电路如图所示,原已处于稳态,t=0时开关断开,求t>=0时的u1(t)

2024-11-24 02:40:39
推荐回答(1个)
回答1:

1)t=0 前,u1=0,Uc(0)=0;

2)t=∞ 后,I2=0.5U1,U1=I1*R1;Is = I1 + I2;

Uc(∞)= U1 - I2*R2 ;

3)运用戴维南等效电阻法求出时间常数中的电阻值;

I = I' + I''  , U1 = I' *R1  ,  I'' = 0.5U1  ;  那么等效电阻 R = U/I ;

4)代入全响应公式,得 Uc(t),那么 

U1(t) = Uc(t) + I2*R2 = I1*R1 ;Is = I1 + I2;  I1=U1(t)/R1

U1(t) = Uc(t) + (Is - I1)*R2 = Uc(t) + (Is - U1(t)/R1)*R2;

U1(t) = (Uc(t) + Is*R2)*R1/(R1+R2) ;