138 ELECTRICAL ENGINEERING 



The e.m.f. has an absolute value 



E = V ei * + e 2 * 

 and is ahead of the axis by an angle 



> >^ 



<f>i = tan" 1 = cos" 1 -= 

 e\ EJ 



The current has an absolute value 



/ = VIS + tf 



and is ahead of the axis by an angle 



<fe = tan" 1 = cos" 1 -^- 

 %\ 1 



The e.m.f. leads the current by an angle 



The impedance of the circuit in rectangular coordinates is 



z = 

 J 



ii + eziz . . cat'i - e^ 



= r+jx, 

 where the resistance of the circuit is 



ejii + 621*2 eii'i + e 2 J2 



and the reactance of the circuit is 



- e & 1 ~ ei ^* 

 " 



tf / 



The admittance of the circuit is 



^ 



- ~ E ei + je 2 



_ eiii + 62^2 _ . ezii e^ 

 = eS + ^2 2 J ei 2 + e2 2 



= g-fi; 



the conductance is 



eit'i + Mi* = ejii + eA 

 " 2 2 " 2 



