GENERAL THEORY OF THE INDUCTION MOTOR. 291 



Data to be used in connection with equations (i) to (v). The 

 values of r x and x^ may be determined from the calculated com- 

 ponents of the magnetizing current at zero load * as explained in 

 Art. 137, sections (ft) and (^). Thus we have 



+ x 



from which r^ and x^ may be calculated when M and M w and 

 E' are known. 



The value of R" may be determined as explained on page 287 

 under the heading " Calculation of equivalent resistance of the 

 rotor per stator phase." 



The value of R f may be determined by direct measurement of 

 resistance of the stator windings, and the value of X may be cal- 

 culated as explained on page 285 under the heading " Calculation 

 of magnetic leakage reactance per phase." 



Calculation of performance curves from equations (i) to (v). 

 Knowing the values of r r x v R" y E ', R f ', X t and ^, the de- 

 tails of the behavior of the motor when running at any arbitrarily. 

 assigned slip s may be calculated as follows : Eliminating A 

 from equations (i), (ii) and (iii), we have two remaining equations 

 (complex equations of course) which completely determine M, 

 /', and (M+ /'). The product of E' by the power component 

 of (M -\- /') gives the power input to the motor per phase, and 

 the cosine of the angle between E' and (M -f I') gives the 

 power factor of the motor when running at the given slip. Equa- 

 tion (iv) determines the mechanical output, ratio of output to in- 

 put gives efficiency, and equation (v) gives the motor torque. 



Graphical solution of equations (i) to (v). The algebraic solu- 

 tion of equations (i), (ii) (iii), (iv) and (v) is quite simple but very 

 tedious, and the following graphical solution may be preferred.* 



*It must be remembered that M in equation (z) is not assumed to be constant, it 

 decreases with increasing load on the motor. 



