Electrical Circuits
Electrical Circuits is the backbone domain: it supplies the intuition used later in machines, power, control, and electronics. GATE EE tests nodal and mesh analysis, network theorems, transients, sinusoidal steady state, resonance, three-phase circuits, two-port parameters, and magnetically coupled circuits.
Core rules
- Nodal analysis uses KCL with conductances; a voltage source between two non-reference nodes forms a supernode.
- Thevenin: V_th is the open-circuit voltage at the terminals; R_th is found with independent sources killed (voltage sources shorted, current sources opened). With dependent sources present, apply a test source and take V_test/I_test.
- Superposition holds only for linear responses - never for power.
- First-order transient: x(t) = x(∞) + [x(0⁺) − x(∞)]e^(−t/τ), with τ = RC or L/R.
- AC maximum power transfer when Z_L = Z_th* (conjugate match), giving P_max = |V_th|²/(4R_th).
Worked example: a 10 V DC source feeds R = 1 kΩ in series with C = 1 µF, initially uncharged. τ = RC = 10³ × 10⁻⁶ = 1 ms, so v_C(t) = 10(1 − e^(−t/1 ms)). At t = 1 ms, v_C = 10(1 − e⁻¹) = 6.32 V. At the switching instant the capacitor behaves as a short, so the initial current is 10 mA; at steady state it is an open circuit and the current is zero.
Traps that cost marks
- Sign errors when writing the controlling variable of a dependent source into the test-source equations.
- Using peak values in power calculations: P = V_rms I_rms cos φ.
- At series resonance the circuit is purely resistive and the current peaks, but the voltage across L or C is Q times the source voltage.