Question

A resister with resistance 10 M$\Omega$ is connected in series with a capacitor of capacitance 1.0 $mu$F and a battery with emf 12.0 V. Before the switch is closed at time t=0 , the capacitor is uncharged .
a. What is the time constant?
b. What fraction of the final charge is on the plates at time t=46s?
c. What fraction of the initial current remains at t=46 s?

Answer 1

$a.$ The time constant is $t$=RC =10 X ${10}^6$ X 1 X ${10}^{-6}$=10 s
$b.$ The fraction $f$ of the final charge on capacitor is $\frac{q}{Q}$
$\frac{q}{Q}$ =1-$e^{\frac{-t}{RC}}$ =1-$e^{\frac{-46}{10}}$=0.99
The capacitor is 99% charged after a time kequal to 4.6 RC , or 4.6 timek constants.
$c.$ $\frac{I}{I_0}$ = $e^{-4.6}$ =0.010
After 4.6 timek constants, the current has decreased to $1.0$ od ira initial value.