Ohms Law Calculator

Ohm's law states that for a linear conductor the current through it is proportional to the potential difference across it, V equals I times R, where resistance R is the constant of proportionality measured in ohms. Physically, resistance arises because charge carriers drifting under an applied field scatter off lattice vibrations and impurities; the material property behind it is resistivity, about 1.68 times ten to the minus 8 ohm-metres for copper at 20 degrees C. Combining this with Joule heating, P equals V times I, generates the four-quantity power wheel used here: substituting V equals IR gives P equals I squared R, and substituting I equals V/R gives P equals V squared over R. Knowing any two of the four quantities fixes the other two. Practical ranges span many decades. Signal circuits work at microamps to milliamps, a typical indicator LED draws 20 mA, a US branch circuit is protected at 15 or 20 A on 120 V, and resistor values commonly run from a few ohms to several megohms in the E12 and E24 preferred-value series. Two limitations matter most. First, the law is not universal: it holds only for ohmic materials, and diodes, transistors, thermistors, and gas discharge lamps all have non-linear V-I curves. Second, resistance varies with temperature, roughly 0.4 percent per degree C for copper, so a conductor carrying heavy current has higher resistance than its cold rating. In AC circuits with capacitance or inductance, resistance must be replaced by complex impedance and real power becomes V times I times the cosine of the phase angle.

Georg Simon Ohm was a schoolteacher in Cologne when he ran the experiments that produced the law, using a thermocouple as a stable voltage source, since the voltaic piles then available drifted badly, and a torsion balance galvanometer of the kind Coulomb had developed to measure current. He published Die galvanische Kette, mathematisch bearbeitet in Berlin in 1827, framing the result by explicit analogy with Fourier's treatment of heat conduction. The reception was hostile: German academic physics of the period favoured qualitative Naturphilosophie over mathematical empiricism, and Ohm resigned his post in frustration. Recognition came slowly from abroad, and the Royal Society awarded him the Copley Medal in 1841, after which he obtained a professorship at Munich in 1852. Henry Cavendish had in fact found a similar relationship in the 1770s using his own body as the ammeter, judging shock strength, but left the work unpublished until James Clerk Maxwell edited his papers in 1879, long after Ohm had priority in print. James Prescott Joule established the heating relationship independently around 1841, supplying the power half of the wheel. Standardisation followed the growth of telegraphy: the International Electrical Congress meeting in Paris in 1881 adopted the ohm as the practical unit of resistance, initially realised as the resistance of a specified column of mercury, and the modern definition arrived with the coherent SI system.