Electrical Circuits and Network Theory
Electrical Circuits and Network Theory is the foundation domain: the exam tests steady-state DC and AC circuit analysis, network theorems, resonance, transients, and power concepts.
Core rules
- KCL: the algebraic sum of currents at a node is zero; KVL: the algebraic sum of voltages around a loop is zero.
- Series resistances add; parallel conductances add. For two resistors, R = R1R2/(R1+R2).
- Thevenin replaces a linear network by Vth in series with Rth; Norton by IN in parallel with RN, with RN=Rth and IN=Vth/Rth.
- Superposition applies only to linear circuits and switches one independent source at a time; dependent sources remain.
- Maximum power transfer to a resistive load occurs at RL=Rth, giving PL,max=Vth²/(4Rth) and 50% source efficiency.
- In AC, use phasors; X_L=2πfL, X_C=1/(2πfC); resonance at f=1/(2π√(LC)).
Worked example
A 12 V source feeds 6 Ω and 3 Ω in parallel. Equivalent resistance is 1/(1/6+1/3)=2 Ω. Total current is 12/2=6 A and total power is 12×6=72 W. The 6 Ω branch carries 2 A and the 3 Ω branch 4 A, confirming KCL.
Traps
Do not add parallel resistances directly; do not call average value RMS; watch passive sign convention; a source transformation must not move a dependent source's controlling variable.