20 ELEMENTS OF ELECTRICAL ENGINEERING. 



at/. Let Adf be the field intensity at p due to that element of the coil which is at 

 a distance x to the right of/, which element is of length Ax and has z Ax turns 

 of wire. Then from equation (8) we have : 



Integrating this expression from x=-\- aa to x= oo gives &C= 



14, Electrical resistance. Joule 's law. When an electric 

 generator produces an electric current in a circuit a part of the 

 work expended in driving the generator reappears as heat in the 

 various parts of the circuit. The electric current seems to be 

 opposed by a kind of resistance somewhat analogous to the 

 resistance which a pipe offers to the flow of water. A portion 

 of a circuit is said to have more or less resistance according as 

 more or less heat is generated in it by a given current. 



Joule's law. The rate at which heat is generated in a given 

 wire is proportional to the square of the current flowing in the 

 wire, or the amount of heat generated in a given wire is propor- 

 tional to the square of the current and to the elapsed time, that is 



H=RPt (11) 



in which H is the amount of heat generated by the current / in 

 t seconds, and R is a constant for the given wire. The constant 

 R, units-of-heat-per-(unit current) 2 -per-second, is adopted as the 

 numerical measure of the resistance of the wire, and it is called 

 the resistance of the wire. 



The c.g.s. unit of resistance. When in equation (n), H is 

 expressed in ergs,* 7 in c.g.s. units, and / in seconds, then R is 

 expressed in terms of a unit called the c.g.s. unit of resistance, or 

 the abohm. 



The Ohm. When in equation (i i), His expressed in joules,* 

 7 in amperes, and / in seconds, then R is expressed in ohms. 



* Heat is best expressed in terms of its energy value. Thus one erg of heat is the 

 quantity of heat which is the equivalent of one erg of work ; one joule of heat is the 

 quantity of heat which is the equivalent of one joule of work. There are 4. 2 joules 

 in one calorie. 



