Reciprocal, not logarithmic

Discussion in 'Feedback and Suggestions' started by rspuzio, Jul 30, 2009.

  1. rspuzio

    Thread Starter Active Member

    Jan 19, 2009
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    In the chapter on Ohmmeters (8.6), it is repeatedly said that the
    scale on an ohmmeter is logarithmic and, in particular, there is the
    statement

    "With a logarithmic scale, the amount of resistance spanned for
    any given distance on the scale increases as the scale progresses
    toward infinity, making infinity an attainable goal."

    This is not correct --- per Ohm's law, the scale on an ohmmeter
    varies as the reciprocal of the current, not as its logarithm. Whilst
    the reciprocal of zero is infinity, the logarithm of no finite number
    is infinity so infinity is not attainable with a logarithmic scale
    although it is attainable with a reciprocal scale.

    Call me a mathematical stickler, but this sloppiness sticks out at
    me like a sore thumb when I read this otherwise excellent
    exposition --- one does not make an ohmmeter by pasting a slide
    ruler on an ammeter movement :) Please consider changing the
    terminology so as to fix this inaccuracy.
     
  2. beenthere

    Retired Moderator

    Apr 20, 2004
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  3. tannercollin655

    Member

    Jul 23, 2009
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  4. rspuzio

    Thread Starter Active Member

    Jan 19, 2009
    77
    0
    > Interesting reasoning, but incorrect.

    Could you kindly please point out what you see as
    incorrect in my post?

    > If you don't like our Ebook,

    Liking or not liking the book is not the issue.
    As I understand it, this forum is the
    place to post corrections and suggestions for
    improving the book "All About Circuits".
     
  5. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    I have to say I agree with rspuzio. The inverse function is not the same a logarithm function. The two funcitons are similar, and related, but not the same. The derivative of a logarithm is the inverse function, or you can say that the logarithm function is the integral of the inverse function.

    It is clear in the example given that resistance in inversely proportional to current. Further, the D'Arsonval meter movement has a needle angular displacement that is proportional to current. Hence, the OP is correct.
     
  6. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    To the Ineffable All,

    This is the equation for the example given below, resistance = 9V/(k*0.001A)-9000 ohms where k is the rotation of the meter needle. k = 0 is the leftmost position and 1.0 is the rightmost position. http://www.allaboutcircuits.com/vol_1/chpt_8/6.html .

    Looking at the plot in the attachment we see that it is a displaced hyperbola which is a form of 1/x or inverse function. Also when you look at the ohmmeter scale, you can tell it is not logarithmic, because log scales don't have a zero, and the displacement from 1 to 2 is not the same as the displacement from 2 to 4 like a log scale would be.

    Ratch
     
    Last edited: Jul 31, 2009
  7. beenthere

    Retired Moderator

    Apr 20, 2004
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    Walked into that one. Funny how you accept the analog ohm scale as logarithmic when it is clearly not under inspection.
     
  8. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    The function is θ = f(R) where R is resistance and θ is angular deflection. The function should either be written down for the example given or just call it "nonlinear". End of discussion. :)
     
  9. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    someonesdad,

    Well, you identified the parameter and the result. What is the range of the result θ? 0° to what? What is the definition of the function "f"?

    Would that help someone who is manufacturing a meter scale? Or give you a good grade on a test?

    Ratch
     
  10. rspuzio

    Thread Starter Active Member

    Jan 19, 2009
    77
    0
    > The function should either be written down for the example given
    > or just call it "nonlinear"

    Agreed. This is the correction I was asking for. Changing the term
    "logarithmic" in the figure caption, the text, and the review point
    to "non-linear" would fix the problem.

    While the function isn't written explicitly in the book, it's value is
    computed for several values of θ, which serves the same purpose.
     
  11. Dcrunkilton

    E-book Co-ordinator

    Jul 31, 2004
    416
    11
    Thanks, all for clearing this up,

    Six instances of logarithmic have been changed to nonlinear in sources at ibiblio.

    Dennis Crunkilton
     
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