Explanation Joule’s Law of Heating

Joule’s Law of Heating

Joule heating, also known as Ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.The heat which is produced due to the flow of current within an electric wire, is expressed in Joules. Now the mathematical representation or explanation of Joule’s law is given in the following manner.

i) The amount of heat produced in current conducting wire, is proportional to the square of the amount of current that is flowing through the circuit, when the electrical resistance of the wire and the time of current flow is constant.

i.e. H ∝ i² (When R & t are constant)

ii) The amount of heat produced is proportional to the electrical resistance of the wire when the current in the circuit and the time of current flow is constant. i.e. H ∝ R (when i & t are constant)

iii) Heat generated due to the flow of current is proportional to the time of current flow, when the resistance and amount of current flow is constant. i.e. H ∝ t (when i & R are constant) When these three conditions are merged, the resulting formula is like this –

Here ‘H’ is the heat generated in Joules, ‘i’ is the current flowing through the circuit in ampere and ‘t’ is in seconds. When any three of these are known the other one can be equated out.

Here, ‘J’ is a constant, known as Joule’s mechanical equivalent of heat. Mechanical equivalent of heat defined as the number of work units which, when completely converted into heat, furnishes one unit of heat.

Obviously the value of J will depend on the choice of units for work and heat. It has been found that

J = 4.2 joules/cal (1 joule = 10⁷ ergs) = 1400 ft. lbs./CHU = 778 ft. lbs/B Th U

It should be noted that the above values are not very accurate but are good enough for general work. Now according to Joule’s law I²Rt = work done in joules electrically when I ampere of current are maintained through a resistor of R ohms for t second.

By eliminating I and R in turn in the above expression with the help of Ohm’s law , we get alternative forms as