Question

如图所示电路,时刻开关S闭合,换路前电路已处于稳态.求换路后 和

Answer 1

用三要素法.

Uc(0+)=2V

再用节点电压法

Uc(∞)=(2V/1kΩ+4ma)/(1/1kΩ+1/1kΩ)=6mA×kΩ/2=3V

再把电容看做负载,其开路电压为3V

用等效电源法计算其内阻Rs=1kΩ//1kΩ=0.5kΩ

时间常数τ= RsC=0.5kΩ×4μF=0.002s=2ms

uc(t)=Uc(∞)+[Uc(0+)-Uc(∞)]exp(-t/τ)

=3V+[2V-3V]exp(-t/0.002)

=[3-exp(-500t)]V