Electrical formulas Formulas Required conductor cross section for electric cables given Direct current Voltage drop, current Voltage drop, power Voltage drop, current Voltage drop, voltage 200 · L · I γ · u0 · U 200 · L · P γ · u0 · U2 200 · L · I2 γ · p0 · P 200 · L · P γ · p0 · U2 Single phase alternating current 200 · L · I · cosϕ γ · u0 · U 200 · L · P γ · u0 · U2 200 · L · I2 γ · p0 · P 200 · L · P γ · p0 · U2 · cos2ϕ Three phase alternating current 173 · L · I · cosϕ γ · u0 · U 100 · L · P γ · u0 · U2 300 · L · I2 γ · p0 · P 100 · L · P γ · p0 · U2 · cos2ϕ Key I = Current in ampère A = Conductor cross section in mm2 γ = Conductivity (copper 56, aluminium 34) uo = Voltage drop in % of the operating voltage L = Conductor lengths (single) in meters U = Operating voltage in volts P = Transmission power in watts cos ϕ = Power factor (usually assumed to be 0.8) po = Power loss in % of the transmission power The formulas stated for alternating and three-phase current do not give any consideration to the inductive resistance. This resistance is a function of the distance of the individual conductors between one another. Determination of the current if the power is known. Direct current: I = P U · η P = Rated power in W U = Voltage in V l = Current in A η = Efficiency Alternating current: l = P U · cosϕ · η P = Rated power in W U = Voltage in V l = Current in A cos ϕ = Phase shift η = Efficiency Three phase current: l = P 1.73 · cosϕ · η · U P = Rated power in W U = Voltage in V l = Current in A cos ϕ = Phase shift η = Efficiency Example: What is the current that a heating unit of 3.4 kW absorbs at 440 V? (η = 1) I = 3400 440 · 1 = 7.7 A Example: What is the current consumption of an alternating current motor of 1.9 kW at cos ϕ = 0.77 and an efficiency of 79 %? The voltage is 230 V, 50 Hz. I = 1900 230 · 0.77 · 0.79 = 13.6 A Example: What current does a three phase motor of 22 kW consume at 400 V, 50 Hz, with cos ϕ = 0,89 and an efficiency of 90 %? I = 22000 1.73 · 400 · 0.89 · 0.9 = 39.7 A 70 HUBER+SUHNER Wires and cables
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