In this section, we will discuss on the Joule's Law of Heating.
In 1841, Joule studied the heating effect of an electric current. He found that, the amount of heat $H$ is produced when an electric current is passed through a conductor after a certain time, called Joule's Heating Effect.
$H = I^2\,R\,t$ .......... (i)
Where, $H$ = amount of heat; $I$ = flow current through a conductor; $R$ = Resistance; $t$ = time taken.
Many electrical devices such as electric heater, soldering iron, electric iron, electric bulb etc. are the example of Joule's heating effect.
Iron used to remove wrinkles from Clothes
Soldering iron, used to melt solder
Mathematically;
1) The amount of heat produced in current conducting wire, is proportional to square of the current flow through the circuit, at constant electrical resistance and time of current flow.
i.e. $H ∝ I^2$ .......... (ii)
2) The amount of heat produced is proportional to the electrical resistance of the wire, at constant current and time of current flow.
i.e. $H ∝ R$ .......... (iii)
3) The amount of generated heat due to a flow of current is proportional to the time of current flow, at constant electrical resistance and amount of current flow.
i.e $H ∝ t$ .......... (iv)
When all these 3 - situation are put together, the resulting formula is,
$H ∝ I^2\,R\,t$
or, $H = \frac{ I^2\,R\,t}{J}$ .......... (v)
Where, $J = 4.18\, J\,cal^{-1}$ is called Joule's Mechanical Equivalent of Heat. It is a conversion factor only.
Expression of Heat developed in a wire:
Let $I$ be the current passing through the resistance, at time $t$. The total charge passing through $A$ to $B$ is,
$Q = I\,t$ (∵$ I = \frac{Q}{t}$) .......... (i)
Potential difference ($V$) between $A$ to $B$ is,
$V = I\,R$ .......... (ii)
Work done to transfer the charge $Q$ from point $A$ to $B$ is,
$W = Q\,V$ .......... (iii)
From equation (i), (ii) and (iii), we get
$W = I\,t. I\,R$
or, $W = H = I^2\,R\,t$ .......... (iv)
This equation (iv) is the expression for heat developed.
Let $I$ be the current passing through the resistance, at time $t$. The total charge passing through $A$ to $B$ is,
