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 this relation known?

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Answer

when an electric charge Q moves against a.p.d.V, the amount of work done is given by
W = Q × V .......(1)
We know, current, $\text{I}=\frac{\text{I}}{\text{T}}$
Q = I × t .....(2)
By ohm's law, $\frac{\text{V}}{\text{I}}=\text{R}$
V = I × R ........(3)
Putting eqs. (2) and (3) in eq (1),
W = I × t × I × R
$W = I^2RT$
Assuming that all the electrical work done is converted into heat energy, we get Heat produced, $H = I^2RT$ joules
This relation is known as Joule's law of heating,

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