Joule’s law is a quantitative relationship between the quantity of heat produced in a conductor and an electric current flowing through it. The law is stated as H = RI², where “H” is the rate of evolution of heat in watts, the unit of heat being the joule; “R” is the resistance in ohms; and “I” is the current in amperes. Also, it is now known that the application of the law is not limited to metallic conductors.
The English scientist James Prescott Joule discovered the aforementioned law in 1841 while investigating the heat released by metals conducting electricity. Here is a diagram of the apparatus he used to conduct his experiment:
A mercury thermometer was used to measure the changing temperature of the water. This experiment was repeated with varying lengths and thicknesses of copper and iron wires and so the galvanometer needle deflected to various degrees depending on this. The results of this experiment were noted in his 1841 publication. In it, he states his concluding remarks, “We see, therefore, that when a current of voltaic electricity is propagated along a metallic conductor, the heat evolved in a given time is proportional to the resistance of the conductor multiplied by the square of the electric intensity.”
Here is a portrait of James Prescott Joule: