Derive the expression for the heat produced 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 the relation known? How much heat will an instrument of 12 W produce in one minute if it is connected to a battery of 12 V?

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Solution

Heat energy = power consumed × time

$∴ H = P \times t$

Let 'I' is the current flowing for a time interval 't' through a resistor 'R' having a potential difference 'V' across its ends.

Power = $I^{2} R$ or $\frac{V^{2}}{R}$

$∴ H = I^{2} R t$ or $\frac{V^{2}}{R} t$

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

Power of the instrument = 12 W

Time for which the instrument is used = 1 minute = 60 Seconds

Heat produced = $P \times t = 12 W \times 60 s = 720 J$

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