CIRCUIT ANALYSIS AND TECHNIQUES
Determining the number of equations needed to analyse a circuit

It can be determined from the number of nodes, branches, meshes etc, how many independent equations can be derived in order to solve a given circuit (analyse the circuit to its voltages and currents).

By observing the figure above for example, there are 9 branches with unknown currents. In case where there are n nodes in the circuit, n-1 independent equations are needed in order to analyse the circuit. These n-1 equations can be derived when applying Kirchoff's current law to any n-1 nodes. On the above circuit there are 7 nodes so 6 independent equations can be derived.

Now when applying  Kirchoff's voltage law, b-(n-1) independent equations are needed in order to analyse the circuit. b represents the number of branches. On the figure above there are 9 branches, so 3 independent equations can be derived.