Question

A 60 μF capacitor that had been charged to 30 V is discharged through a resistor. The figure (Figure 1) shows the capacitor voltage as a function of time. What is the value of the resistance?

Answer 1

A capacitor initially charged at VO when discharges through a resistor
voltage across the capacitor is given by V(t) = Vo*e^(-t/RC)
so, C = 60 micro F
Vo = 30 V
at t = 2*10^-3 s, V = 10 V
so, 10 = 30 e^(-2*10^-3/R*60*10^-6)
ln(3) = 2*10^-3/R*60*10^-6
R = 30.3413075 ohm