \]
\[ \Rightarrow \frac{t}{rc} = - \ln \left( 0 . 5 \right)\]
\[ = - \left( - 0 . 69 \right) = 0 . 69\]
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