Problem 6 please How long will it take for the current in the circuit to drop to

Question

Problem 6 please

How long will it take for the current in the circuit to drop to 0.37I_1? The circuit in the figure below contains two resistors R_1 = 4.00 k Ohm and R_2 = 5.00 k Ohm, and two capacitors. C_1 = 4.00 mu F and C_2 = 5.00 mu F, connected to a battery with emf epsilon = 100 V a) If no charges exist on die capacitors before switch S is closed, determine the charge on capacitor q_1 = 1.00 ms after the switch is closed. b) Determine the charge on capacitor q_2 = 1 00 ms after the switch is closed.

Explanation / Answer

no charge existed before closing the switch.

equivalentcircuit is a series RC circuit with

R = R1*R2/R1+R2 = 20/9 = 2.22 kilo ohms

C=C1 and C2 in parallel= 4 + 5 = 9 uF

so time constant=R*C= 2.22*9 = 19.98 ms

so voltage across capacitor=100*(1-e^(-t/19.98 ms))

at t=1 ms,

voltage = 48.818 volts

as C1 and C2 are in parallel,they will have same voltage across them

so

a) charge on C1= C1*V = 4*48.818 = 195.272 uC

b) charge on C2 = C2*V = 5*48.818 = 244.09 uC

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