C. K. Alexander & M. N. O. Sadiku, Fundamentals of Electric Circuits, 7th ed., Ch. 2–3.
Series/parallel resistance, divider relations and network reasoning from Kirchhoff's current and voltage laws.
DC-03
Course overview
Series/parallel networks, dividers & equivalent resistance
The first reusable circuit patterns should be derived, not memorized. This course starts from topology, Kirchhoff's current law, Kirchhoff's voltage law and Ohm's law to build series and parallel equivalents, then voltage/current dividers and finally the loading limits that decide when those shortcuts are valid.
5 chapters5 available · 0 plannedintroductory
Prerequisites
- DC-01 — Ohm's law and resistive elements
- DC-02 — Kirchhoff current and voltage laws
By the end of the course
- Recognize true series and parallel connections from topology.
- Derive equivalent resistances from Kirchhoff's laws and Ohm's law.
- Derive voltage- and current-divider relations instead of memorizing recipes.
- Recognize when loading invalidates a shortcut divider formula.
- Validate results using limiting cases, units and power balance.
Syllabus
Five readings that turn the first recurring network patterns into reliable tools.
The first reusable circuit patterns should be derived, not memorized. This course starts from topology, Kirchhoff's current law, Kirchhoff's voltage law and Ohm's law to build series and parallel equivalents, then voltage/current dividers and finally the loading limits that decide when those shortcuts are valid.
- 01→
Series resistors
A true series connection forces one current through every element; Kirchhoff's voltage law (KVL) and Ohm's law then make the equivalent resistance a sum.
85–110 min · Introductory · available - 02→
Parallel resistors
A true parallel connection gives every branch the same two terminal nodes and therefore the same voltage; Kirchhoff's current law (KCL) then makes branch conductances add.
90–115 min · Introductory · available - 03→
Voltage divider
An unloaded tap on a true series string samples a predictable fraction of the input voltage; the divider relation follows directly from the common current and Ohm's law.
100–125 min · Introductory · available - 04→
Current divider
Parallel branches share one voltage, so their currents divide in proportion to conductance; the familiar opposite-resistance formula is only a two-branch algebraic form of that principle.
100–125 min · Introductory · available - 05→
Loading & equivalent resistance
Connecting a load changes the network. This chapter quantifies that change, defines resistance seen from a port, derives loading error, and prepares the transition to Thévenin/Norton reasoning.
115–145 min · Introductory → foundational · available
Reference backbone
References used
Standard circuit texts provide the formal series/parallel derivations; MIT 6.002 is used as an independent pattern-recognition reference, while practical resistor limits remain tied to real component data rather than ideal formulas.
J. W. Nilsson & S. A. Riedel, Electric Circuits, 11th ed., early chapters.
Independent treatment of series and parallel networks, equivalent resistance and power checks.
A. Agarwal & J. H. Lang, Foundations of Analog and Digital Electronic Circuits, Ch. 1–3; MIT 6.002.
Lumped-network reasoning and the recurring voltage-divider/current-divider patterns.
MIT 6.002, Circuits and Electronics, lecture transcripts 10 and 13.
Independent pedagogical emphasis that series/parallel resistors and divider forms are recurring patterns to recognize after they have been derived.
P. Horowitz & W. Hill, The Art of Electronics, 3rd ed., Ch. 1.
Practical resistor selection, loading intuition and the distinction between ideal network formulas and real components.
OpenStax, University Physics Vol. 2, §10.2 — Resistors in Series and Parallel.
Open-access independent derivation of parallel resistance from common branch voltage, current conservation and Ohm's law.
BIPM, The International System of Units (SI), 9th ed., updated 2026.
Normative SI naming and symbol for electric conductance: siemens (S), with S = A/V = Ω⁻¹.
AoN ADR-0018 — Electrical notation and sign conventions.
Normative voltage/current references used in derivations and figures.