The capacitor is initially uncharged. At time t-0, the switch is closed at posit

Question

The capacitor is initially uncharged. At time t-0, the switch is closed at position a. (20 points) a) At what time is the voltage on the capacitor 45 V? (6 pts) b) What is the charge on the capacitor at this time? (2 pts) c) What is the current at this time? (4 pts) 7. 125 ? After a long time, the switch is flipped to position b: What is the current immediately after the switch is flipped to position b? (2 pts) d) e) What is the current at time t - 0.50 ms? (4 pts) f Does the current calculated in part e) flow through the 50-0 resistor, the 125-2 resistor or both? (2 pts)

Explanation / Answer

a)

In a RC circuit Voltage as a function of time for charging is given by

V=Vo(1-e-t/T)

Time Constant

T=RC =125*(20*10-6)=2.5*10-3 s =2.5 ms

=>45=50(1-e-t/2.5 ms)

Ln(0.1)=-t/2.5

t=5.756 ms or 5.756*10-3s

b)

Charge on the capacitor at t=5.756 ms

Q=CV =(20*10-6)(45)

Q=9*10-4C or 900 uC

c)

In a RC circuit current as a function of time is given by

I=Ioe-t/T

I=(50/125)e-5.756/2.5=0.04 A

d)

I=50/50=1 A

e)

time constant

T=RC=50*20*10-6=1 ms

In a RC circuit current as a function of time for discharging is given by

I=Io[1-e-t/T)

I=1*(1-e-0.5/1)

I=0.393 A

f)

50 ohms resistor

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