####

**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.