Electrical Circuits and Network Theory
Electrical Circuits and Network Theory
This domain tests DC and AC circuit analysis, network theorems, resonance and first-order transients. Numerical questions often combine source transformation with Thevenin or maximum power transfer.
Core rules
- KCL and KVL apply to every lumped network; use passive sign convention consistently.
- Thevenin voltage is the open-circuit voltage; Thevenin resistance is found by killing independent sources (voltage sources shorted, current sources opened). Dependent sources stay in place and are handled with a test source.
- Superposition applies only to linear quantities such as voltage and current, never to power.
- Maximum power transfer occurs at R_L = R_th, giving P_max = V_th^2/(4R_th).
- In AC, Z = R + jX, and S = VI* = P + jQ. Series resonance has f0 = 1/(2π√(LC)), minimum impedance Z = R, and Q = (1/R)√(L/C).
- An RC circuit reaches 63.2% of final value in one time constant τ = RC.
Worked example
A 24 V source feeds 6 Ω in series with a 12 Ω shunt branch. The load is connected across the 12 Ω branch. Open-circuit voltage: V_th = 24 × 12/(6 + 12) = 16 V. Kill the source: R_th = 6 || 12 = 4 Ω. For maximum power, R_L = 4 Ω and P_max = 16^2/(4 × 4) = 16 W.
Traps
Do not deactivate dependent sources. Do not mix peak and RMS values in power calculations. Do not use superposition for power. For parallel resonance, impedance is maximum, not minimum.