138 ELEMENTS OF ELECTRICAL ENGINEERING. 

 Therefore : 



77* T 



Efficiency 



Differentiating this expression with respect to /, assuming L to be constant, and 

 placing the differential coefficient equal to zero, we find : 



which shows that the efficiency is a maximum when the sum of armature and series 

 field losses is equal to the sum of shunt field and stray power losses. 



The efficiency of a series generator is also zero at zero current 

 output, it increases with increase of current output, reaches a 

 maximum, and falls off with further increase of current output. 



The efficiency of a generator depends also upon its size. A 

 generator of one or two kilowatts rated capacity would have an 

 efficiency of about 65 per cent, at best, while very large generators 

 have efficiencies as high as 95 per cent., or even higher. 



68. Efficiency of a motor. The efficiency of a motor is defined 

 as the ratio : output of power divided by intake of power. This 

 ratio is sometimes called the true efficiency or the commercial 

 efficiency to avoid confusing it with the two partial efficiencies 

 defined later. 



Calculation of true efficiency. When the stray power loss of 

 a dynamo has been determined for a given speed and voltage, it 

 is easy to calculate the efficiency of the dynamo when operating 

 as a motor at the given speed and voltage, and supplied with a 

 specified intake * of electrical power ; the resistances of the vari- 

 ous windings of the dynamo being known. 



This calculation is based upon the equation : 



power intake losses 

 efficiency = - -. r 



power intake 



It is more instructive to discuss this matter of efficiency calcu- 

 lation by means of several typical examples than by deriving a 

 general formula. 



* The calculation of the efficiency of a motor for a specified output of power is 

 more complicated than for a specified intake of power or current. 



