⚡ Electrical formulas

Ohm's law and the power wheel

• V = I × R, I = V ÷ R, R = V ÷ I
• P = V × I = I² × R = V² ÷ R
• I = P ÷ V = √(P ÷ R); V = P ÷ I = √(P × R); R = V² ÷ P = P ÷ I²
• Units: volts (V), amperes (A), ohms (Ω), watts (W).

Series and parallel resistance

• Series: R_T = R1 + R2 + R3 … The current is the same through each, and the voltage divides.
• Parallel: 1/R_T = 1/R1 + 1/R2 + 1/R3 … The voltage is the same across each, and the current divides. For two resistors, R_T = (R1 × R2) ÷ (R1 + R2).
• Parallel total is always less than the smallest branch.

Voltage drop

Using the conductor's resistance per unit length (from the maker or a conductor resistance table, at operating temperature):

• Single-phase (2-wire): VD = 2 × I × R × L
• Three-phase: VD = √3 × I × R × L
• L is the one-way length and R is the resistance per the same length unit (for example Ω per km with L in km). % drop = VD ÷ supply voltage × 100.
• This ignores reactance, which is fine for small conductors at unity power factor. Allowed limits are set by code, so check the current CEC.

Single- and three-phase power

• Single-phase: P (W) = V × I × PF; apparent power S (VA) = V × I
• Three-phase: P = √3 × V_L × I_L × PF; S = √3 × V_L × I_L (√3 ≈ 1.732)
• PF = P ÷ S. Motor input current ≈ output W ÷ (√3 × V × PF × efficiency).

Transformer ratios

• For an ideal transformer, Vp ÷ Vs = Np ÷ Ns = Is ÷ Ip. Voltage goes down, current goes up.
• Full-load current: single-phase I = VA ÷ V; three-phase I = VA ÷ (√3 × V_L).
• Overcurrent protection and conductor sizing are code matters, so check the current CEC.