Derive an expression for heat produced in a conductor using Joule's law of heating.

Explanation

Let 'V' be the potential difference applied across the two terminals of a resistor of resistance 'R' by a cell and 'I' be the current flowing through the resistor in time 't'.
ii. If charge Q flows through the resistor, then the electrical power 'P' is given by
`P=("Energy")/("time")" ...(1)"`
where, energy is the work done by cell to move charge Q across the resistor
`therefore" Energy " = VxxQ" ...(2)"`
`therefore" P"=(VQ)/(t)" ....[from equations (1) and (2)]"`
`=VI" ..."(because(Q)/(t)=I)" ....(3)"`
iii. The cell provides the energy to the resistor which is converted into heat energy, given by
`H=Pxxt=VxxIxxt" ...[from (3)](4)"`
iv. According to Ohm's law,
`V=IR" ...(5)"`
From equation (4) and (5),
`H=(V^(2)t)/(R) or H=I^(2)Rt`
This is called as Joule's law of heating.