230 ALTERNATING CURRENTS 



Thus, when the rotor is at rest, and the stator supplied with 

 current, excessive heating will take place in some of the rotor coils, 

 while others will remain quite cool. This behaviour of a single-phase 

 motor at rest is in striking contrast to that of a polyphase motor, in 

 whose rotor coils uniform heating would take place. 



It will be noticed that the coil in which the induced current has 

 a maximum value has its sides placed in a field of zero intensity, and 

 is thus unable to exert any torque, while the coil whose sides are in 

 the region of maximum field intensity conveys no current, and is thus 

 also unable to develop any torque. Any coil in an intermediate 

 position, such as the coil shown in Fig. 144, will, however, be sub- 

 jected to a definite tangential pull, which will obviously be equal to 

 twice the tangential force on one side of it ; * this latter force is given 

 by the product of length of conductor, current, and field intensity. 

 We thus get for the total tangential pull T on the coil in the position 

 shown in Fig. 144 



or, using the values for & and i obtained above 



T = TO . sin x . 2 sin pt . cos (pt 0) 

 where 



T = 



Since 2 sin pt . cos (pt 0) = sin (2pt - 0) + sin 0, the above 

 may be written 



T = - To sin a{sin (2pt - 0) + sin 0} 



Now, since the mean value of sin (2pt - 0) over any complete 

 number of periods vanishes, we see that the mean value of the 

 tangential pull on the coil is given by 



T m = TO sin . sin % 



In order to find out the direction of the pull, let us imagine a 

 positive current sent round the coil in Fig. 144, i.e. a current tending 

 to produce a magnetic field in the same (upward) direction as the 

 given field. Since both field and current are positive, their product 

 will be positive; but an application of Dr. Fleming's rule easily 



* We are assuming the coils to be placed on the surface of the rotor core, so that 

 the pull is exerted on the coils ; in reality, the coils would be embedded in the core, 

 and the pull would come mainly on the core. Since, however, the total pull would 

 remain unaltered, it is immaterial, so far as calculation goes, whether we assume the 

 coils to be placed on the surface or in slots. 



