please explain each part in detail The values of all circuit elements are given

Question

please explain each part in detail

The values of all circuit elements are given in the figure. The capacitor is initially uncharged. Then, at time t = 0, the switch is closed. What is the current through the battery immediately after the switch is closed? What is the current through resistor R1 after the switch is closed? Find the charge on the capacitor a long time after the switch is closed. A long time after the switch has been closed, it is reopened. What is the time constant for discharging the capacitor? What is the charge on the capacitor 3 us after the switch was reopened?

Explanation / Answer

a.) Immediately after the switch is closed, the capacitor is unimportant, so to find I, use V=IR or I=V/R

R(eq)=1/[(1/R1)+(1/(R1+R2)]=20/3

I=V/R(eq)=6/(20/3)=9/10 A

b.) current through the branch with R1 and R2 is 1/3 of the total current because it has double the R of the other pathway.

I=3/10 A

c.) Q=CV No current will flow at this point, so the entire voltage of the battery is dropped across the capacitor

Q=(1)*(6)= 6 micro coulombs

d.) Time constant = RC the battery is now disconnected, so R is still equivalent resistance

Time Constant=(20/3)*(1)= 20/3 microseconds

e.) Q=CV(e^(-t/RC))

Q=(1)*(6)*(1-e^(-3/(20/3)))= 6 microcoulombs

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