C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits, 7th ed., Ch. 2–3.
Nodes, branches, loops, KCL/KVL and systematic circuit equations.
DC-02
Course overview
Kirchhoff current and voltage laws
Ohm's law describes one resistor. Kirchhoff's laws describe how many elements are connected. This course introduces nodes, branches and loops, derives Kirchhoff's current law (KCL) from charge conservation, derives Kirchhoff's voltage law (KVL) from potential consistency in lumped circuits, and builds a disciplined sign method before larger network analysis.
5 chaptersintroductory → foundational
Prerequisites
- EF-00 — electrical quantities
- EF-01 — references and notation
- DC-01 — Ohm's law
By the end of the course
- Identify nodes, branches and loops.
- Write Kirchhoff's current law (KCL) with fixed current references.
- Write Kirchhoff's voltage law (KVL) with explicit traversal signs.
- Combine Kirchhoff laws with Ohm's law.
- Explain the physical limits of the lumped model.
Syllabus
Five readings from an isolated component to an electrical network.
Ohm's law describes one resistor. Kirchhoff's laws describe how many elements are connected. This course introduces nodes, branches and loops, derives Kirchhoff's current law (KCL) from charge conservation, derives Kirchhoff's voltage law (KVL) from potential consistency in lumped circuits, and builds a disciplined sign method before larger network analysis.
- 01→
Nodes, branches and loops
Circuit topology comes before equations: know what is connected to what.
75–100 min · Introductory - 02→
Kirchhoff's current law (KCL)
Charge cannot disappear at an ideal lumped node: signed branch currents must balance.
80–105 min · Introductory - 03→
Kirchhoff's voltage law (KVL)
Around a closed path in the lumped-circuit model, the signed voltage changes sum to zero.
80–105 min · Introductory - 04→
Sign discipline in circuit equations
Most beginner errors with Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL) come from changing conventions mid-equation, not from difficult algebra.
75–100 min · Introductory - 05→
Conservation laws behind Kirchhoff's laws
Kirchhoff's current law (KCL) is charge bookkeeping; Kirchhoff's voltage law (KVL) is the lumped electroquasistatic potential relation. Their limits matter.
90–120 min · Foundational
Reference backbone
References used
The course treats Kirchhoff's laws as the network-level consequence of the lumped-circuit abstraction, not as isolated recipes. Standard circuit texts are cross-checked against MIT's explicit connection between KCL/KVL, charge conservation and the lumped-matter discipline; the electromagnetic limit is deferred but stated correctly.
J. W. Nilsson & S. A. Riedel, Electric Circuits, 11th ed., Pearson, early chapters.
Independent treatment of topology, Kirchhoff laws and sign discipline.
A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits, Ch. 1–3; MIT 6.002 lectures 1–2.
Lumped-matter discipline, topology, KCL/KVL and the transition from physical laws to algebraic network equations.
MIT 6.061, Introduction to Electric Power Systems, Ch. 1.
Concise independent definitions of node and loop plus the explicit statement of KVL/KCL as topological network laws.
D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Faraday-law sections.
Electromagnetic limit of a naive electrostatic KVL interpretation when time-varying magnetic flux matters.
AoN ADR-0018 — Electrical notation and sign conventions.
Normative voltage/current reference arrows used in every KCL/KVL equation.