Induction Motor. 157' 



circuits (i.e., one-half the number of. strips), and L.cm. the induct- 

 ance of each of the circuits. 



The quantity Hlc is the magnetic flux threading the armature, 

 and is denoted by <^. Thus we have 



We may write R—fju where p is a constant depending on the- 

 resistance of the original copper cylinder. 

 Thus 



Let L=An where A is a constant 



It should be noticed that writing L/n=X (a constant) takes into' 

 account the mutual action of the induced currents on one another. 

 For suppose that Ave replace the original copper armature first 

 by one consisting of n circuits and second by one consisting of 2?i 

 circuits where n is large. The currents flowing in adjacent cir- 

 cuits will be nearly the same both in magnitude and in phase, and 

 since the circuits are near together the mutual inductance of two 

 adjacent circuits will be practically equal to the self-inductance- 

 of either of them. Thus the flux threading a circuit when a certain 

 current flows in it will, in the case of the armature of 2n circuits,-. 

 Ije approximately twice what it is for the same current in the arma- 

 ture of n circuits. Writing L = »\ we assume that it is exactly 

 twice the value. 



In order to determine p and A. for particular cases, the fol- 

 lowing experiments wei'e carried out :— 



Experiment (a). — A U-shaped permanent magnet was weighed 

 and suspended by means of a bifilar suspension so^ that the poles 

 hung downwards. An armature, consisting of a cylinder of copper 

 with an iron core was placed midway between the poles and at- 

 tached to a spindle, by means of which it could be rotated, a revolu- 

 tion cotmter was attached to the spindle. The couple acting when 

 the spindle was rotated was measured by observing the deflection of 

 a spot of light, which was reflected from a mirror attached to the 

 magnet. The couple was measured for different rates of rotation 

 of the armature. The value of ^ was determined by winding the- 

 exploring coil of a Grassot fluxmeter around the armature and 

 rotating it through 180°. This of course gives twice the value of 

 2.<^ The result obtained was <^ = 6.2.3 x 10'^/2 Maxwell. Mass of 

 magnet, 2870 gm. Distance from mirror to scale, 54.5 cm. Length: 

 of suspending Avires, 44.2 cm. Distance lietween suspending Avires,. 

 2 cm. 



