RESISTANCE AND ELECTROMOTIVE FORCE. 27 



ohms is never used because it is tedious and inaccurate. Practi- 

 cal methods for measuring resistance are described in Chapter X. 



> 



13. Power required to maintain a current in a circuit, expressed 

 in terms of resistance and current. When all of the energy 

 which is delivered to an electrical circuit by a generator reappears 

 in the circuit as heat, then the rate at which work is delivered to 

 the circuit by the generator is equal to the rate at which energy 

 reappears in the circuit as heat. Equation (2) expresses the 

 amount of heat in joules which appears in a circuit of wire in / 

 seconds ; dividing this amount of heat by the time /, gives the 

 rate at which heat appears in the circuit in joules per second 

 (watts), and this is equal to RP. Therefore the power P, in 

 watts, required to maintain a current of / amperes in a circuit 

 of which the resistance is R ohms, is 



P=RP (3) 



14. Dependence of resistance upon length and size of a wire. 



The resistance R of a wire of given material is directly propor- 

 tional to the length / of the wire and inversely proportional to 

 the sectional area s of the wire ; that is, 



R = k l - (4) 



in which k is a constant for a given material ; it is called the 

 resistivity * of the material. The exact meaning of the factor k 

 may be made apparent by considering a wire of unit length 

 (/= i) and unit sectional area (s = i). In this case k is 

 numerically equal to R, that is to say, the resistivity of a 

 material is numerically equal to the resistance of a wire of that 

 material of unit length and unit sectional area. Electrical engi- 

 neers nearly always express lengths of wires in feet and sectional 

 areas in circular mils.f If equation (4) is to be used to calculate 



* Sometimes called specific resistance. The reciprocal of the resistivity of a sub- 

 stance is called its conductivity. 



f One mil is a thousandth of an inch. One circular mil is the area of a circle of 

 which the diameter is one mil. The area of any circle in circular mils is equal to the 

 square of the diameter of the circle in mils. > 



