Circuit Analysis and Network Theory
Circuit Analysis and Network Theory is the domain where ESECE checks whether you can turn a schematic into a solvable system and back again. Expect node and mesh formulation, source transformations, Thévenin and Norton equivalents, superposition, first- and second-order transients, sinusoidal steady state with phasors, and two-port parameters. The questions reward systematic sign discipline more than clever tricks.
Systematic formulation
- Node-voltage: choose a reference node, write KCL at every other node. A floating voltage source forces a supernode; write one extra constraint equation for its value.
- Mesh-current: use b − n + 1 independent windows. A current source shared by two meshes forces a supermesh plus a constraint.
- Dependent sources never disappear: keep them when finding R_th, and drive the dead network with a 1 V or 1 A test source to get R_th = V_test/I_test.
Equivalent circuits and power
Thévenin and Norton convert at any pair of terminals, with V_th = I_N·R_th. Maximum power transfer needs R_L = R_th and delivers P_max = V_th²/(4R_th). Superposition applies to voltages and currents only - never square a superposed current to obtain power.
Transients
First order: τ = R_th·C or L/R_th, and x(t) = x(∞) + [x(0⁺) − x(∞)]e^(−t/τ). Capacitor voltage and inductor current cannot jump. Second order: α = R/(2L) and ω₀ = 1/√(LC); ζ = α/ω₀ decides overdamped, critically damped, or underdamped ringing.
Worked example
A 10 V source drives 2 kΩ into a 1 µF capacitor that is initially uncharged; the switch closes at t = 0. Then τ = 2000 × 10⁻⁶ = 2 ms, v_C(∞) = 10 V and v_C(0⁺) = 0, so v_C(t) = 10(1 − e^(−500t)) V. For v_C = 6 V: e^(−500t) = 0.4, giving t = −ln(0.4)/500 = 1.83 ms. The resistor current at that instant is (10 − 6)/2000 = 2 mA.
Traps
Mixing resistor-sign conventions inside a supernode; applying superposition to power; reporting R_th from a network that still contains dependent sources; assuming capacitor voltage can jump when a switch throws; forgetting that a second-order circuit with a resistor across the capacitor has α = 1/(2RC) only in the parallel-only case.