We know that a battery or a cell is a source of electrical energy.
The chemical reaction within the cell generates the potential difference between its two terminals that sets the electrons in motion to flow the current through a resistor or a system of resistors connected to the battery.
We have also seen, in Section 12.2, that to maintain the current, the source has to keep expending its energy. Where does this energy go?
A part of the source energy in maintaining the current may be consumed into useful work (like in rotating the blades of an electric fan). Rest of the source energy may be expended in heat to raise the temperature of gadget.
We often observe this in our everyday life. For example, an electric fan becomes warm if used continuously for longer time etc. On the other hand, if the electric circuit is purely resistive, that is, a configuration of resistors only connected to a battery; the source energy continually gets dissipated entirely in the form of heat.
This is known as the heating effect of electric current. This effect is utilised in devices such as electric heater, electric iron etc. Consider a current I flowing through a resistor of resistance R. Let the potential difference across it be V (Fig. 12.13).
Let t be the time during which a charge Q flows across. The work done in moving the charge Q through a potential difference V is VQ. Therefore, the source must supply energy equal to VQ in time t. Hence the power input to the circuit by the source is
` P = V Q/t = V I` .........(12.19)
Or the energy supplied to the circuit by the source in time t is `P xx t`, that is, VIt. What happens to this energy expended by the source? This energy gets dissipated in the resistor as heat.
Thus for a steady current I, the amount of heat H produced in time t is
`H = V I t` ..........(12.20)
Applying Ohm’s law [Eq. (12.5)], we get
`H = I^2 Rt` .............(12.21)
This is known as Joule’s law of heating. The law implies that heat produced in a resistor is (i) directly proportional to the square of current for a given resistance, (ii) directly proportional to resistance for a given current, and (iii) directly proportional to the time for which the current flows through the resistor.
In practical situations, when an electric appliance is connected to a known voltage source, Eq. (12.21) is used after calculating the current through it, using the relation `I = V//R`.