﻿146 
  Dr. 
  Drysdale 
  on 
  the 
  Use 
  of 
  Shunts 
  and 
  Transformers 
  

   from 
  which 
  

   V, 
  = 
  E 
  + 
  A 
  s 
  |r 
  p 
  (cos 
  <)>, 
  + 
  £) 
  + 
  x 
  T 
  (sin 
  </>,+ 
  ^=) 
  

  

  -i 
  [* 
  p 
  (cos 
  * 
  s 
  ■+ 
  £) 
  - 
  r,(«n 
  *. 
  + 
  £)]} 
  . 
  (18) 
  

  

  and 
  

  

  — 
  V,=E 
  - 
  AJ 
  r, 
  cos 
  <£,+ 
  x 
  s 
  sin 
  $ 
  9 
  —j(x 
  8 
  cos 
  </>,—?*, 
  sin 
  <£ 
  s 
  ) 
  j- 
  (19) 
  

  

  Voltage 
  Ratio. 
  — 
  Taking 
  the 
  ratio 
  of 
  ^, 
  simplifying, 
  and 
  

  

  p 
  

   neglecting 
  squares 
  of 
  small 
  quantities, 
  we 
  have 
  

  

  f 
  A 
  Ac 
  A 
  "1 
  

   E« 
  = 
  Rh 
  1— 
  ^[(r 
  p 
  + 
  r 
  s 
  )cos<£, 
  + 
  (# 
  p 
  + 
  ^sin<£j 
  — 
  ~r 
  p 
  ~ 
  x 
  p 
  j% 
  

  

  which 
  will 
  be 
  seen 
  to 
  be 
  correct 
  from 
  the 
  vector 
  diagram. 
  

   Denoting 
  r. 
  p 
  + 
  r 
  8 
  by 
  r 
  the 
  equivalent 
  resistance, 
  

   x 
  p 
  + 
  oc 
  s 
  hjx 
  „ 
  „ 
  reactance, 
  

  

  and 
  ^/r'-tx' 
  2 
  by 
  I 
  „ 
  „ 
  impedance, 
  

  

  R„=E 
  t 
  {l-| 
  5 
  (rcos^. 
  + 
  .r 
  S 
  in^)-| 
  C 
  '>-%•'>}• 
  (20) 
  

  

  For 
  an 
  electrostatic 
  or 
  high-resistance 
  voltmeter, 
  A 
  s 
  = 
  

   and 
  we 
  have 
  

  

  B,=B,{l- 
  A 
  °' 
  > 
  + 
  A 
  '- 
  r 
  " 
  }. 
  . 
  . 
  . 
  (21) 
  

  

  For 
  a 
  hot-wire 
  instrument 
  <£ 
  = 
  and 
  

  

  B.=B,-[l- 
  A 
  ' 
  r+ 
  A< 
  g 
  + 
  A 
  "^ 
  |. 
  . 
  . 
  (22) 
  

  

  Returning 
  to 
  formula 
  (20) 
  wo 
  have 
  

  

  if 
  the 
  instrument 
  and 
  internal 
  impedances 
  are 
  constant. 
  

   This 
  is 
  independent 
  of 
  the 
  phase 
  of 
  the 
  secondary 
  current 
  and 
  

   can 
  only 
  be 
  zero 
  if 
  A 
  c 
  and 
  A,„ 
  arc 
  proportional 
  to 
  E, 
  which 
  is 
  

   only 
  the 
  case 
  for 
  an 
  air-core 
  transformer. 
  For 
  an 
  iron-core 
  

   transformer 
  the 
  best 
  constancy 
  of 
  ratio 
  is 
  thus 
  obtained 
  by 
  

   making 
  A,, 
  and 
  A„, 
  and 
  also 
  r 
  r 
  and 
  x 
  v 
  as 
  low 
  as 
  possible, 
  the 
  

   core 
  being 
  of 
  the 
  best 
  quality 
  iron, 
  and 
  the 
  coils 
  subdivided 
  

   and 
  intercalated. 
  

  

  