Question

Derive the expression for the heat produced due to a current ‘I’ flowing for a time interval ‘t’ through a resistor ‘R’ having a potential difference ‘V’ across its ends. With which name is this relation known ?

Answer 1

When an electric charge Q moves against a. p.d. V, the amount of work done is given by

w = Q x V ............(1)

we know, current, I = Q/t

Q = I x t ........(2)

By Ohm's law, V/I = R

V = I x R ............(3)

Putting eqs.(2) and (3) in eq, (1),

W = I x t x I x R

W = I²Rt

Assuming that all the electrical work done is converted into heat energy, we get

Heat produced, H = I²Rt Joules

This relation is knows as Joule's law of heating.