Electrical Circuits — General Electrical Engineering Notes

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Electrical Circuits is the foundation chapter of the AEE professional syllabus — nearly every other technical topic (machines, power systems, traction) builds on the concepts here. It is also, in practice, one of the most heavily tested chapters: circuit-law questions are compact, unambiguous, and easy to set at CBT scale, which is exactly why they show up often in real papers.

Circuit Elements

Every electrical circuit is built from three basic passive elements — resistance (R), inductance (L), and capacitance (C) — plus active sources (voltage or current). Each element relates voltage and current differently, and that difference is the basis of almost every circuit question you'll see.

Resistance (R) — voltage and current are in phase; V = IR at every instant (Ohm's law).
Inductance (L) — current lags voltage by 90°; opposes any change in current (stores energy in a magnetic field).
Capacitance (C) — current leads voltage by 90°; opposes any change in voltage (stores energy in an electric field).

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Memory Aid — CIVIL

"CIVIL": in a Capacitor, I (current) leads V; in an Inductor, V leads I (current lags). A quick way to settle phase-relation questions under exam pressure.

Ohm's Law

V = I × R

Voltage across a resistor equals current through it multiplied by resistance, at a constant temperature. Ohm's law applies to resistors, but NOT to non-linear/reactive elements the same way — this distinction is a favourite exam trap. A common real-exam question style: "which of the following elements cannot be analysed using Ohm's law?" — the answer is a non-linear active device (e.g. a transistor), not a passive R/L/C element, since Ohm's law describes a linear V–I relationship that active semiconductor devices don't follow.

Kirchhoff's Laws

Kirchhoff's Current Law (KCL) — the sum of currents entering a node equals the sum of currents leaving it. Based on conservation of charge.
Kirchhoff's Voltage Law (KVL) — the sum of all voltage drops around any closed loop equals zero. Based on conservation of energy.

DC & AC Circuit Analysis

DC circuits (series, parallel, and series-parallel combinations of R) can be solved directly with Ohm's and Kirchhoff's laws. AC circuits add a complication: R, L, and C don't just add up like plain numbers — their combined opposition to current is called impedance (Z), a complex quantity with both a magnitude and a phase angle.

Impedance (R-L series)

Z = √(R² + XL²), where XL = 2πfL

XL (inductive reactance) grows with frequency — this is why inductors behave differently at 50 Hz mains versus high-frequency switching circuits.

Magnetic Circuits

A magnetic circuit is the closed path a magnetic flux follows, analogous to how current follows a closed electrical path. Magnetomotive force (MMF = N×I) plays the role of voltage, flux plays the role of current, and reluctance plays the role of resistance — the same Ohm's-law-shaped relationship applies: MMF = Flux × Reluctance.

Poly-phase Circuit Analysis

Railway power systems are overwhelmingly 3-phase. In a balanced 3-phase star (Y) connection, line voltage = √3 × phase voltage, while line current = phase current. In a delta (Δ) connection, it's the reverse — line voltage = phase voltage, while line current = √3 × phase current. This √3 relationship is one of the most frequently tested single facts in AEE papers.