21. For the circuit of Fig. 10.82 FIG. 10.81 Problem 20 a. Determine the time co

Question

21. For the circuit of Fig. 10.82 FIG. 10.81 Problem 20 a. Determine the time constant of the circuit when the switch is thrown into position 1 b. Find the mathematical expression for the voltage across the capacitor after the switch is thrown into position 1. 3 kn rent following the closing of the switch (position 1) 2 2 d. Determine the voltage vc and the current ic if th 50 V switch is thrown into position 2 at t = 100 ms. e. Determine the mathematical expressions for the voll- age vc and the current ic if the switch is thrown into position 3 at t = 200 ms. Plot the waveforms of Uc and ic for a period of time extending from t = 0 to t 300 ms. FIG. 10.82 Problems 21 and 22

Explanation / Answer

for the given diagram

a. when the switch is in posiiton 1

Reff = R1 + R2 = 5 kohm

Ceff = 2 uF

hence

time constant = 1/RC = 100 s

b. after the switch is thrown into position 1

charge on C at time t = q

at time t = inf, charge = Q

Q = CV

C = 2 uF

V = 50 V

hence

q = Q(1 - e^(-t*RC))

hence

voltage acrss capacitor

v = (Q/C)(1 - e^(-t*RC))

v = 50(1 - e^(-0.01t))

c. ic = dq/dt = Q*RC*r^(-t*RC)

ic = 0.000001*e^(-0.01t)

d. at t = 100 ms

hence v = 0.049975 V

i = 9.99*10&-7 A

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