Electric Circuit Analysis
Every method in this subject — mesh, nodal, Thevenin, phasors — is bookkeeping on top of two conservation laws. These topics animate the bookkeeping so the method stops looking like a recipe.
Start from the beginning →9 topics you can watch now, 16 still to come.
Foundations
The two laws, and the elements they are applied to.
- Charge, current, voltage and power
- R, L and C element equations
- Independent and dependent sources
- Series-parallel reduction and dividers
- Star-delta transformation
Systematic methods
Turning a circuit into a set of equations, mechanically.
- Source transformation
- Graph theory, trees and cutsets
Network theorems
Shortcuts that are only shortcuts once you know what they assume.
- Reciprocity and Millman's theorem
- Substitution and compensation theorems
AC steady state
Sinusoids, made algebraic by turning them into phasors.
- Phasors and ImpedanceReplace calculus with complex arithmetic and every DC technique carries over intact — at the price of steady state, one frequency, and linearity.
- Real, Reactive and Apparent PowerReactive power delivers no energy and still costs money, because copper cannot tell the difference. Then modern loads make cos φ the wrong measure entirely.
- Series and Parallel ResonanceA passive circuit developing 500 V from a 10 V source, with no amplifier in it — and KVL never violated.
- RMS and average values derived
- Three-phase circuits
- Coupled circuits and mutual inductance
Transient analysis
What happens in the instant after a switch closes.
- First-Order TransientsTwo continuity rules turn a differential equation into two DC circuits joined by an exponential — and explain why opening a switch can produce hundreds of volts.
- Second-Order RLC TransientsTwo storage elements let energy slosh between them. Overdamped, critical, underdamped — and a car suspension is the same problem in a different costume.
- Laplace transform methods
- Initial and final value theorems
Two-port networks and topology
Treating a whole circuit as a black box with four terminals.
- S-parameters and the Smith chart
- Image and characteristic impedance
About Electric Circuit Analysis
Circuit analysis is the grammar of electrical engineering. Almost everything later — amplifiers, filters, machines, power systems — is analysed with the handful of laws introduced here, so time spent making them automatic pays back across several subjects at once.
The core is conservation stated twice: charge cannot pile up at a node, and energy cannot be gained going round a loop. Kirchhoff's two laws are those statements, and node and mesh analysis are just systematic ways of writing them down without missing an equation.
The subject becomes interesting when capacitors and inductors arrive, because circuits stop having a single answer and start having a history. A transient response is a circuit remembering where it was a moment ago, which is why these topics are animated over time rather than solved once.
What to know first
- Algebra, and comfort rearranging simultaneous equations
- Basic calculus for the transient and second-order material
Where it gets used
- Sizing a resistor or capacitor for a real circuit rather than a textbook one
- Reducing a messy network to a Thevenin equivalent before analysing it
- Predicting what a circuit does at switch-on, not just in steady state