ELECTRICAL FUNDAMENTALS

DC follows V = IR, P = VI. AC adds reactance: X_L = 2πfL (inductor), X_C = 1/(2πfC) (capacitor), and impedance Z = sqrt(R² + (XL - XC)²). Power splits into real P (W), reactive Q (VAR), apparent S (VA): S = V·I, P = V·I·cosφ, Q = V·I·sinφ, where cosφ is power factor. Three-phase systems add a sqrt(3) factor: S₃φ = sqrt(3)·V_LL·I_L. RC charging follows V(t) = V_f·(1 - e^(-t/RC)).

• V = I·R; P = V·I (DC)
• Z = sqrt(R² + (XL - XC)²)
• PF = cosφ = P/S
• S₃φ = sqrt(3)·V_LL·I_L
• V(t) = V_f·(1 - e^(-t/τ)), τ = RC

References & StandardsIEEE Std 141 (Red Book), IEEE 519, NFPA 70

Use for any AC or DC circuit analysis: motor branch sizing, capacitor-bank power-factor correction, transformer rating, RC filter design, transient analysis of switch-on inrush. For three-phase loads, line-to-line voltage and line current relate by the configuration (wye or delta). Improve power factor with capacitors to reduce kVA demand.