Experimental Verification of Joule's Law of Heating

Joule in 1841 experimentally studied the heating effect of electric current. He found that the amount of heat, H produce in a conductor due to the flow of current,

(i)  is directly proportional to the square of the current flowing through the conductor i.e. H∝I² 

(ii) is directly proportional to the resistance across the conductor, H∝R

(iii)is directly proportional to time for which the current is passed, H∝t

Mathematically, 

H∝I² RT

H= I² RT/J

Where J is called Joule’s mechanical equivalent of heat. Its value is 1/4.2 calorie(cal) 

And it is a conversion factor only

Derivation

Expression of heat developed in a wire

When an electric charge Q moves against a p.d. V, the amount of work done is given by

W=Q×V                           ------------(1) 

We know, current, I=Q/t​
Q=I×t                               ------------(2)

By ohm's law,

V=I×R                             ------------(3)

Putting eqs. (2) and (3) in eq. (1),

W=Q×V

W=I×t×I×R
W=I²Rt

Assuming that all the electrical work done is converted into heat energy,(taking wire as passive resistor ), we get
Heat produced , H=I2Rt joules
This relation is known as Joule's law of heating.