PLEASE ANSWER ALL 3 PARTS AND SHOW ALL WORK NEATLY! THANK YOU :) Consider the ci
ID: 1420856 • Letter: P
Question
PLEASE ANSWER ALL 3 PARTS AND SHOW ALL WORK NEATLY! THANK YOU :)
Consider the circuit shown on the attached figure where E = 100 V, R1 =3.0k?,R2 =4.0k?,C1 =5.5?F,andC2 =8.5?F.Notethatthe charge on both capacitors is initially zero before the switch S is closed.
a) Determine the maximum charge on each capacitor long after the switch has been closed.
b) How long will it take the charge on C1 to be at 0.49 mC?
c) What current will be coming out of the EMF at the time determined
in part b? If you cannot solve part b use t = 200 ms.
Explanation / Answer
a) After a long time the total potentail drops across capacitors.
so,
Q1 = C1*V = 5.5*10^-6*100 = 550 micro C or 5.5*10^-4 C
Q2 = C2*V = 8.5*10^-6*100 = 850 micro C or 8.5*10^04 C
b) Time constant of the ckt, T = (R1+R2)*(C1+C2)
= (3+4)*10^3*(5.5+8.6)*10^-6
= 0.0987 s
q1 = Q1*(1 - e^(-t/T))
0.49*10^-3 = 5.5*10^-4*(1 - e^(-t/T))
0.49/0.55 = 1 - e^(-t/T)
e^(-t/T) = 1 - 0.49/0.55
e^(-t/T) = 0.109
t = -T*ln(0.109)
= -0.0987*ln(0.109)
= 0.2187 s
= 218.7 ms
c)
I = Imax*e^(-t/T)
= (V/(R1+R2))*e^(-t/T)
= (100/(7*10^3))*e^(-0.2187/0.0987)
= 1.56*10^-3 A or 1.56 mA
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