when the Frequency is below a certain Critical Value. 397 

 Hence 



+nn ,_^ r 2 _ br 2 -apR _ P I 2 2 



x&n< P- bpN" ar 2 + bp^" r p\W ' W 

 ar 2 x I 2 2 



From (9) it is evident that the difference in phase between 

 the primary current and the P.D. is always diminished on 

 closing the secondary, since, when the latter is open 



tancf>=— . 



r Ti 



In the same manner from (5) we obtain 



C 2 sja 2 + b 2 sin (pt + 6 + <f ) = — pME cos (^ + <£) 



=pMEsinArt + <£+^\ 



Hence p pME 



V« 2 + b 2 ' 



but yjr = (j) + >x. 



Hence 



(10) 



0= — — V = 7T + I 



3tt 



2 X=*" + ^ 



2 %)> 



or is greater than ir and less than — . Also 



Now from equation (8), 



C 1= K 



tan^=cot X =^. ..... (11) 



Va 2 + 6 2 ' 



Call I the apparent impedance of the primary when the 

 secondary is closed (l x is its impedance with secondary open) . 

 Then 



T _ \/aJ+¥ 



" — T 2 ' 



or I 2 I 2 2 = a 2 + 6 2 



= r 1 V 2 2 + i > 4 (LN-M 2 ) 2 -2/r 1 r 2 (LN-M 2 ) 



+p*N*r x * +p 2 L 2 r 2 2 + 2p\r 2 LN 

 = I, 2 !, 2 -j9 2 M 2 { p 2 (2LN - M 2 ) - 2r,r 2 \ , 



