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XLIX. Choking Coils. 

 By Professor John Perry, D.Sc, F.R.S* 



THERE is eddy-current loss of power in all the conducting 

 masses of a choking coil. Hence a choking coil is 

 really a transformer with one primary coil and many secon- 

 daries, and much magnetic leakage. In a transformer with 

 many coils, whether or not they have magnetic leakage, it 

 may be shown that any given group of secondaries of given 

 numbers of turns and resistances may be replaced by one 

 secondary without affecting the currents in the other coils; 

 and we may take a choking coil to be a transformer with a 

 primary coil of N turns and resistance R ohms, with C 

 amperes flowing at any instant, the potential difference at its 

 terminals being V, and a secondary coil closed on itself of n 

 turns, resistance r ohms, and current c amperes. 



If we assume that the induction per square centimetre /3 is 

 the same everywhere, and if it follows the law 



ft in C.Gr.S. units = ^a i sin (ikt + e^, 



the average power in watts, wasted in eddy currents in the 

 iron per cubic centimetre is 



6'25xl0~ U i> 2 k 2 ti 2 a?, 



if the specific resistance of the iron is taken to be 10 4 C.G.S. 

 units. It is less at higher temperatures, being inversely 

 proportional to the specific electric resistance of the iron. 

 The iron is supposed to be of wire of radius r centimetres. 

 Even when we leave the eddy-current loss in the copper 

 out of account, it is to be remembered that the induction is 

 not uniform in the section of a wire, nor is the average 

 induction in each v ire the same for all the wires, and there- 

 fore the real loss oi power in the iron by eddy currents is 

 always greater than the result of applying this formula. 



I am going to assume that one secondary coil with no 

 magnetic leakage may be substituted for all the eddy-current 

 circuits, and this is the same as assuming the truth of the 

 above rule. I ignore magnetic leakage because this is only a 

 preliminary note, and such experiments as have hitherto been 

 made do not enable me to take account of it, for there are no 

 experimental measurements as yet of the want of uniformity 

 of the induction. 



The equations of the two circuits are 



V = RC + N0I and O=ro-+n0I, 



* Communicated by the Physical Society : read March 11, 1892. 



