U = R · I and P = U · I are the foundation of all electrical calculation. Here is the relationship between voltage, current, resistance and power — with practical examples and an explanation of what cos φ does to the power in AC.
Introduction
Ohm's law links voltage (U, volts), current (I, amperes) and resistance (R, ohms): U = R · I. If you know two of them, you can always find the third.
Power
Example: A 230 V heating element with 50 Ω resistance draws I = 230/50 = 4.6 A and dissipates P = 230 · 4.6 ≈ 1058 W.
Alternating current and cos φ
For inductive or capacitive loads (motors, fluorescent fittings) current and voltage are phase-shifted. The real (active) power becomes P = U · I · cos φ, where cos φ is the power factor.
Series and parallel connection
Resistors rarely sit alone. Two basic configurations cover most: in series, the same current flows through all resistors, and voltage divides between them; in parallel, voltage is the same across all while current divides.
Eksempel (serie): Tre modstande på 10, 20 og 30 Ω i serie giver R = 60 Ω. På 230 V trækker kredsen I = 230/60 ≈ 3,83 A, og spændingen fordeler sig 38,3 V, 76,7 V og 115 V — størst spændingsfald over den største modstand.
Eksempel (parallel): To modstande på 10 Ω og 40 Ω parallelt giver R = (10 · 40)/(10 + 40) = 400/50 = 8 Ω — bemærk at resultatet altid er mindre end den mindste enkeltmodstand.
Kirchhoff's laws
Kirchhoff's two laws are the tools for circuits that are more than a simple series or parallel. Current law (junction law): the sum of currents entering a junction equals the sum leaving — no charge is lost. Voltage law (mesh law): the sum of voltages around a closed loop is zero — what you raise the voltage with in the source, you lose again across the resistances.
Resistivity and temperature
En leders modstand afhænger af materialet, længden og tværsnittet: R = ρ · L / A, hvor ρ er resistiviteten. Kobber har ρ ≈ 0,0175 Ω·mm²/m (dansk tabelværdi for ledningsevnen κ ≈ 56 ved 20 °C; regner man teoretisk 1/0,0175 giver det ≈ 57), aluminium ρ ≈ 0,028 Ω·mm²/m (κ ≈ 35). Aluminium leder altså kun ca. to tredjedele så godt som kobber ved samme tværsnit — derfor kræver et aluminiumskabel et større tværsnit for samme opgave.
Modstanden stiger med temperaturen. For kobber er temperaturkoefficienten α ≈ 0,0039 pr. K, så en leder, der varmes fra 20 °C til 70 °C, får ca. 20 % højere modstand: R_70 ≈ R_20 · (1 + 0,0039 · 50) ≈ R_20 · 1,20. Det er en af grundene til, at spændingsfald altid regnes ved driftstemperatur, ikke ved 20 °C.
Energy, consumption and money
Effekt gange tid er energi: E = P · t. Regnes P i kilowatt og t i timer, får du kilowatt-timer (kWh) — den enhed elregningen afregnes i.
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