Mathematical Expression for Heat Produced
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Potential difference is a measure of work done in moving a unit charge across a circuit. Current in a circuit is equal to the amount of charge flowing in one second.
Therefore, the work done in moving 'Q' charges through a potential difference 'V' in a time 't' is given by
Work done = potential difference x current x time
W = VIt
The same can be expressed differently using ohm's law.
According to ohm's law V = IR
Therefore work can be expressed as
W = VIt
or W = (IR) It = I
2Rt

Thus, heat produced is directly proportional to the resistance, to the time and to the square of the current.
Application of the Heating Effect of Current
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The heating effect of current is utilized in electrical heating appliances such as electric iron, room heaters, water heaters, etc. All these heating appliances contain coils of high resistance wire made of nichrome alloy. When these appliances are connected to power supply by insulated copper wires then a large amount of heat is produced in the heating coils because they have high resistance, but a negligible heat is produced in the connecting wires because the wires are made to have low resistance.

The heating effect of electric current is utilized in electric bulbs for producing light. When electric current passes through a thin high resistance tungsten filament of an electric bulb, the filament becomes white hot and emits light.
An 'electric fuse' is an important application of the heating effect of current. When the current drawn in a domestic electric circuit increases beyond a certain value, the fuse wire gets over heated, melts and breaks the circuit. This prevents fire and damage to various electrical appliances.