ELEMENTARY THEORY OF ELECTROMAGNETISM. 65 



in which LI is the inductance of the primary circuit and L 2 

 is the inductance of the secondary circuit as denned in Art. 31, 

 ii is the current in the primary circuit, i z is the current in the 

 secondary circuit, and M is the mutual inductance of the two 

 circuits. 



To establish equation (i) let us assume both circuits to have 

 zero resistance for the sake of simplicity of statement, and let us 

 consider (a) the amount of work required to increase the primary 

 current from zero to a given value ii, with the secondary circuit 

 open; (b) the amount of work (done on the primary circuit) to 

 keep the primary current ii constant while the secondary current 

 is being increased uniformly from zero to a given value i% in t 

 seconds; and (c) the amount of work (done on the secondary 

 circuit) to increase the secondary current from zero to the given 

 value i%. 



The amount of work (a) is equal to \~L\i? according to Art. 35. 



To find the amount of work (b) assume that the secondary 



current is increased at the constant rate so that an electro- 

 motive force equal to M -7- = is induced in the pri- 



at t 



mary coil, according to equation (4) of Art. 41. Therefore to 



keep ii constant, an electromotive force equal to - - must act 



t 



on the primary coil for t seconds doing work at the rate X *i. 



Therefore the amount of work done will be ( - X ii 1 X t 



which is equal to Mi\i^. 



The amount of work (c) is equal to \"L& according to Art. 35. 

 The argument of Art. 35 applies to the calculation of the amount 

 of work done on the secondary coil while the secondary current 

 is increased fr6m zero to i z and while the primary current is 

 kept at a constant value, because the only electromotive force 

 induced in the secondary coil is the self-induced electromotive 

 force due to the increasing secondary circuit. 

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