He was a native of Göttingen, the son of the Royal Hanovarian director general of schools Friedrich Kohlrausch. He was a high-school teacher of mathematics and physics successively at Lüneburg, Rinteln, Kassel and Marburg. In 1853 he became an associate professor at the University of Marburg, and four years later, a full professor of physics at the University of Erlangen.
In 1854 Kohlrausch introduced the relaxation phenomena, and used the stretched exponential function to explain relaxation effects of a discharging Leyden jar (capacitor). In 1856, with Wilhelm Weber (1804-1891), he demonstrated that the ratio of electrostatic to electromagnetic units produced a number that matched the value of the then known speed of light. This finding was instrumental towards Maxwell's conjecture that light is an electromagnetic wave. Also, the first usage of the letter "c" to denote the speed of light was published in an 1856 paper by Kohlrausch and Weber.
He was the father of physicist Friedrich Kohlrausch.
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