JOULE'S LAW. 237 



electrical inertia seems to intervene in the phenomena of the perma- 

 nent state. 



If, on the other hand, the conductor is rigid, at any rate as a 

 mechanical whole, and if, finally, the current produces no external 

 work, the energy is necessarily spent in the conductor itself. 



244. JOULE'S LAW. Two cases may present themselves : either 

 the fall of potential between the points A and B is continuous, and 

 takes place in accordance with Ohm's law ; or there are, somewhere 

 between these two points, two adjacent surfaces between which there 

 is a sudden fall of potential, constant and independent of the strength 

 of the current that is to say, a constant electromotive force H. 

 The manner in which the electrical energy is distributed along the 

 conductor, depends on the law according to which the potential 

 varies, and is not identical in the two cases. Wherever the variation 

 of potential is continuous, energy is expended in a continuous 

 manner ; it is transformed into thermal energy, and gives rise to a 

 disengagement of heat along the conductor. Wherever there is a 

 sudden fall of potential, there is a sudden change of electrical 

 energy, which reveals itself either by some thermal phenomenon or 

 by some other equivalent physical effect. 



Let us first consider the former case, and let us suppose that 

 there are no variations of potential independently of the current. 

 If R is the resistance of the conductor between two points A and B, 

 Ohm's law gives 



The expression for the energy expended between the two points 

 is therefore 



W = IE = I 2 R = . 

 R 



Accordingly, the thermal energy developed in a conductor during 

 unit time, is equal to the product of the square of the current strength 

 into the resistance of the conductor. If Q be the quantity of heat, 

 such as is measured by calorimetrical methods, and J is the 

 mechanical equivalent of heat, we have 



The quantity of heat disengaged is proportional to the resistance of 

 the conductor, and to the square of the strength of the current. 

 This is Joule's law. 



