Nodal analysis

Nodal analysis solves electric circuits by applying Kirchhoff’s current law at circuit nodes to determine node voltages relative to a reference node.

Kirchhoff’s current law: At any circuit node, the algebraic sum of currents is zero, expressing conservation of electric charge. This current-balance rule supplies the equations at each nonreference node.
Electric potential: The electric potential energy per unit charge at a point in an electric field. Node voltage is a difference in electric potential between a node and the reference.
Modified nodal analysis: A circuit-analysis formulation that combines node voltages with selected branch currents to accommodate ideal voltage sources and other elements. It extends ordinary nodal equations for computer-aided analysis of complex circuits.
Mesh analysis: A circuit-solving method that applies Kirchhoff’s voltage law around independent loops to find mesh currents. It uses loop currents rather than node voltages as the primary unknowns.
Reference node: A circuit node chosen as the zero-voltage reference for measuring all other node voltages. Every unknown voltage in nodal analysis is measured relative to this chosen node.
Electric current: The rate at which electric charge passes a point in a circuit. Nodal equations balance currents entering and leaving each node.
Phasor analysis: A sinusoidal steady-state method that represents voltages and currents as complex-valued phasors. Replacing resistances with impedances lets nodal analysis solve AC circuits.
Thevenin’s theorem: A theorem that replaces a linear two-terminal network with an equivalent voltage source in series with a resistance or impedance. Reducing a network first can make its node equations unnecessary or simpler.
Conductance: A measure of how readily an electrical component or path conducts current, equal to the reciprocal of resistance. Writing branch currents as conductance times voltage difference makes node equations linear.
Ohm’s law: The relation between voltage, current, and resistance for an ohmic element: voltage equals current times resistance. It converts each resistor’s voltage difference into a branch current.

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