1. The switch has been open for a long time when at time t = 0, the switch is cl

Question

1. The switch has been open for a long time when at time t = 0, the switch is closed. What is I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?

2. What is Q(), the charge on the capacitor after the switch has been closed for a very long time?

3. After the switch has been closed for a very long time, it is then opened. What is Q(topen), the charge on the capacitor at a time topen = 697 s after the switch was opened?

4. What is IC,max(closed), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is closed? A positive value for the current is defined to be in the direction of the arrow shown.

5. What is IC,max(open), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is open? A positive value for the current is defined to be in the direction of the arrow shown.

Explanation / Answer

for the given circuit

1. switch has been open for a long time

switch is closed at t = 0

just after the switch is closed, the capacitor acts like a short circuited compoennt

hence

I4(0) = V/(R1 + R4)

I4(0) = 12/(39+151) = 0.0631578 A

2. after the switch has been closed for a long time

voltage drop across C = voltage drop across R3

V3 = I3*R3 = V*R3/(R1 + R3 + R4)

hence

Q = CV3

Q = CV*R3/(R1 + R3 + R4) = 1.2099*10^-5 C

3. after the switch is open

capacitor discharge equation is given by

q = Qe^(-t*(R2 + R3)C)

hence for t = 697*10^-6 s

q = 1.2098*10^-5 C

4. when the switch is closed, the maximum current throuhg capacitor is I4(0) = 0.0631578 A

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