Electrical Circuit Theory and Analysis
What this domain tests
Circuit Theory and Analysis checks whether you can apply Kirchhoff's laws, reduce networks, analyse first-order transients, and handle AC and three-phase power with correct sign conventions.
Core rules
- KCL: the algebraic sum of currents at a node is zero. KVL: the algebraic sum of voltages around a loop is zero. Adopt the passive sign convention and keep it.
- Superposition, Thevenin and Norton apply only to linear circuits. To find Thevenin resistance, kill independent sources: voltage sources become short circuits, current sources become open circuits. Dependent sources stay in the circuit and are handled by test-source methods.
- Maximum power transfer to a resistive load occurs at R_L = R_th; efficiency at that point is 50%.
- First-order transient: tau = RC or L/R; after 5 tau the response is within about 1% of final value.
- Impedance: Z_R = R, Z_L = j omega L, Z_C = 1/(j omega C). Complex power S = P + jQ = V I*; power factor = cos phi.
- Balanced three-phase: total power = sqrt(3) V_LL I_L cos phi.
Worked example
A 12 V source feeds 4 ohm in series then 6 ohm to return. Find the Thevenin equivalent at the 6 ohm terminals and the maximum load power. V_th is the open-circuit voltage across 6 ohm: 12 x 6/(4+6) = 7.2 V. R_th is 4 ohm in parallel with 6 ohm: 2.4 ohm. Maximum power = V_th^2/(4 R_th) = 51.84/9.6 = 5.4 W.
Traps
- Applying superposition to power: power is nonlinear, so add currents or voltages first, then calculate power.
- Omitting the j in reactive impedances, or mixing peak and RMS values.
- Reversing a dependent source sign while killing independent sources.
- Confusing maximum power transfer with maximum efficiency.