76 Dr. McLacblan on Effective Inductance, Effective 



explained if we consider the effect of the iron loss on the 

 natural period of the circuit. 

 Consider the relation 



„2 = J_ _ Re 2 



L e C 4L e 2 

 This can be written 



go" = ( — j- ) x, where x — 1/L e 



= (a-bx)x (16) 



If we plot co 2 and x, the curve obtained is of the form 

 shown in fig. 22, i. e. a parabola. Draw 7 any line xx' 



Fig. 22. — Curve showing relation between or and 1/L in an oscillatory 

 circuit having resistance of appreciable magnitude such that 

 it affects the natural period. 











co Z =x(a 

 / 



-bx.) 



X 









X 



X' 



/ 



/A 







a\ 





/ 











\ 



\ 



/ 



1 





1 — ^ — 4 







\ 



'*b=7CRe 



%=?cr§ 



.r = l/L 



parallel to the x axis. This cuts the curve in two points 

 A, B. The value of go 2 , and therefore of co and /, is the 

 same at A and B, but the value of x and therefore of L e is 

 quite different. Thus, so long as l/L e >4/CR e 2 or CR e 2 <4L e 

 and the resistance and condenser are fixed, there are tw r o values 

 of L e which give the same frequency. When L e > CR e 2 /4 but 



