CH. VI EFFICIENCY 133 



maximum and fall again to nothing at the point d. The 

 curve of total efficiency has also been plotted in the same 

 figure on a speed base. 



If ?7 3 is the total efficiency and t f the torque loss we 



have : 



71 r)(t-t t ) /R -~ 



"*=--;E- (o6) ' 



Assuming that t f is constant at all loads, and that M is 

 constant, this becomes 



c f cR Re 



where c f is the current at no load. Differentiating with 

 respect to c, and equating to nothing, we find that rj 3 is a 

 maximum when 



<*= (58). 



-i 



where c x = -=. Inserting this value of c in Equation 57, 



we find that the maximum efficiency is 



Example 34. A motor with an internal resistance 

 of O'l ohm takes 4 amperes when running on a line of 

 125 volts tension. The current for maximum efficiency is 

 70'7 amperes, the power is 8'35 k.w., and the total 

 efficiency is 89 per cent. 



The limiting value of c f is since the current c f 

 cannot be greater than that given by ~. When c f has 



