IMPEDANCES IN PARALLEL 



21 



rule as that lohich governs the composition of impedances in a series 

 circuit. 



It will be noticed that the sum of the r.m.s. values of the branch 

 currents is in general greater than the r.m.s. value of the total current ; 



P.D. 



FIG. 15. Vectorial Addition of Admittances. 



but may become equal to it in the special case in which all the 

 phase angles 0i, 2 , ^3 ... are equal. 



In order to secure accuracy, we may as before calculate the joint 

 impedance. The joint admittance is given by 



+ A 2 cos0 2 + A 3 cos0 a + . 



and the reciprocal of this is the joint impedance. The phase angle 

 corresponding to the joint impedance is such that 



I sin Si + A 2 sin 2 + A 3 sin 3 + . . . 



tan = 



cos 



4- A 2 cos 2 + A 3 cos 8 + . . . 



io. Numerical Example. 



In order to illustrate the application of the above principles, we 

 shall work out in detail a fairly complicated numerical example. 

 In Fig. 16 is shown an arrangement of a number of resistances, 



