Derive the expression for the heat produced due to a current ‘I’ … - Vidyadip

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

✓

Answer

Work done in moving the charge W = VQ

Power input,

$\text{P} = \frac{VQ}{t}$

$= {VI}$

$\therefore \text{Eergy, E = P}\times t = \text{V I t}$

This energy gets dissipated in the form of heat.

$\therefore \text{H = V I t}$

Applying Ohm's law, we get,

$H = \text{I}^{2}Rt$

The relation is known as Joule's law of heating.
$\text{P = 12 W} {\text{ t = 1 minute = 60s}}$

$H = P \times t$

$\text{= 12 W} \times \text{60s}$

$\text{H = 720 J}$

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