Electrical Circuits and Network Theory
Electrical Circuits and Network Theory is a high-yield ESE Prelims domain. Questions test node and mesh analysis, network theorems, first- and second-order transients, AC resonance, coupled circuits and two-port parameters. The exam favours compact numericals where one theorem or one initial condition decides the answer.
Core rules
- KCL and KVL hold for instantaneous, phasor and Laplace-domain variables; fix sign conventions before writing equations.
- Superposition applies only to linear circuits and cannot be used to compute power directly.
- Thevenin/Norton equivalent: independent sources are zeroed; dependent sources remain and are handled by test-source methods.
- For a first-order RC/RL circuit, the variable follows x(t)=x(infinity)+[x(0+)-x(infinity)]e^(-t/tau); capacitor voltage and inductor current cannot jump.
- Series resonance gives minimum impedance and unity power factor at omega0=1/sqrt(LC); parallel resonance is dual.
Worked example
A 10 V source feeds 5 ohm in series with 10 ohm to ground; terminals are across the 10 ohm. Remove the 10 ohm: Vth=10x10/(5+10)=6.667 V. Zero the source: Rth=5||10=3.333 ohm. Maximum power transfer to a variable load requires RL=Rth, so Pmax=Vth^2/(4Rth)=44.44/13.33=3.33 W. The reasoning is: open-circuit voltage, dead-source resistance, then conjugate match.
Traps
Do not zero dependent sources when finding Rth; do not apply maximum power transfer as an efficiency rule (efficiency is 50% at match); check t=0+ continuity; and remember that average power in a resistor is Irms^2R, not the sum of superposition powers.