.48 IMPEDANCE. 



4-44 Z n t x 10 8 - F where 



F = back electromotive force 



Z = number of lines 



t number of turns, 



n = frequency. 



In the coil experimented upon the number of windings 

 was 160. Hence, the number of lines corresponding to each 



10 8 



v0 ^ = o* rsT^ -A = 3,800 nearly. The vertical scale 



37 x 160 x 4-44 



might, consequently, be plotted in terms of lines of force, 

 and similarly the horizontal scale might have been given in 

 ampere turns. A curve of considerable theoretical interest 

 would thus be obtained, although for practical purposes the 

 scales actually employed are generally more useful as well 

 as more easily obtained. 



As regards the form of Curve II. it is practically straight 

 after a small initial bend, but bends slightly to the right at 

 the upper end. If the current were increased to much higher 

 values the curve would bend decidedly to the right, showing 

 the well-known " knee " of a magnetisation curve. All cores 

 which are excited by alternating currents are employed with 

 magnetic densities far below the knee, in order to avoid the 

 heavy hysteresis losses which would occur at higher satura- 

 tion. 



Graphic Calculation of Impedance. The triangle of impedance 

 shown in Fig 15 forms the basis of a convenient method of 

 obtaining the value of the impedance of a circuit from values 

 of the self-induction and the reactance, requiring the use of 

 accurately ruled squared paper only. 



Thus, set out from the same point, the resistance of the 

 circuit horizontally and the reactance ( = 2 TT n L) vertically. 

 The value of the impedance is then given by joining the 

 extremities of the lines thus drawn. This is really the 

 converse of the operation for determining the reactance and 

 self-induction from observations of resistance and impedance 

 given on page 35. 



Example. If the coil experimented upon, with the results 

 shown in Fig. 17, page 38, had a reactance of 10-4 ohms, 

 instead of 5-2 ohms, find graphically the points to give a 

 curve similar to that in Fig. 17. This is equivalent to 

 calculating the curve which would have been observed at 

 double the frequency. 



