如下图所示电路的US1=60 V,US2=‒90 V,R1=R2=5 Ω,R3=R4=10 Ω,R5=20 Ω,试用支路电流法求I1、I2、I3。
【正确答案】:节点电流方程I2= I3- I1;
R5左侧节点电压方程 I3R5 = Us1 - I1 ( R1+ R3 ),20I3 = 60 - 15I1,I3 = 3 - 3I1/4;
I2 = I3 - I1 = 3 - 3I1/4 - I1 = 3 - 7I1/4;
R5右侧节点电压方程 -I3R5 = Us2 + I2 ( R2 + R4)
-20( 3 - 3I1/4 ) = -90 + 15( 3 - 7I1/4 ),I1 = 4/11 A;
I2 = 3 - 7I1/4 = 3 - 7/4 * 4/11 = 26/11 A;
I3= I1+ I2 =4/11+26/11=30/11 A.