# Derive an expression for the heat produced by electric current and state Joule's law.

When a charge Q moves between two points whose potential difference is V, the amount of work done is given by

$W = Q \times V$

We know, current, $I = \frac{Q}{t}$

So, $Q = I \times t$

From Ohm’s law, we have $V = I \times R$

Let us substitute the values of Q and V, in the Work done formula.

$W = I \times t \times I \times R$

$W = I^2Rt$

This work done is converted into heat energy.

So, Heat produced, $H = I^2Rt \ joules$

This relation is known as joule’s law of heating.

Joule's law of heating states that heat produced in joules when a current of I amperes flows in a wire of resistance R ohms for time t seconds is given by $H = I^2Rt$.

Thus the heat produced in a wire is directly proportional to:

(i) Square of current

(ii) Resistance of the wire

(iii) Time for which current is passed

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Updated on: 10-Oct-2022

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