DC Cable Size and Voltage Drop

Calculations

{"type":"doc","attrs":{"background":{"dim":11,"id":"none"}},"content":[{"type":"heading","attrs":{"level":1},"content":[{"type":"text","text":"Cable size and voltage drop (DC, 12 V / 24 V / 48 V)"}]},{"type":"paragraph","content":[{"type":"text","text":"Too thin a cable wastes power and heats up. Check before you buy."}]},{"type":"heading","attrs":{"level":2},"content":[{"type":"text","text":"Inputs"}]},{"type":"numbox","attrs":{"code":"systemVoltage = 12 V\nloadPower = 300 W"}},{"type":"heading","attrs":{"level":2},"content":[{"type":"text","text":"Length one way, the current flows there and back"}]},{"type":"numbox","attrs":{"code":"cableLength = 5 m\ncrossSection = 6 mm^2"}},{"type":"paragraph","content":[{"type":"text","text":"Annealed copper at 20 C: 1/58 ohm mm^2/m (IEC 60028 standard value), warm cables have about 20 % more"}]},{"type":"numbox","attrs":{"code":"copperResistivity = 0.0172 ohm mm^2 / m\nmaxDrop = 3 %"}},{"type":"heading","attrs":{"level":2},"content":[{"type":"text","text":"Current and resistance"}]},{"type":"numbox","attrs":{"code":"current = loadPower / systemVoltage to A\nresistance = copperResistivity * 2 * cableLength / crossSection to ohm"}},{"type":"heading","attrs":{"level":2},"content":[{"type":"text","text":"Voltage drop"}]},{"type":"numbox","attrs":{"code":"drop = current * resistance to V\ndropShare = drop / systemVoltage\nlostPower = current^2 * resistance to W"}},{"type":"paragraph","content":[{"type":"text","text":"Is this cable big enough? Smallest cross section for the allowed drop"}]},{"type":"numbox","attrs":{"code":"neededCrossSection = copperResistivity * 2 * cableLength * current / (maxDrop * systemVoltage) to mm^2"}},{"type":"paragraph"}]}