200分.英文版的..ans是答案
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200分.英文版的..ans是答案
200分.英文版的..ans是答案
200分.英文版的..ans是答案
1. (a) Vc(0+)=Vc(0-)=30*(4+6)/(4+6+5)=20V.
(b) Equivalent capacitance C'=4+4=8µF. (The capacitor should be 4µF instead of 4F. 4F is too big a value for capacitance in reality).
Equivalent resistance R'=4+1/(1/6+1/6))=7Ω.
The time constant τ=R'*C'=56µs.
(c) Vc(∞)=4*1/(1/6+1/6)=12V.
So Vc(t)=Vc(∞)+(Vc(0+)-Vc(∞))e^(-t/τ)=12+8e^(-t/56e-6).
2. (a) When S2 is kept closed, VL=L*dI/dt=L*0=0V so there is no current flowing through the 50Ω resistor. So IL(0-)=2A. The inductor current cannot be changed instantly when S1, S2 are flipped so IL(0+)=IL(0-)=2A.
(b) Equivalent resistance R'=20+1/(1/20+1/20)=30Ω.
So the time constant τ=L/R'=1µs.
(c) IL(∞)=30/(20+1/(1/20+1/20))*20/(20+20)=0.5A.
So IL(t)=IL(∞)+(IL(0+)-IL(∞))e^(-t/τ)=0.5+1.5e^(-t/1e-6).
(d) IL(τ)=0.5+1.5e^(-1)=1.05A.
IL(2τ)=0.5+1.5e^(-2)=0.703A.
IL(3τ)=0.5+1.5e^(-3)=0.575A.
IL(5τ)=0.5+1.5e^(-5)=0.510A.