A series combination of a 12k Ohm resistor and an unknown ca

A series combination of a 12-k Ohm resistor and an unknown capacitor is connected to a 12-V battery. One second after e circuit is completed, the voltage across the capacitor is 10 V. Determine the capacitance of the capacitor.

Solution

since the capacitor is charging

s0 Vf= V (1- e ^(-t/RC))

Now Vf = 10 , V=12 , t=1 R= 12000 ohm

10/12 = 1- e ^(-t/RC)

e ^(-t/RC) =.1666

t/RC= 1.792 .

so C =1/(12000*1.792) = 4.6 * 10^-5 F