Network Theory and Electrical Fundamentals
What this domain tests
This domain covers DC and AC circuit laws, network theorems, phasors, impedance, resonance, power, and basic electrical fundamentals. Numerical questions often reduce to identifying the right theorem and applying it cleanly.
Core concepts
- KCL: algebraic sum of currents at a node is zero. KVL: algebraic sum of voltages around a closed loop is zero.
- Thevenin's theorem replaces a linear network by Vth in series with Rth. Norton's theorem uses IN in parallel with RN, where RN = Rth and IN = Vth/Rth.
- Superposition applies to linear circuits with multiple independent sources; turn off one source at a time (voltage source shorted, current source opened).
- In AC, impedance Z = R + jX. Inductive reactance XL = 2πfL; capacitive reactance XC = 1/(2πfC). Series resonance occurs at f = 1/(2π√(LC)), where XL = XC and impedance is minimum.
- RMS value = peak/√2 for a sine wave. Real power P = VI cosφ; power factor is cosφ.
Worked example
A 10 V source feeds a 2 kohm resistor in series with a 3 kohm resistor to ground. The open-circuit voltage across the 3 kohm resistor is Vth = 10 × 3/(2 + 3) = 6 V. Looking back, Rth = 2 kohm || 3 kohm = 1.2 kohm.
Traps
Do not apply superposition to power or to non-linear circuits. Dependent sources are not turned off like independent sources. Distinguish RMS from peak when calculating power. An ideal voltmeter has infinite resistance; an ideal ammeter has zero resistance.
Key points
- Thevenin: Vth in series with Rth.
- Norton: IN = Vth/Rth in parallel with Rth.
- Resonance: XL = XC and impedance is minimum.
- Sine RMS = peak/√2.
- P = VI cosφ.