PEC EPE Electrical cheat sheet

Three-phase power: P = √3·V_L·I_L·cosφ; reactive power Q = √3·V_L·I_L·sinφ; apparent power S = √3·V_L·I_L.

Per-unit system: Z_pu = Z_actual/Z_base, with Z_base = V_base²/S_base for single-phase and V_base²/S_base for three-phase line-to-line values.

Transformer efficiency peaks when copper loss equals core loss; maximum efficiency condition: I²R_cu = P_core.

Synchronous machine: induced EMF E = 4.44·f·Φ·T·k_w; synchronous speed n_s = 120f/P rpm.

Induction motor slip s = (n_s − n_r)/n_s; rotor frequency f_r = s·f; torque ∝ s·V² near synchronous speed.

DC machine EMF: E_g = (P·Φ·N·Z)/(60·A); developed torque T = (P·Φ·I_a·Z)/(2π·A).

Transmission line short-line model: V_s = V_r + I_r·Z; regulation = (|V_r,noload| − |V_r,full load|)/|V_r,full load|.

Power factor correction: capacitor kVAR = P·(tanφ₁ − tanφ₂) to raise power factor from cosφ₁ to cosφ₂.

Protection: inverse-time overcurrent coordination uses time-multiplier and pickup settings; CT ratio and burden must keep relay within accuracy class.

Kirchhoff's laws: ΣI at a node = 0; ΣV around a loop = 0; superposition applies only to linear circuits.

Thevenin equivalent: V_th = open-circuit voltage; R_th = equivalent resistance with sources deactivated (voltage sources shorted, current sources opened).

Resonance: series resonance at f₀ = 1/(2π√(LC)); at resonance X_L = X_C and impedance is purely resistive.

Maximum power transfer occurs when load resistance equals source resistance (R_L = R_th) for resistive networks.

Norton equivalent: I_N = short-circuit current; R_N = R_th; convert with V_th = I_N·R_th.

RMS value of sinusoid = peak/√2; average value of full-wave rectified sinusoid = 2·peak/π.

Balanced three-phase Y load: line voltage = √3 × phase voltage; line current = phase current.

First-order transient: time constant τ = RC for capacitive circuits and τ = L/R for inductive circuits; reaches 63.2% in one τ.

Cable sizing considers ampacity, voltage drop (≤ ~3% typical for feeders), short-circuit withstand, and derating for temperature and grouping.

Earth fault loop impedance must be low enough to trip protective devices within the required disconnection time.

Motor starting: direct-on-line current is typically 5–8× full-load current; star-delta reduces starting current to one-third.

Earthing systems: TN-S, TN-C-S, TT, and IT differ in how neutral and protective earth are arranged; TT requires RCD protection.

Insulation resistance testing uses a DC voltage (commonly 500 V or 1000 V) and results are recorded in MΩ; minimum acceptable values depend on installation standard.

Cable voltage drop: ΔV = (2·I·L·R)/1000 for single-phase and √3·I·L·R/1000 for three-phase, with R in Ω/km.

Circuit breaker selection: rated current ≥ design current; breaking capacity ≥ prospective short-circuit current at the point of installation.

Lighting design uses lumen method: N = (E·A)/(Φ·UF·MF), where E is illuminance, A area, Φ lumens per luminaire, UF utilization factor, MF maintenance factor.

Digital logic: De Morgan's laws (A·B)' = A' + B' and (A + B)' = A'·B'; used to simplify Boolean expressions.

Flip-flops: SR, JK, D, and T; JK with J = K = 1 toggles; D flip-flop output follows input on the clock edge.

Analog-to-digital conversion: resolution = V_ref/2^n; quantization error ≤ ±½ LSB.

PID controller: u(t) = K_p·e + K_i∫e dt + K_d·(de/dt); integral action removes steady-state error, derivative action adds damping.

Sampling theorem: sampling frequency must exceed twice the highest signal frequency (Nyquist rate) to allow reconstruction.

Transfer function of a first-order low-pass filter: H(s) = 1/(1 + sRC); cutoff frequency f_c = 1/(2πRC).

Op-amp ideal assumptions: infinite open-loop gain, infinite input impedance, zero output impedance; virtual short applies under negative feedback.

PLC scan cycle: input scan → program execution → output update; scan time affects response to fast events.