In the circuit of the figure below, the switch s has been open for a long time.

Question

In the circuit of the figure below, the switch s has been open for a long time. It is then suddenly closed. Take E 10.0 V, R 59.0 kn, R 125 kn, and C 14.0 HF. (a) Determine the time constant before the switch is closed. 2.5 (b) Determine the time constant after the switch is closed. 1.75 0. Determine the current in the switch as a function of time. (Assume I is in A and t is in s. Do not enter units in your expression. Use (c) Let the switch be closed at t the following as necessary: t.) 169.49 80e 1.75 2

Explanation / Answer

1. tou = time constant = RC = (R1 + R2)*C = 2.57

2.tou = R2*C = 1.75

3. Discharging of capacitor = -(10*14)*exp(-t/1.75) microC

so, current due to discharging of capacitor = 80*exp(-t/1.75) microAmp

Current due to Voltage source = E/R1 = 169.5 microAmp

So, net current = [169.5 + 80*exp(-t/1.75)] microAmp

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