If V is the potential difference applied across a metallic conductor of resistance R, the current through the conductor, given by Ohm’s law, is I = V/R ……(1)
The charge passing through the conductor in time t when the current I flows in the conductor is Q = It…….(2)
The work done in this process is W = VQ …..(3)
From Eqs. (1), (2) and (3), we have,
W = (IR) (It) = I2Rt = VIt
= \(V(\frac{V}{R})t=\frac{V^2}{R}t\)
This work is converted into heat.
When I is expressed in ampere, R in ohm, t in second and V in volt, W is expressed in joule. In that case,
W = I2Rt = VIt = \(\frac{V^2}{R}\) t (in joule)
Usually heat energy (H) is expressed in calorie. Using the relation 4.18 J = 1 cal, we have
This is the required equation.
