# 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? - Science

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?

#### Solution

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.

Is there an error in this question or solution?

#### APPEARS IN

Lakhmir Singh Class 10 Physics (Science)
Chapter 1 Electricity
Q 21.1