Electric Circuits and Networks

5.3 SUBSTITUTION THEOREM

Consider the three-mesh circuit shown in Fig. 5.3-1. Mesh analysis reveals that the mesh currents are 1 A, 2 A and 3 A as shown in the figure. Two nodes a and a′ have been identified in the circuit and the current crossing the node a from left to right is marked as 2 A. The voltage of a with respect to a′ is calculated to be 1 V and is marked in the figure.

 

 

Fig. 5.3-1 A Three-mesh Circuit with Two Nodes – a and a′ – Identified

 

Now, we add two current sources between the two nodes, a and a′, as shown in Fig. 5.3-2. The current sources have equal and opposite currents of 2 A magnitude.

 

 

Fig. 5.3-2 Circuit in ...