C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits, 7th ed., chapter on methods of analysis.
Node-voltage analysis, mesh-current analysis, supernodes, supermeshes and systematic equation construction.
DC-04
Course overview
Nodal & mesh analysis
Small networks can often be simplified by pattern recognition. Larger linear circuits need a systematic method. This course turns Kirchhoff's current law, Kirchhoff's voltage law and Ohm's law into reusable procedures: first node-voltage analysis, then supernodes, mesh-current analysis and supermeshes, with explicit checks that expose sign and modelling errors.
5 chapters5 available · 0 plannedfoundational
Prerequisites
- DC-02 — Kirchhoff current and voltage laws
- DC-03 — series/parallel networks, dividers & equivalent resistance
By the end of the course
- Choose node voltages or mesh currents as unknowns for a reason.
- Construct nodal equations systematically from Kirchhoff's current law.
- Handle voltage sources correctly with supernodes.
- Construct mesh equations from Kirchhoff's voltage law.
- Handle current sources with supermeshes.
- Choose the method that minimizes unknowns and verify the result independently.
Syllabus
Five readings from local Kirchhoff laws to systematic network solution.
Small networks can often be simplified by pattern recognition. Larger linear circuits need a systematic method. This course turns Kirchhoff's current law, Kirchhoff's voltage law and Ohm's law into reusable procedures: first node-voltage analysis, then supernodes, mesh-current analysis and supermeshes, with explicit checks that expose sign and modelling errors.
- 01→
Node-voltage analysis: foundations
Choose one reference node, make the remaining node voltages the unknowns, express every branch current from those voltages, and let Kirchhoff's current law generate the equations.
115–145 min · Foundational · available - 02→
Multi-node systems & matrix form
With several unknown node voltages, write one Kirchhoff-current-law equation per node, solve the coupled system, then recognize the conductance matrix hidden inside the equations.
125–155 min · Foundational · available - 03→
Supernodes & voltage sources
An ideal voltage source between two unknown nodes fixes their voltage difference but does not provide a resistor-like branch-current equation. Enclose the source in a supernode, write one boundary KCL equation, then add the source-voltage constraint.
125–155 min · Foundational · available - 04→
Mesh-current analysis
For a planar circuit, choose one mesh current per elementary loop, express shared-branch currents as differences of mesh currents, and let Kirchhoff's voltage law generate the coupled equations.
125–155 min · Foundational · available - 05→
Supermeshes, method selection & verification
A current source shared by two meshes fixes a current difference but hides its own voltage from direct KVL. Build a supermesh around the source, add the current constraint, then close DC-04 with a disciplined choice-and-verification workflow for nodal versus mesh analysis.
140–175 min · Foundational → synthesis · available
Reference backbone
References used
The course follows standard circuit-analysis texts for node-voltage and mesh-current methods, cross-checked against MIT's lumped-network treatment. AoN keeps topology, reference directions and equation construction explicit so the methods remain derivations rather than memorized recipes.
J. W. Nilsson & S. A. Riedel, Electric Circuits, 11th ed., chapters on nodal and mesh analysis.
Independent derivations, sign conventions and worked linear-network examples.
A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits; MIT 6.002.
Node-based lumped-circuit reasoning, constitutive relations and the transition from topology to algebraic equations.
W. H. Hayt, J. E. Kemmerly & S. M. Durbin, Engineering Circuit Analysis, chapter on nodal and mesh analysis.
Alternative systematic treatment and comparison of analysis methods.
AoN DC-02 — Kirchhoff current and voltage laws.
Prerequisite topology, Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL) and sign discipline.
AoN DC-03 — Series/parallel networks, dividers & equivalent resistance.
Prerequisite branch-current expressions, equivalent resistance and loading intuition.
AoN ADR-0018 — Electrical notation and sign conventions.
Normative voltage/current reference conventions used in every derivation and figure.