24 ALTERNATING CURRENTS 



We may note, in passing, that the sum of the r.m.s. voltages 

 across LM and MN, namely, 426 + 75 = 501, is very nearly equal 

 to the voltage of 500 across LN. This close coincidence is purely 

 accidental, and is due to the fact that the joint phase angle between 

 L and M (54) is not very different from that between M and N 

 (62 22'). 



Having determined the voltages across LM and MN", we at once 

 obtain the branch currents by multiplying the admittance of each 

 branch by the voltage across it. We thus find 



Current in a = 426 X 0-0121 = 515 

 j3 = 426 x 0-0256 = 10-9 

 y = 75 x 0-00314 = 0-235 

 = 75 x 0-0537 = 4-03 

 = 75 x 0-0411 = 3-08 



It will be noticed that the current in the branch |3 is considerably 

 greater than the total current. 



ii. Mutual Inductance and its Effects 



When two circuits are placed near each other, a current sent 

 through one of them will in general produce an appreciable magnetic 

 flux through the other, some of the lines produced by the first circuit 

 becoming linked with the second. The circuits are said to possess 

 mutual, inductance, and their mutual inductance is defined to be the 

 magnetic flux linked with either circuit when unit current flows 

 round the other.* 



By taking into account the principle known as Lenz's law, it is 

 easy to arrive at the general nature of the effects produced by mutual 

 inductance when the first circuit is supplied with an alternating 

 current, and the second circuit, which contains no impressed e.m.f., 

 is simply closed on itself. According to Lenz's law, the current 

 induced in any circuit by a varying flux always opposes the changes 

 of flux which give rise to it ; and the circuit in which the current is 

 induced is subject to mechanical forces tending to move the circuit 

 so as to reduce the extent of the flux variations. 



If both circuits are rigidly fixed, the currents induced in the 

 second circuit when an alternating current is allowed to flow in 

 the first circuit will tend to reduce the amplitude of the flux 



* The flux linked with the second circuit when unit current flows round the first 

 is equal to the flux linked with the first circuit when unit current flows round the 

 second. For a simple proof of this relation, the reader is referred to the author's 

 " Principles of Alternate-Current Working." 



