ELEMENTARY ELECTRICITY AND MAGNETISM. 21 



That is, a wire has a resistance of one ohm when one joule of 

 heat is generated in it per second by one ampere of current. 

 One ohm is equal to io 9 abohms. 



Specific resistance. The resistance of a wire is proportional to 

 the length of the wire and inversely proportional to the sectional 

 area of the wire. That is : 



R = P-- S (12) 



in which R is the resistance of a wire of given material, / is the 

 length of the wire, s is the sectional area of the wire, and p is a 

 constant which is called the resistivity or specific resistance of the 

 material of which the wire is made. The specific resistance is the 

 resistance of a wire of unit length and of which the sectional area 

 is unity. Electrical engineers ordinarily express length of wire 

 in feet and sectional area in circular mils. In this case p is the 

 resistance of a wire one mil in diameter and one foot long ; the 

 " mil-foot " of wire as it is sometimes called. The resistance of 

 a mil-foot of ordinary commercial copper wire at ordinary room 

 temperature is about 10.8 ohms. 



Influence of temperature on resistance. The resistance of a 

 wire depends not only upon length, size and material, but also 

 upon temperature. Most metallic wires increase in resistance 

 with rise of temperature. 



The increase of resistance of a given wire due to a rise of tem- 

 perature is proportional to the initial resistance and approximately 

 proportional to the rise of temperature ; that is, if ^ is the resist- 

 ance of a wire at some standard temperature, say o C, then the 

 increase of resistance when the wire is heated to / C. is equal 

 to f$R Q t, where & is a proportionality factor. Therefore the total 

 resistance R t of the wire at t C. is R t = R Q +0RJ, or 



* ( = K (i+#) (13) 



The quantity /3 is called the temperature coefficient of resist- 

 ance of the given material. For many pure metals ft has nearly 



