a) Time constant, T = R*C
= 250*200*10^-6
= 0.05 s
maximum current, I_max = V/R
= 20/250
= 0.080 A
maximum charge on the capacitor, Q_max = C*V
= 200*10^-6*20
= 4.0*10^-3 C
b) at t = 0.04 s
I = I_max*e^(-t/T)
= 0.08*e^(-0.04/0.05)
= 0.0359 A
Voltage across the capacitor,
Vc = V_max*e^(-t/T)
= 20*e^(-0.04/0.05)
= 8.99 V
charge on the capacitor, Qc = Qmax*e^(-t/T)
= 4*10^-3*e^(-0.04/0.05)
= 1.80*10^-3 C
c) use, I = I_max*e^(-t/T)
0.02 = 0.08*e^(-t/0.05)
==> t = 0.069 s
d) at t = 0.069 s
Voltage across the capacitor,
Vc = V_max*e^(-t/T)
= 20*e^(-0.069/0.05)
= 5.03 V
charge on the capacitor, Qc = Qmax*e^(-t/T)
= 4*10^-3*e^(-0.069/0.05)
= 1.01*10^-3 C
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