Question

State Joule's law of heating.

Answer 1

Joule's law of heating

1. The passage of current through a conductor having a resistance is accompanied by the liberation of heat.
2. Suppose there exists a potential difference $V$ between the two ends of a homogeneous conductor of resistance $R$.
3. According to Ohm's law, the current is $I=\frac{V}{R}$.
4. The work done in taking $dq$ amount of charge from one end to the other is $dw=Vdq$.
5. Therefore, the rate at which energy is dissipated in the resistance is

$P=\frac{dw}{dt}=V\frac{dq}{dt}=VI=I^{2}R$

This is the expression of the well-known Joule's law.