Nodal Analysis

The first step is selecting a reference or datum node, whose voltage is assigned zero. The remaining non-reference nodes are then assigned nodal voltages relative to this reference node. This establishes a baseline for measuring all other voltages in the circuit, simplifying the analysis process.

Kirchhoff's Current Law is applied to non-reference nodes to establish relationships between branch currents. It states that the algebraic sum of currents entering a node equals zero, based on charge conservation. This principle generates equations that, combined with Ohm's Law, allows you to express currents in terms of node voltages.

Node voltages serve as primary variables because they simplify circuit analysis and allow you to determine voltage distribution throughout the circuit. Once node voltages are known, other quantities like branch currents and power can be calculated. This approach reduces complexity by focusing on voltage relationships rather than individual current paths.

For a circuit with n nodes, you obtain n - 1 independent equations. For example, a three-node circuit requires two simultaneous equations. These equations are derived by applying Kirchhoff's Current Law to each non-reference node and expressing currents using Ohm's Law in terms of node voltages.

Ohm's Law expresses branch currents passing through resistors in terms of node voltages. Since current is directly proportional to voltage across a conductor, Ohm's Law enables you to convert voltage differences between nodes into current expressions. These expressions are then substituted into Kirchhoff's Current Law equations to solve for unknown node voltages.

You need the values of all resistors and source currents in the circuit. Once these values are substituted into the simultaneous equations derived from Kirchhoff's Current Law and Ohm's Law, the equations can be solved to obtain the node voltages. This information reveals the voltage distribution and enables calculation of other circuit parameters.

Nodal analysis uses node voltages as primary variables, while alternative methods like mesh analysis use loop currents. Nodal analysis with voltage sources provides a systematic approach to circuits containing voltage sources and resistors. Both methods simplify complex circuits, but nodal analysis is often preferred when voltage information is the primary goal.