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 c = 10.0 V_f, R_1 = 47.0 k Ohm, R_2 = 150 k Ohm, and C = 10.5 mu F. (a) Determine the time constant before the switch is closed. (b) Determine the time constant after the switch is closed. (c) Let the switch be closed at t = 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 the following as necessary: t.)

Explanation / Answer

c)

The current through the closed switch will produced by the battery Ib and while the capacitor is discharging a current Ic, the total current trough the switch is then

I=Ib+Ic=10/(47*103)+[10/(150*103)]e-t/1.575

I=[(2.128*10-4)+(6.67*10-5)e-(t/1.575 s)] A

I=[(2.128*10-4)+(6.67*10-5)e-0.635t] A

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