Electrical Circuits and Networks
Electrical Circuits and Networks tests whether you can reduce a linear circuit to a simple equivalent, solve AC steady state with phasors, and handle first-order transients. Questions often combine source transformation with a theorem rather than asking for a single definition.
Core rules
- KCL and KVL apply to instantaneous values; in phasor form use complex impedance Z = R + jX.
- Thevenin and Norton equivalents preserve terminal behavior for linear networks. Dependent sources stay active when independent sources are set to zero.
- Superposition applies to currents and voltages in linear circuits, never directly to power.
- Maximum power transfer to a resistive load occurs at R_L = R_th, with P_max = V_th^2/(4R_th).
- For a first-order RC circuit, v_C(t) = v_C(inf) + [v_C(0+) - v_C(inf)]e^(-t/tau), where tau = RC.
- Series resonance has f_0 = 1/(2pisqrt(LC)); at resonance impedance is minimum and current is maximum.
Worked example
A 12 V source feeds 4 ohm in series with 12 ohm; the 12 ohm resistor is the load terminals. Find the Thevenin equivalent and maximum load power. Open-circuit voltage: V_th = 12 × 12/(4+12) = 9 V. Kill the source: R_th = 4 parallel 12 = 3 ohm. Maximum power: P = 9^2/(4×3) = 81/12 = 6.75 W. The reasoning is to remove the load, compute open-circuit voltage, then deaden independent sources for resistance.
Traps
Do not apply superposition to power; do not deactivate dependent sources; check capacitor voltage continuity and inductor current continuity; convert degrees and radians correctly in phasor problems.