Question: There are two switches, S1 and S2, as the figure shown. Those switches

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Question:

There are two switches, S1 and S2, as the figure shown. Those switches are intially open, as well as the capacitors are initially uncharged. At time t=0, S1 and S2 are both closed. Assume VB=18V, R1=10 omega, R2=20 omega, R3=30 omega, C1=10uF, C2=20uF, C3=30uF.

1) Calculate the current through R1 immediately after the switches are closed.

2) Calculate the current through R2 a very long time after the switches are closed.

3) Calculate the charge on the capacitor C2 a very long time after the switches are closed.

Figure:

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Thanks for you guys help me solve this problem!!!

Question: There are two switches, S1 and S2, as the figure shown. Those switches are intially open, as well as the capacitors are initially uncharged. At time t=0, S1 and S2 are both closed. Assume VB=18V, R1=10 omega, R2=20 omega, R3=30 omega, C1=10uF, C2=20uF, C3=30uF. 1) Calculate the current through R1 immediately after the switches are closed. 2) Calculate the current through R2 a very long time after the switches are closed. 3) Calculate the charge on the capacitor C2 a very long time after the switches are closed. Figure:

Explanation / Answer

Capacitor acts as a short circuit immediately after switching on the circuit and acts as open circuit long time after switches are closed.

part 1) This means only the R1 is active and current passes through the Capacitor branch.
Hence current = VB / R1 = 18/22 = 0.818 Amperes.

part 2) Here C1 will act as open circuit and current through R2 will be 'zero'.

part 3) After long time current passes through R1 and R3 , current = VB / (R1 + R3) = 18 / (10+30) = 0.45 Amperes.
and voltage across Capacitor C2 will be equal to that across R3 which is 0.45*30 = 13.5 Volts.
Charge across capacitor = Voltage*Capacitance,

Q = 13.5*20*10^(-6) = 270 Micro Coloumbs.

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