Ohm Wheel Calculator

The Ohm wheel, or Ohm pie chart, is a compact statement that four DC quantities are algebraically closed under two relations. Ohm's law, V = I x R, and the power law, P = V x I, can be rearranged into twelve equivalent expressions, so knowing any two of voltage, current, resistance, and power determines the other two. The derived forms carry the practical weight: P = I squared x R gives heat dissipated in a conductor or resistor and drives wattage rating and wire gauge choices, while P = V squared / R is the convenient form when a fixed supply rail feeds a load and current is not measured. R = V squared / P is how a heating element or lamp resistance is inferred from its nameplate rating. Ohm's law is a description of a material, not a universal law of nature. It holds well for metals at constant temperature, where copper resistivity is about 1.68 x 10 to the minus 8 ohm-meters with a temperature coefficient near 0.00393 per degree C, meaning a conductor that warms 50 degrees rises roughly 20 percent in resistance. It fails outright for nonlinear devices: a diode follows an exponential relation, a tungsten filament can be ten times more resistive when hot than cold, and thermistors and electric arcs exhibit negative resistance regions. The relations here also assume steady DC. In AC circuits resistance must be replaced by impedance, which includes reactance from inductance and capacitance and introduces a phase angle, so power becomes V x I x power factor rather than simply V x I. A common practical rule is to select resistors rated at least twice the calculated dissipation.

Georg Simon Ohm carried out the defining experiments in Cologne in the mid 1820s. Voltaic piles of the period drifted badly, so Ohm switched to a thermoelectric junction of bismuth and copper as a stable source and used a torsion balance galvanometer to measure current through wires of varying length and cross section. He published Die galvanische Kette, mathematisch bearbeitet in 1827, presenting the proportionality between what he called electroscopic force and current. The work was received coldly in Germany, where the prevailing philosophical approach distrusted such mathematical treatment of nature, and Ohm resigned his teaching post. Recognition came from abroad: the Royal Society awarded him the Copley Medal in 1841, and he finally obtained a professorship at Munich in 1852. The power half of the wheel came from James Prescott Joule, who established in 1841 that the heat produced in a conductor is proportional to the square of the current times resistance, the result now called Joule's first law. Unit standardization followed the commercial spread of telegraphy and electric light: the International Congress of Electricians meeting in Paris in 1881 adopted the ohm, volt, and ampere as practical units, tying them to earlier work by the British Association committee on electrical standards. The circular pie chart layout itself is a twentieth century teaching device, popularized through trade school curricula, military electronics training manuals, and technician handbooks as a way to recall all twelve rearrangements without deriving them each time.