﻿Measurement 
  by 
  Alternating 
  Currents. 
  11 
  

  

  Should 
  the 
  circuits 
  R 
  and 
  r 
  also 
  have 
  small 
  self-inductances, 
  

   L 
  and 
  Z, 
  we 
  can 
  use 
  the 
  exact 
  equation 
  

  

  Lr 
  

  

  T 
  , 
  T 
  R 
  + 
  R' 
  + 
  /R 
  R+R'r. 
  , 
  Lr 
  b*Ll 
  B 
  -i 
  

  

  1- 
  

  

  v 
  

  

  R 
  

  

  When 
  1/ 
  and 
  -Z 
  are 
  approximately 
  known, 
  we 
  can 
  write 
  the 
  

   following, 
  using 
  the 
  approximate 
  value 
  on 
  the 
  right 
  side 
  of 
  the 
  

   equation, 
  

  

  L' 
  R 
  + 
  R'n 
  I> 
  V 
  r 
  b*Ll 
  p 
  l 
  

  

  Taking 
  out 
  L' 
  and 
  putting 
  a 
  condenser, 
  C, 
  in 
  R 
  we 
  have 
  

  

  A=^R'-^CR(R 
  + 
  R'). 
  

   For 
  a 
  condenser, 
  R 
  can 
  be 
  small 
  or 
  zero. 
  

  

  Method 
  13. 
  

  

  r 
  1-1* 
  [R.R-R^CR^r 
  + 
  R^ 
  + 
  R^ 
  + 
  R'O] 
  

   (A) 
  \bh 
  -^„j 
  = 
  ^ 
  . 
  

  

  This 
  determines 
  capacities 
  or 
  self-inductions 
  in 
  absolute 
  

   value. 
  As 
  described 
  above, 
  mutual 
  induction 
  can 
  also 
  be 
  

   determined 
  by 
  converting 
  it 
  into 
  self-induction. 
  

  

  W|_ 
  »~UT 
  U 
  \- 
  "' 
  R'(r+R,) 
  • 
  

  

  ,C\ 
  l"ftT 
  1 
  V_ 
  [R'R,-B"R 
  ) 
  ][R 
  / 
  (r+R») 
  + 
  R 
  JI 
  ( 
  y 
  + 
  R 
  ; 
  )l 
  

  

  ^> 
  L 
  ' 
  60, 
  J 
  ~ 
  ' 
  R"[r 
  + 
  R" 
  + 
  R„j 
  * 
  

  

  [ 
  w 
  -£*]'= 
  

  

  Jf<?£//od 
  14. 
  

  

  [R 
  i 
  R 
  // 
  -R 
  // 
  R 
  / 
  ]{r[R 
  / 
  + 
  R 
  / 
  + 
  R 
  // 
  + 
  R 
  i/ 
  ] 
  + 
  [R 
  / 
  + 
  R 
  / 
  ][R 
  // 
  + 
  R 
  i/ 
  ]} 
  

  

  R„[> 
  + 
  R" 
  -f 
  R„] 
  ~ 
  ' 
  

  

  Of 
  course, 
  in 
  any 
  of 
  these 
  equations, 
  methods 
  13 
  or 
  14, 
  L" 
  

   is 
  eliminated 
  by 
  making 
  L" 
  = 
  or 
  the 
  condenser 
  G 
  is 
  omitted 
  

   by 
  making 
  C 
  = 
  oo 
  . 
  

  

  