456 



Prof. J. Perry. 



[May 12, 



If the law connecting A and I is known, it is possible to calculate I 

 from (1), and then substituting for I in each of the circuit equations, 

 each of the currents is known. 



Instead of ei being the electromotive force in a complete circuit, it 

 may be the potential difference maintained at the terminals of a 

 circuit and the letter Vi will then be used, the resistance between the 

 terminals being Rj. If e» or V» has any value, the circuit is called a 

 primary circuit. When no independent electromotive force is main- 

 tained in a circuit, it is called a secondary circuit. 



II. Substitution of one coil for two or more : — It is evident from 

 the way in which (1) is derived, that instead of a primary coil 

 (Vi, N\, R x ) and a secondary (N 2 , R 2 ), if we substitute a primary 

 (V l5 m, n) and if n x \r x = Ni/Ri and also if V/n = ~N 1 2 IR l + T$ 2 2 jl& 2 , 

 then the currents in all the other coils will be the same as before. 

 We can therefore replace a primary and any group of secondaries 

 by one primary coil. 



It is also evident that if any group of secondaries (N p , Rp), 

 (Nt, Rf), &c, be replaced by one secondary r 2 ) such that n£\r % = 

 N^/Rp-f-JSTVYRi-f &c., all the other currents will remain as before. It 

 is, in fact, evident that if for groups of primaries and secondaries we 

 substitute one primary coil of suitable potential difference at its 

 terminals and resistance and number of turns, all the currents in the 

 remaining coils will remain the same. 



If two secondaries of numbers of turns N p and and internal 

 resistances r p and n have the same terminals, and together supply a 

 current to an outside circuit, for them we may substitute one second- 

 ary of n turns and internal resistance r ohms with a permanent short 

 circuit of resistance /> between its terminals, if 



n = (isV/n+W/^/C^n+N^), 



r = r p r t (N/r t + N7?>) / (N p rt + N t r p ) 2 , 

 and P = (N/^ + N^)/^-^) 8 . 



Hence no good results can be expected from compound winding. 

 If, instead of requiring a perfect similarity in all respects, we desire 

 a substitution which is almost absolutely perfect in practical cases, 

 we can obtain it by the use of a single coil with no short circuit 

 outside, and therefore without the excessive waste of power which 

 occurs when two coils of different numbers of turns are compounded. 

 This last result is obtained by regarding A as a negligible term 

 in (1). 



Two coils in parallel to one another, used as a primary or second- 

 ary, will evidently waste energy in idle currents inside the trans- 

 former unless they are exactly equal in their numbers of turns. 



III. If condensers are connected with any of the circuits the 



