﻿with 
  Alternate 
  Current 
  Measuring 
  Instruments. 
  137 
  

  

  on 
  the 
  instrument 
  and 
  the 
  main 
  current 
  or 
  voltage. 
  Am- 
  

   meters 
  and 
  voltmeters 
  are 
  of 
  course 
  only 
  affected 
  by 
  the 
  first 
  

   error, 
  but 
  the 
  phase-displacement 
  may 
  be 
  o£ 
  much 
  greater 
  

   importance 
  in 
  wattmeters. 
  

  

  Shunts. 
  

   Multiplying 
  Power. 
  — 
  In 
  fig. 
  1, 
  we 
  have 
  an 
  instrument 
  or 
  

  

  Fig. 
  1. 
  

   c, 
  

  

  T® 
  

  

  *z 
  

  

  npmm 
  

  

  PL 
  

  

  resistance 
  r 
  x 
  and 
  reactance 
  x 
  x 
  shunted 
  by 
  a 
  circuit 
  of 
  resist- 
  

   ance 
  r 
  2 
  and 
  reactance 
  x 
  2 
  . 
  Then, 
  if 
  V 
  is 
  the 
  P.D. 
  between 
  

   the 
  terminals, 
  and 
  Cj 
  and 
  C 
  2 
  are 
  the 
  currents 
  in 
  the 
  instrument 
  

   and 
  shunt 
  respectively, 
  we 
  have 
  

  

  ft 
  = 
  4- 
  

  

  Y 
  

  

  Ii 
  n—j*h 
  

  

  and 
  

  

  c 
  2 
  = 
  7 
  = 
  

  

  V 
  

  

  I 
  

  

  *2-JX 
  2 
  

  

  Hence 
  the 
  total 
  current 
  in 
  the 
  circuit 
  C 
  = 
  C 
  1 
  + 
  C 
  2 
  

  

  

  J%i 
  r 
  2 
  —jx 
  2 
  

  

  (n-ph) 
  (r 
  2 
  -jx 
  2 
  y 
  

  

  (1) 
  

  

  and 
  the 
  virtual 
  current 
  C 
  = 
  Vy-j-, 
  where 
  I 
  is 
  the 
  impedance 
  

  

  of 
  the 
  whole 
  circuit 
  formed 
  by 
  the 
  instrument 
  and 
  shunt 
  

   in 
  series, 
  and 
  Ij 
  and 
  I 
  2 
  are 
  the 
  impedances 
  of 
  the 
  instrument 
  

   and 
  shunt 
  respectively. 
  

  

  _ 
  V 
  

  

  Consequently, 
  since 
  C 
  x 
  = 
  y 
  the 
  multiplying 
  power 
  of 
  the 
  

  

  shunt 
  

  

  X 
  Is 
  

  

  (2) 
  

  

  