In a conductor, due to thermal agitation, the free electrons are always at random motion making collisions with ions or atoms of the conductor. When a voltage V is applied between the ends of the conductor, resulting in the flow of current I, the free electrons are accelerated. Hence the electrons gain energy at the rate of VI per second. The lattice ions or atoms receive this energy from the colliding electrons in random bursts. This increase in energy is nothing but the thermal energy of the lattice.

Thus for a steady current I, the amount of heat H produced in time t is

H = VIt …..… (1)

For a resistance R,

H = I^{2}Rt …….. (2) and

H =(V^{2}/R) t ………(3)

*The above relations were experimentally verified by Joule and are known as Joule’s law of heating. *

With the help of equation (2) above we can state Joule’s law. From this equation we find the following:

H α I^{2}

H α R

H α t

## Joule’s law – Heating effect of electric current | Joule’s law statement, formula

Joule’s law of heatingstates that the heat produced due to electric current is (i) directly proportional to the square of the current for a given Resistance (ii) directly proportional to resistance for a given current and (iii) directly proportional to the time of passage of current.Joule’s law of electrical heating can be expressed by the equationH = Iwhere H is the heat caused by an electric current, I through a conductor of resistance, R for a time, t.^{2}Rt,

Also by the equation (3) above, H =(V^{2}/R) t, the heat produced is inversely proportional to resistance for a given Voltage (PD) applied between the ends of the conductor.

### Verification of Joule’s law

Joule’s law is verified using Joule’s calorimeter. It consists of a resistance coil enclosed inside a copper calorimeter.