16 TKEATISE ON ALTERNATING CURRENTS. 



instantaneous values are e\ t c 2 be applied between their respective 

 terminals. Let also i\ y ? 2 be the corresponding instantaneous 

 values of the currents flowing in the two circuits. 



First consider one of the circuits alone. 



The function of ^ is to drive the current i\ against the resist- 

 ance r l of the circuit, and to balance the E.M.F.s due to self and 

 mutual induction. 



At any instant, therefore, e\ must equal the sum of 



thus we get the equation 



In exactly the same way for the other circuit 



These are relations between the RM.F.s in the two circuits 

 respectively, and are also two simultaneous equations to determine 

 ii and i' 2 in terms of the other quantities. 



The case of greatest practical interest is that in which c 2 = o. 

 The equations then refer to the primary and secondary circuits 

 of a transformer or an induction coil, and are discussed fully in the 

 chapter on Transformers. 



Equations (8), (9), and (10) are formed on the supposition that 

 the coefficients of self and mutual induction are constant. This 

 condition will often hold good since, in most alternating-current 

 machinery, to which these equations can refer, the induction in the 

 iron does not approach saturation. 



Equations (9) and (10) may be deduced from the law of 

 conservation of energy in the same way as equation (8) ; but this 

 is left as an exercise for the reader. 



PROBLEMS ON CHAPTER II. 



1. A straight conductor 1 metre long is displaced parallel to itself and at 

 right angles to a uniform field at a rate of 100 metres per second. If the field 

 strength is 100 C.G.S. units, what E.M.F. is generated in the conductor ? 



Answer. 1 volt. 



