Electrical Engineering: Circuit Laws, AC Steady State and Three-Phase Fundamentals
Electrical Engineering carries the shared fundamentals every other PGCIL section leans on: circuit laws, network theorems, single- and three-phase AC steady state, transients and basic device behaviour. Questions are usually short numericals, so sign conventions and units decide the score.
Circuit laws and theorems
- KCL and KVL hold for any lumped network; superposition, Thevenin, Norton and reciprocity need linear, bilateral, time-invariant elements.
- Thevenin voltage is the open-circuit voltage; the Thevenin resistance is measured with independent sources killed (voltage sources shorted, current sources opened).
- Maximum power transfer needs R_L = R_th and gives 50% efficiency. Maximum power and maximum efficiency are different operating points - a favourite trap.
AC and three-phase
For a series branch, Z = R + j(X_L − X_C), and resonance at f₀ = 1/(2π√LC) makes the branch purely resistive with maximum current. In a balanced three-phase system P = √3 V_L I_L cos φ for both star and delta, but line and phase quantities differ by √3, and delta/star impedance conversion uses a factor of 3.
Worked example
A coil with R = 6 Ω and X_L = 14 Ω sits in series with X_C = 6 Ω across 200 V, 50 Hz. Net reactance = 14 − 6 = 8 Ω, so Z = 6 + j8 Ω, |Z| = 10 Ω and I = 200/10 = 20 A. Power factor = R/|Z| = 0.6 lagging, because the net reactance is inductive. Real power P = I²R = 400 × 6 = 2400 W.
Traps
Mixing RMS and peak values in power formulas, applying superposition to power (it is nonlinear), reversing the sign of capacitive reactive power, and forgetting that a wattmeter reads average power while a moving-iron meter reads RMS.