1) The switch has been open for a long time when at time t = 0, the switch is cl

Question

1)

The switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

2)

What is I1(), the magnitude of the current that flows through the resistor R1 a very long time after the switch has been closed?

3)

What is Q(), the charge on the capacitor after the switch has been closed for a very long time?

4)

Consider the circuit above, with R5 = 94 in series with the capacitor. Once again, the switch has been open for a long time when at time t = 0, the switch is closed. What is I1(0), the magnitude of the current through the resistor R1 just after the switch is closed?

5)

Continuing with the new circuit, what is Q(), the charge on the capacitor after the switch has been closed for a very long time?

Explanation / Answer

1) I1(0) = V/(R1+R4)

I1(o) = 24/(41+104) = 24/(145) = 0.165 A

2) I1(infinite) = V/(R1+R2+R3+R4) = 24/(41+41+70+104) = 0.09375 A

3) Q(infinite) = C*Vc

Voltage across capacitor is Vc= V-(i1*R1)-(i4*R4) = 24-(0.09375*41)-(104*0.09375) = 10.4 V

Q(infinite) = (82*10^-6*10.4) = 852.8*10^-6 C = 852.8 uC

4) I1(0) = V/(R1+R4+R5) = 24/(41+104+94) = 0.1004 A

At t=0
V=IR1+IR523+IR4
where R235 is the equivalent resistance you get when you collapse R2, R3 and R5
into a single resistor. R23=R2+R3
= 41+70 = 111 ohm

and 1/
R235=1/R23+1/R5

so that R235=50.9

I = V/(R1+R235+R4) = 24/(50.9+41+104) = 0.122 A

5) After a long time V = I*(R1+R2+R3+R4)

I = 24/(41+41+70+104) = 0.09375 A

V across C is Vc = I*R23 = 0.09375*(41+70) =10.4 V

charge Q = C*V = 82*10^-6*10.4 = 852.8 uC

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