Prob 1 In the circuit shown, R1 212, R2-3D, R3-60, and C-Zpf (a) Determine the p

Question

Prob 1 In the circuit shown, R1 212, R2-3D, R3-60, and C-Zpf (a) Determine the potential difference Vc across the capacitor after switch S has been closed for a long time. (b) Determine the energy stored in the capacitor after switch S has been closed for a long time (c) After the switch is opened, what is the time constant, the time it takes for the charge to drop to e-, for the discharging of the capacitor? (d) Find the total current flowing through the resistors as a function of time after the switch is opened. 3.3 5.3 38.1 40.2 1. 42.1 44.1 13 40.3 44.2 44.3 R2 Rs 12 V

Explanation / Answer

(A) after long time, no current will pass through C.

current through bettery = 12 / Req

Req = R1 + (R2 R3 / (R2 + R3)) = 4 ohm

I = 3 A

Vc = 12 - (3 x 2) = 6 Volt

(b) U = C V^2 / 2 = (2 x 10^-6)(6^2) /2

U = 12 x 10^-6 J

(C) R = R2 R3 / (R2 + R3) = 2 ohm

T = R C = 2 x 2 x 10^-6 = 4 x 10^-6 s

(d) i_R1 = 0

v_c = 6 e^(-t/T)

i_R2 = 2 e^(-t/T)

i_R3 = e^(-t/T)

where T = 4 x 10^-6 sec

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