Let us consider the circuit in Figure 27a.

Circuit Fundamentals - Fig27
Figure 27

Converting voltage sources to the current sources we achieve the scheme in Figure 27b. All the current sources are form one equivalent current source I, where:

I=I1+I2+...In=E1Z1+E2Z2+...EnZn=k=1nYkZk, and Z=1k=1Ykn

Thus:

E=ZI=k=1YkZknk=1Ykn

This means that n parallel voltage sources can be replaced with one current source or voltage source.

Current in the external network is the following:

In+1=IZZ+Zn+1=EZ+Zn+1

Voltage between two nodes can be found the following way:

U=IZZn+1Z+Zn+1=I1k=1n+1Yk=k=1nEkYkk=1n+1Yk

Shifting sources in an electric circuit

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