Derive the formula of the heat energy produced in the conductor because of electric current flows in it for the relax time-interval .t.. Give its unit.

Explanation

A metallic conductor (or a resistance wire) offers resistance to the flow of current, so work must be done by the current-source for a continuous flow of electric current through a conductor.

Consider a current I flowing through a resistor (or conductor) of resistance R. Let V be the potential difference across the resistor (see figure).
Let t be the time-interval during which a charge Q flows through the resistor (conductor).
The work done by the current source in moving charge Q through a potential difference V is vg.
Therefore, the current source must supply energy to the circuit equal to VQ in time t.
Thus, energy spent by the source or the work done by the source,
`W = VQ`
`= V ("It") ( :. I = Q/t)`
`=(IR) ("It")` (By the Ohm.s law V =IR)
`:. W = I^2Rt... ....(12.15)`
This electrical energy gets dissipated as heat in the resistor. Thus for a steady current I, the amount of heat H generated (produced) in time- interval t is
`H = I^2 Rt`.......(12.16)
This is known as the Joule.s law of heating.
The SI unit of electrical energy and heat energy is the joule (J). Its other units are watt-second (Ws) and kilowatt-hour (kWh) or unit (commercial unit for electrical energy).