Question Consider the circuit in the figure below, in which V = 9 V, and the swi

Question

Question Consider the circuit in the figure below, in which V = 9 V, and the switch has been in position a for a long time. The switch is changed to position b at t = 0 s. What are the charge Q on the capacitor and the current I through the resistor at the times tabulated below?

Question Consider the circuit in the figure below, in which V = 9 V, and the switch has been in position a for a long time. The switch is changed to position b at t = 0 s. what are the charge Q on the capacitor and the current I through the resistor at the times tabulated below? 50 seconds (a) What is the time constant for this circuit? Q (pC) | 1 (mA) time (b) immediately after the switch is closed (c) at t = (d) at t = 200 s

Explanation / Answer

a)

time constant = RC = 50*2*10^(-6) sec = 100*10^(-6) sec = 100 us

b) switch is connected at point a for long time so volatage across capacitor = 9 V

immediately after the switch is closed

Q = CV = 2*9 = 18 uC

I = V/R = 9/50 = 180 mA

c)

at t = 100 us

For a RC discharging circuit, the voltage across the capacitor

V = Vs*e^(-t/RC)

V = 9*e^(-1) = 3.31 volt

Q = CV = 2*3.31 = 6.62 uC

I = V/R = 3.31/50 = 66.2 mA

d)

at t = 200 us

For a RC discharging circuit, the voltage across the capacitor

V = Vs*e^(-t/RC)

V = 9*e^(-2) = 1.218 volt

Q = CV = 2*1.218 = 2.436 uC

I = V/R = 1.218/50 = 24.36 mA

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