Measuring Poiver in Transformers. 187 



To get an idea of the importance of even a little leakage 

 let us eliminate C^ from equations (1) and we have the 

 result 



V=EC-E'> + ] ^C (2) 



The usual assumption that if LI/ only differs by a very little 

 from M 2 the error is unimportant, is seen to be inadmissible 

 when we consider how great a value C sometimes may have 

 in comparison with C or C. Thus, for example, in a trans- 

 former with which I have had something to do experiment- 

 ally, L = 15, L'^0'15, R=10, and M is very nearly 1/5; so 

 that (2) becomes 



V = 10C+10R'C' + (l5-^)c. 



Now, to take the very simplest kind of periodic current, 

 and the one for which the above wrong assumption is least 

 wrong, and a frequency of 106 per second — writing, in fact, 



0=A sin 1000 1, 



we know that 



= 1000 A cos 1000 £. 



So that, even if M differs only by 1 per cent, from what it 



has been assumed to be, that is, if there is only 1 per cent, of 



/ M 2 \ • 



magnetic leakage, the neglected term ( 15 — -^7 )C becomes 



of the value 



{15-«}C, 



or 0*3 G, or 300 A cos 1000 t. In fact,, the neglected term 

 becomes thirty times as important as the important and 

 certainly hitherto non-neglected term RC in the equation. 



Now in no case is the current truly a sine function of the 

 time, and any departure from this simplest kind of periodic 

 current makes the error of which I speak much greater.* 



* As an example, one of many worked out by my students at Finsbury 

 during the last few years : taking the sizes of iron from a certain Mordey 

 transformer which I have occasionally used ; assuming permeability con- 

 stant and no eddy currents in copper or iron ; assuming currents to be 

 true sine functions of the time. If V is voltage at terminals of primary, 

 primary resistance 10 ohms, internal secondary resistance 0*1 ohm, out- 

 side resistance of secondary in ohms being called p ; self-induction of 

 primary 15 secohms, self-induction of secondary 015 secohm ; assum- 

 ing V in volts = 1000 sin— t, and taking frequency 106 or r=l-fl06 

 second, it is quite easy to calculate to any number of places of decimals 



