Question

Write the mathematical expression for Joule’s law of heating.

Answer 1

Hint : To answer this question, we have to use the formula for the power developed in a conductor when a current is passed through it. Then using the formula of energy in terms of power, we will get the required expression of Joule’s law of heating.

Complete step by step answer
We know that when a voltage is applied across a conductor, current flows through it. This current is constituted by the free electrons flowing within the conductor. While flowing they collide with other electrons, and also with the atoms of the conductor. This collision results in the generation of heat. We all have experienced this heating in our day to day life. Whenever an electrical appliance is used for a long time, then it gradually gets heated up.
Joule found that the power of this heating, also called the rate of heating of the electrical conductor, is equal to the square of the current and also to the resistance, that is,
 $ P = {I^2}R $ .............(1)
Now, we know that the energy is related to the power by
 $ E = Pt $
From (1)
 $ E = {I^2}Rt $
Since the power is the power of heating, the energy obtained is the heat energy. So we get the mathematical expression for Joule’s law of heating as
 $ H = {I^2}Rt $ .

Note
The Joule heating is also known as Ohmic heating, or the resistive heating. This law finds its application in many of the electrical devices used. In electric fuses, this law is applied to find the current required for melting the fuse in order to break the circuit in emergency. An incandescent bulb glows when its filament is heated. This heating is governed by Joule heating.