Induction Motor. ir,7 



circuits (i.e., one-half the unmW^r of strips), ami L.i i„. the induct- 

 ance of each of the circuits. 



The quantity Hlc is the magnetic flux tlireading the armature, 

 and is denoted by <^. Thus we have 



,/.=r7rN7iH«/,-*(R''-|- 47r-N-'J;-) ~ * 



We may write R=i>n where p is a constant depending on the 

 resistance of the original copper cylinder. 

 Thus 



Let L=\n wliere A is a constant 



./.=7rNp<^'V+47r'^^''^')' ' • (1) 



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

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

 For suppose that we replace the original copper armature first 

 by one consisting of 7t circuits and second by one consisting of 2n 

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

 cuits will be nearl}' the same both in magnitude and in phase, and 

 since the circuits are near togetlier the mutual inductance of two 

 adjacent circuits will be practically ecjual to tlie 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,, 

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

 ture of n circuits. Writing L = 7^X we assume that it is exactly 

 twice the value. 



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

 lowing experiments were carried out : — 



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

 and suspended by means of a bifilav .suspension so tliat the poles 

 hung downwards. An armature, consisting of a cylindei 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 rotate^l, a revolu 

 tion counter was attached to the spindle. Tlie couple acting when 

 the spindle was rotated was measured by o))serving tlie. deflection of 

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

 magnet. The couple was measured for different rate's of rotati.ui 

 of the armature. The value of </> was determined by winding the- 

 exploring coil of a Grassot fluxmetei- around the armature and 

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

 '2.</> The result obtained was «/, = 6.23 x 10^2 Maxwell. Ma^s oi 

 magnet, 2870 gm. Distance fn.m mirror to scale, 54.5 cm. Ix-ngtU 

 of suspending wires, 44.2 cm. rH^'M,.-.. l.-tw^vn suspen.lim: win^. 

 2 cm. 



