A student performing the experiment concerning capacitors and RC circuits forgot

Question

A student performing the experiment concerning capacitors and RC circuits forgot to print the graph of the charging curve for a 2.00 times 10^-6 - F capacitor. She did remember, however, that the potential difference across the capacitor reached 1/2 of its final value of 16.0 volts after 20.0 seconds. Calculate the resistance of the resistor connected in series with the capacitor. Calculate the time constant for this RC circuit. Calculate the current through the resistor alter 2.16 seconds. After the capacitor was fully charged, it was discharged. Calculate the potential difference across the capacitor 3.60 seconds after discharging started?

Explanation / Answer

(A) for charging,

V = Vo[1 - e^(-t/T)]

1/2 = 1 - e^(-20 / T)

e^(-20 / T) = 0.50

- 20 / T = ln(0.50)

T = R C = 28.86 s

(2 x 10^-6) (R) = 28.86

R = 14.4 x 10^6 Ohm

(B) RC = R = 28.86 sec

(C) Vc = 16 [1 - e^(-2.16 / 28.86)]

Vc = 1.15 Volt

VR = V - Vc = 14.85 volt

I = VR / R = 14.85 / (14.4 x 10^6) = 1.03 x 10^-6 A

(D) Vc = V[e^(-t/T)]

Vc = 16[e^(-3.60 / 28.86)]

Vc = 14.12 Volt

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