Millman's theorem

Millman's theorem finds the voltage of a node connected to parallel branches, each containing a voltage source in series with an impedance. It expresses the node voltage as a conductance-weighted average of source voltages, adjusted for any current sources.

Kirchhoff's current law: Kirchhoff's current law states that the algebraic sum of currents entering a circuit node is zero. Applying current balance at the shared node produces Millman's voltage formula.
Ohm's law: Ohm's law relates voltage, current, and resistance in an electrical element. It converts each branch's voltage difference into the current used in the node balance.
Resistive circuit: A resistive circuit is an electrical network whose ideal elements are sources and resistors. With resistors in the branches, Millman's theorem gives a real-valued node voltage.
Mesh analysis: Mesh analysis solves planar circuits by applying Kirchhoff's voltage law around independent loops. It uses loop currents rather than the shared-node voltage central to Millman's theorem.
Nodal analysis: Nodal analysis solves circuit voltages by applying current conservation at selected nodes. Millman's theorem is a compact shortcut for a particular nodal-analysis configuration.
Impedance: Impedance is the frequency-dependent opposition that a circuit element or network presents to alternating current. Millman's theorem uses branch impedances, including resistance as the direct-current case.
AC circuit analysis: AC circuit analysis studies sinusoidal electrical networks using voltage, current, and impedance. Complex impedances let Millman's method handle sinusoidal steady-state node voltages.
Source transformation: Source transformation exchanges an ideal voltage source in series with a resistance for an equivalent current source in parallel with it. It can reshape branches before analysis, whereas Millman's theorem directly combines their node contributions.
Thevenin's theorem: Thevenin's theorem replaces a linear two-terminal network with an equivalent voltage source in series with a resistance. Both methods simplify linear source networks, though Millman's theorem targets a shared parallel node.
Voltage source: A voltage source is a circuit element that maintains a specified voltage across its terminals. Each branch source supplies the voltage value weighted in the theorem's numerator.

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Norton's theoremCompared with: It can combine parallel source branches directly rather than first reducing the whole network at its terminals.