The circuit in Figure P28.61 contains two resistors, R 1 5 2.00 k V and R 2 5 3.

Question

The circuit in Figure P28.61 contains two resistors, R1 5 2.00 kV and R2 5 3.00 kV, and two capacitors, C1 5 2.00 mF and C2 5 3.00 mF, connected to a battery with emf e 5 120 V. If there are no charges on the capacitors before switch S is closed, determine the charges on capacitors (a) C1 and (b) C2 as functions of time, after the switch is closed.

The circuit in Figure P28.61 contains two resistors, R1 5 2.00 kV and R2 5 3.00 kV, and two capacitors, C1 5 2.00 mF and C2 5 3.00 mF, connected to a battery with emf e 5 120 V. If there are no charges on the capacitors before switch S is closed, determine the charges on capacitors (a) C1 and (b) C2 as functions of time, after the switch is closed.

Explanation / Answer

Here , For

for time constant ,

1/R = 1/2 + 1/3

R =1.2 K ohm

and

Ceq = C1 + C2

Ceq = 2 + 3

Ceq = 5 mF

then , Time constant , T = RC

T = 1.2 * 10^3 * 5*10^-3

T = 6 s

Now ,

as Vc = 120*(1- e^(-t/6))

then charge on capacitor 1

Q1 = 2 * 120*(1- e^(-t/6))

Q1 = 0.24(1- e^(-t/6))   C

and Q2 = 3*120*(1- e^(-t/6))

Q2 = 0.36*(1- e^(-t/6))   C

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