Circuit Analysis
Core concepts
Circuit analysis questions reward a systematic approach: identify the unknown, then choose node-voltage, mesh-current, superposition, or Thevenin/Norton as appropriate. For sinusoidal steady state, convert sources to phasors, work in impedance (Z_R = R, Z_L = jωL, Z_C = 1/(jωC)), and remember the result is RMS only if the source was RMS. Series resonance occurs at ω₀ = 1/√(LC), where impedance is purely resistive and current is maximum; parallel resonance gives maximum impedance. Transients follow first-order exponentials with τ = RC or τ = L/R, reaching 63.2 % of final value in one time constant. Three-phase loads may be wye or delta; convert with Z_Y = Z_Δ/3 before combining.
Traps to expect
Peak versus RMS confusion is routine - a "120 V" source means RMS, and peak is √2 times that. Sign errors arise from the passive sign convention and from forgetting that capacitor impedance carries a negative angle. In superposition, turn off voltage sources by shorting them and current sources by opening them, and never deactivate dependent sources. Average power is dissipated only in resistors; ideal inductors and capacitors exchange energy but consume no real power.
Worked example
A series RLC with R = 10 Ω, L = 10 mH, C = 10 µF: f₀ = 1/(2π√(LC)) = 1/(2π√(1×10⁻⁷)) ≈ 503 Hz. At resonance Z = 10 Ω, so with a 100 V RMS source the current is 10 A RMS and real power is I²R = 1000 W. Off resonance the impedance magnitude exceeds 10 Ω, so current and power both fall.