Question

How many time constants will elapse before the power delivered by the battery drops to half of its maximum value in an RC circuit ?

Answer 1

Power = CV${}^2$ = q ${\times }^V$

Now, $\frac{qV}{2}=qV\times e^{\frac{t}{rc}}$

$\Rightarrow \frac{1}{2}=e^{\frac{-t}{rc}}$

$\Rightarrow \frac{t}{rc}=-ln\left(0.5\right)$

=$-(-0.69)=0.69$