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?

Answer 1

$q=Q{e}^{-t/RC}$

$q=0.1\%Q$ $RC\Rightarrow$ Time constant

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

So, $1\times {10}^{-3}Q=Q\times e^{-t/RC}$

$\Rightarrow e^{-t/RC}=in{10}^{-3}$

$\Rightarrow t/RC=-(-6.9)=6.9$