Let us consider a simple network (Fig.1) where the branch equivalence of the load resistance is .
Fig. 1. A simple dc circuit to explain substitution theorem.
Fig. 2. Equivalent of branch x-y of Fig. 1.
Figure 2 represents the branch equivalents of the x-y branch where it may be noted that in all the cases of Fig. 2 , the terminal voltages and through currents are identical and equal to that of the branch x-y .
It may also be observed that a known potential difference and current in a branch can be replaced by an ideal voltage and current source respectively.
Limitation: This theorem can not be used to solve network containing two or more sources that are not in series or in parallel.