A 10V source through a switch is in series with a 10M Ohm re

A 10V source, through a switch, is in series with a 10M Ohm resistor and a 1 mu F capacitor. How many seconds will it take for the capacitor to charge to 9.5V after the switch is closed?

Solution

The equation for voltage across capacitor is Vo(t)=Vin*(1-e^(-t/RC)),Vin=10 V,R= 1M ohms ,C=1 micro Farad

Vo(t)=10*(1-e^(-t))=9.5 V

1-e^-t=9.5/10=0.95

e^-t=1-0.95=0.05

t=-ln(0.05)=2.9957 sec

So to charge capacitor to 9.5 V it needs 2.9957 sec

t=2.9957 sec