设KP间电压为U,K端流入电流I
分别设K到N,K到M,N到M,N到P,M到P的电流为i1,i2,i3,i4,i5
由基尔霍夫定理(就是你那个Loop Method)得到以下5个方程
i1=i3+i4
i2+i3=i5
i1+i2=i4+i5=I
i1(Rkl+Rln)+i3Rnm-i2Rmk=0
i3Rnm+i5(Rmo+Rop)-i4Rnp=0
最后解出i1,i2,i3,i4,i5 (用I表示)
i2=I-i1,i5=I-i4 ,i3=i1-i4
1390i1+390i3-560i2=0
390i3+340i5-270i4=0
1390i1+390(i1-i4)-560(I-i1)=0
390(i1-i4)+340(I-i4)-270i4=0
2340i1-390i4=560I
390i1-1000i4=-340I
所以 i1=0.3166I, i4=0.4635I
KN两点的电阻为U/I=[i1(Rkl+Rln)+i4Rnp]/I
=0.3166*1390+0.4635*270=565.2 欧