A circuit as shown is constructed with a 100 ohm resistor and a 20 microF capaci

Question

A circuit as shown is constructed with a 100 ohm resistor and a 20 microF capacitor. The capacitor initially has a charge of 360 microC

a) Before the switch is closed, determine the potential difference across the capacitor, the potential difference across the resistor, and the current through the resistor.

b) At the instant the switch is closed, determine the potential difference across the capacitor, the potential difference across the resistor, and the current through the resistor.

c) At a time 2.0 ms after the switch is closed, determine the charge of the capacitor, the potential difference across the capacitor, the potential difference across the resistor, and the current through the resistor.

Explanation / Answer

the charge on the capacitor decreases as q = Q*e^-(t/RC)

Vc = (Q/C)*e^-(t/RC)

current i = (Q/RC)*e^-(t/RC)

(a)

at t= 0

Vc = Q/C = 360*10^-6/20*10^-6 = 18 V

VR = 0

I = 0

(b)

VC = 18 V

VR = 18 V

I = VR/R = 18/100 = 0.18 A

(c)

q = 360*10^-6*e^-(2*10^-3/(100*360*10^-6))

q = 340.5*10^-6 C

Vc = 18*e^-(0.002/(100*20*10^-6))

Vc = 6.62 V

VR = VC = 6.62 V

current i = VR/R = 6.62/100 = 0.0662 A

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