Ohm's Law
Enter any two of voltage, current, and resistance — get the third plus power.
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The engineering
Ohm's law relates voltage, current, and resistance in a linear (ohmic) element. Give the card any two and it solves the triangle, plus the power dissipated.
Watch the power number: a 1 kΩ resistor at 24 V is only 0.58 W — but the same resistor at 120 V is 14.4 W, well past any common package rating.
Where this math comes from
Henry Cavendish measured the proportionality of current and voltage around 1781 — using his own body as the meter, judging current by the strength of the shock — but never published. The law waited for Georg Simon Ohm, a Cologne schoolteacher who worked through it with thermocouple sources and published Die galvanische Kette in 1827.
German academia initially savaged the book — one critic called it "a web of naked fancies" — and Ohm resigned his post. Vindication came slowly: the Royal Society awarded him the Copley Medal in 1841, and the unit of resistance now carries his name. The power row on this card belongs to James Prescott Joule, whose 1840s experiments tied electrical flow to heat.
- 1781Henry CavendishMeasures V–I proportionality using shocks to his own body; never publishes.
- 1827Georg Simon OhmPublishes Die galvanische Kette — V = IR, to initial ridicule.
- 1841James Prescott JouleQuantifies electrical heating — the P = VI power relation.
- 1841Royal SocietyAwards Ohm the Copley Medal; the law finally sticks.
See the full timeline of the math behind every calculator →
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