1. Question Consider the circuit in the figure below, in which V = 3 V, and the

Question

1. Question Consider the circuit in the figure below, in which V = 3 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?

(a) What is the time constant for this circuit?  seconds

3. The voltage and current graphs for a resistor are shown in the figure below, in which each interval along the horizontal axis corresponds to 0.4 s, and each interval along the lefthand vertical axis corresponds to 1 V.

Explanation / Answer

I am allowed to answer only 1 question at a time

for capcitor discharging:
I(t) = -Io*e^(-t/RC)
Io = Qo/RC

a)
= R*C
= 50 * (2*10^-6)
= 1*10^-4 s

b)
Immediately after switch is closed,
Qo = C*Vo
= 2*10^-6 * 3
= 6*10^-6 C

Io = Qo/
= 6*10^-6/(1*10^-4)
= 0.06 A

c)
at t=
Q(t) = Qo*e^(-t/ )
= Qo*e^(-/ )
= 6*10^-6 *e^(-1)
= 2.21*10^-6 C
I(t) = Q(t) /
= 2.21*10^-6/(1*10^-4)
= 0.0221 A

d)
at t = 200 µs = 2*10^-4 s = 2*

Q(t) = Qo*e^(-2/ )
= 6*10^-6 *e^(-2)
= 8.12*10^-7 C

I(t) = Q(t) /
= 8.12*10^-7/(1*10^-4)
= 8.12*10^-3 A

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