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

 Since a conductor offers resistance to the flow of current, some work must be done by the current continuously to keep itself flowing. When an electric charge, Q moves against a potential difference, V, the amount of work done is given by:
          W = Q x V                (1) 

From the definition of current, we know that:
Current,`I=Q/t` 

So,`Q=1xxt`                      (2)         And from Ohm's law, we have:

`V/I=R`

or `V=IxxR`                       (2) 
 Now, substituting Q = I x t and V = I x R in equation (1), we get:
                      W = I x t x I x R
So, the work done, W = I² x R x t

Assuming that all the electrical work done is converted into heat energy:
Heat produced = Work done in the above equation
Thus heat produced, H = I² x R x t joules
This is known as Joule's law of heating.