Obtain the mathematical expression for the heat generated in a metallic condactor by electric current (Joule's law).

Explanation

If V is the potenial difference applied across a metallic given by Ohm's law, is
`I = V//R `
The charge passing through the conductor in timet when the current I flows in the conductor is Q= It .
The work done in this process is `W= VQ ` ….
`W = (IR)(It) = I^2 Rt = Vit = V(V/R) t = V^2 / R t `
This work is converted into heat.
When I is expressed in ampere, R in ohm, t in second and V in volt, W is expressed in joule. In that case,
`W =I^2 Rt+ V "It" = V^2/R t ` (in joule )
Usually heat energy (H) is expreseed in calorie. Using the relation 4.18 J = 1 cal , we have
`H = W =(I^2RT)/(4.18) (" in cal" ) =(V^2t)/(4.18R)("in cal" ) `
This is the required expression .