2i 6 ALTERNATING CURRENTS 



or 



W W\ Wi W , , N S 



= - , so that w = (w Wi) 



s Si si s 's si 



But since w Wi total output of generator = Vi + ri 2 , we 

 have 



w = - -(Vi + ri 2 ) (2) 



Thus w, the total mechanical power of the motor, becomes known. 

 In order to find its useful or brake-power, we have to determine 

 the power Wj corresponding to the rotor Motional loss at the speed 

 for which the total mechanical power of the motor is w. Let iy be 



the corresponding torque. Then we have = = . To find the 



w Tf 



latter ratio, we remove the belt, allow the motor to run light, and 



S 11) ^ 



measure its slip s . Then =- = - so that = . Proceeding as 



T/ Sf Wf 8 



before, we find 



brake-power of motor = w w/ = (s s/)-^ = (s s/) 



or, using (2) 



brake-power = ^(Vt + ri 2 } 



s Si 



The brake-power being known, the efficiency is at once obtained 

 by dividing it by the total power supplied to the motor, as measured 

 by the two-wattmeter method. 



Now, in rough measurements, it would not be necessary to 

 measure the slip corresponding to any other value of the load in 

 order to find the brake-power. For, using the same method as 

 before, we find 



losses of generator with belt = w\ Wf = - ~(Vi + ri 2 ) . (3) 



s ~ s 



and hence 



brake-power = total output of generator + losses in belt and generator 



Thus the brake-power is obtained by simply adding to the total 

 generator output the value of the losses as given by (3), the assump- 

 tion being made (which is obviously not quite correct) that these 

 losses are constant within the working range of the motor speed. 



