Question

Write Joule's law of heating

Answer 1

Hint: The Heat produced within a conductor due to flow of current (within an electric wire) is known as the heating effect of Joule.

Complete step-by-step answer:
Consider a current I flowing through a resistor of resistance R. Let the potential difference across it be 'V' and ‘t’ be the time during which a charge flows across. The work done in moving the charge Q through a potential difference V is VQ. Therefore, the source must apply energy equal to ‘VQ’ in time ‘t’.
Hence power input \[\left( P \right)=V\dfrac{Q}{t}=VI\]
As \[\dfrac{Q}{t}=I\]
Energy supplied to the circuit in ‘t’ time \[=P\times t=VIt\]
This amount of Energy is dissipated in the resistor as heat thus for a steady current I.
The amount of Heat H Produced in time \[H=IVt\]
\[\Rightarrow H={{I}^{2}}RT\]
This is known as Joule's law of heating.
The law implies that heat produced in a resistor is directly proportional to the square of current. For a given resistance, directly proportional to resistance for a given current and directly proportional to the time for which the current flows through the resistor.

Note: The amount of heat produced in a type of energy which is produced in current conducting wire is proportional to the square of the amount of current, the resistance of wire and time of current flowing.
Hence \[H={{I}^{2}}RT\]