The circuit in the figure below contains two resistors, R 1 = 5.00 k? and R 2 =

Question

The circuit in the figure below contains two resistors, R1 = 5.00 k? and R2 = 6.00 k?, and two capacitors, C1 = 5.00 ?F and C2 = 6.00 ?F, connected to a battery with emf ? = 100 V.

a)If no charges exist on the capacitors before switch S is closed, determine the charge on capacitor q1 1.00 ms after the switch is clo

b)Determine the charge on capacitor q2 1.00 ms after the switch is closed.

The circuit in the figure below contains two resistors, R1 = 5 O k and R2 = 6.00 kQ, and two capacitors C,-5.00 F and C2 6.00 connected to a battery with emf 100 V a) If no charges exist on the capacitors before switch S is closed, determine the charge on capacitor q 1.00 ms after the switch is closed Submit Answer Tries 0/6 b) Determine the charge on capacitor q2 1.00 ms after the switch is closed. Submit Answer Tries 0/6

Explanation / Answer

R1 and R2 are in parallel connection,
so equivalent of these two is R

then 1/R = 1/R1 + 1/R2

1/R = 1/5 + 1/6

R = 2.73 k ohm

and C1 and C2 are also in parallel connection,

so equivalent capacitance, C = C1 + C2 = 5 + 6 = 11 uF

now its is a simple series RC circuit.

time constant, T = 2.73 x 10^3 x 11 x 10^-6 = 0.03 s

so

Q = CV0 [1 - e^(-t/T)]

at t = 0.001 s

Q = (11 x 10^-6 x 100 ) [ 1 - e^(-0.001/0.03)]

Q = 36.06 x 10^-6 C = 36.06 uF

this is the charge on equivalent capaictorC.

a) Q1 = Q x C1 / (C1 + C2) = 36.06 x 5 / (5 +6) = 16.39 uC

b) Q2 = 36.06 x 6 / (5 +6) = 19.67 uC

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