The pair of capacitors in the figure below are fully charged by a 24.0-V battery

Question

The pair of capacitors in the figure below are fully charged by a 24.0-V battery. The battery is disconnected, and the switch is then closed. After 1.8 ms has elapsed, how much charge remains on the 3.00-mu F capacitor? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. mu C After 1.8 ms has elapsed, how much charge remains on the 2.00- mu F capacitor? What is the current in the resistor at this time?

Explanation / Answer

equivalent capacitance

C=C1+C2=5 uF

Time Constant

T=R*C=500*5*10^-6 =2.5 ms

Voltage across the capacitor is

V=Voe-t/T

V=24e-1.8/2.5=11.68 Volts

a)

Charge on 3uF at t=1.8 ms

Q3=C3V =3u*11.68 =35.05 uC

b)

Charge on 2uC at t=1.8 ms

Q2=2u*11.68 =23.36 uC

c)

current through the resistor is

I=V/R =11.68/500

I=23.36 mA

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