Nodal analysis is a systematic method to determine the voltage
at each node relative to the reference node by repeatedly applying
KCL. In Nodal analysis, also called node-voltage analysis
or branch-current method, the voltage between nodes is determined
in terms of the branch currents. In this method, a system
of equations in which the unknowns are the voltages at the
principal nodes of the circuit is set up and solved. The set of
equations developed in the nodal analysis in fact represents and
describes the circuit. After determining these nodal voltages,
the currents in the various branches of the circuit can be easily
found.
The nodal analysis starts with selecting one of the nodes as the
reference node. Since one of the nodes is selected as the reference
node, if there are N nodes in the circuit there will be N −1
linearly independent equations in general. The solution of this
set of equations yields the N −1 unknown node voltages. These
node voltages can be used with the Ohm’s law to determine all
currents in the circuit.