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t=0时开关S闭合,闭合前电路处于稳态,求uc和ic

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t=0时开关S闭合,闭合前电路处于稳态,求uc和ic
 
t=0时开关S闭合,闭合前电路处于稳态,求uc和ic
ic(t)=Cduc(t)/dt
{[ic(t)*2k+uc(t)]/4k+ic(t)}*4k+ic(t)*2k+uc(t)=20V
=[3ic(t)/2+uc(t)/4k]*4k+ic(t)*2k+uc(t)
=8k*ic(t)+2uc(t)
=8k*Cduc(t)/dt+2uc(t)
=0.016duc(t)/dt+2uc(t)

duc(t)/dt+125uc(t)=1250
uc(t)=ae^(bt)+c,duc(t)/dt=abe^(bt)
(125+b)ae^(bt)+125c=1250
b=-125,c=10
uc(t)=ae^(-125t)+10,
t=0,uc(0-)=uc(0+)=20V=a+10,a=10,uc(t)=10e^(-125t)+10
duc(t)/dt=-1250e^(-125t)
ic(t)=Cduc(t)/dt=-2.5*10^(-3)e^(-125t)=0.0025e^(-125t)