22 PRINCIPLES OF ELECTRICAL DESIGN 



to emphasize the danger of carrying too far the analogy between 

 the magnetic and electric circuits. The product PR in the 

 electric circuit is always associated with loss of energy; but 

 $> 2 X reluctance does not represent a continuous loss of energy in 

 the magnetic circuit. If the energy wasted in the exciting coil 

 is ignored, it may be said that the magnetic condition costs 

 nothing to maintain. It does, however, represent a store of 

 energy which has not been created without cost; but, with the 

 extinction of the magnetic field, the whole of this stored energy is 

 given back to the electric circuit with which the magnetic circuit 

 is linked. This may be illustrated by the analogy of a frictionless 

 flywheel which dissipates no energy while running, but which, 

 on being brought to rest, gives up all the energy that was put 

 into it while being brought up to speed. 



The dotted lines on the right-hand side of the magnetic circuit 

 shown in Fig. 5 indicate two extra iron paths for the magnetic 

 flux. It should particularly be observed that the closed iron 

 ring D can be linked with the exciting coil as indicated Without 

 modifying the amount of the useful flux through path (1): 

 there may obviously be a large amount of flux in this closed 

 iron ring, but it has cost nothing to produce because the exciting 

 ampere-turns have not been increased. The same might be 

 said of the circuit C except that the flux in this circuit has to 

 go through the common core (3), and in so far as extra ampere- 

 turns would be necessary to overcome the increased reluctance 

 of the iron under the coil, the m.m.f. available for sending flux 

 through paths (1) and (2) would be reduced, and if path C 

 were of high-grade iron of large cross-section relatively to A 3 , 

 the useful flux in path (1) might be appreciably reduced. A 

 proper understanding of the points brought out in the study of 

 Fig. 5 will greatly facilitate the solution of practical problems 

 arising in the design of electrical machinery. 



6. Calculation of Leakage Paths. The total amount of the 

 magnetic leakage cannot be calculated accurately except, by 

 making certain assumptions which are rarely strictly permissible 

 in the design of practical apparatus. Whether the machine is 

 an electric generator or an electromagnet of the simplest design, 

 the useful magnetic flux is always accompanied by stray magnetic 

 lines which do not follow the prescribed path. This leakage 

 flux will always be so distributed that its amount is a maxi- 

 mum; that is to say, the paths that it will follow will always 



