please fully explain each part The values of all circuit elements are given in t
ID: 2279195 • Letter: P
Question
please fully explain each part
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 re-opened. What is the time constant for discharging the capacitor? What is the charge on the capacitor 3 mu s after the switch was re-opened?Explanation / Answer
a) immediately after closed then
capacitor short circuit.. then R1 and R3 parallel...
Req = 5 ohms
current = 6/5 = 1.2A
b) current through R1 after immediate closure of switch = 1.2/2 = 0.6 (by current divison rule)
c)after long time means steady state.. and capacitor gets open circuited..so its voltage across R2 only..
=> Voc = Vr2 = 6*R2/(R1+R2) = 3 volts
charge = Q= cv = 3*1uF = 3micro coulombs
d) time constant for discharging = Req*C
Req = {view from capacitor terminals} = (R1+R3)||R2 = 2/3
time constant = 2/3 * 1uF = 0.67 micro seconds = T
e) Vc = Vi*e^(-t/T)
Vc at t= 3 micro secs = 3*e^(-3/2/3) = 3*e^(-4.5) = 0.0333 volts
Q= cv = 0.0333*1uF = 33.3 nano coulombs
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