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total resistance in parallel circuits

Discussion in 'Electronic Basics' started by Midnight Oil, Oct 5, 2005.

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  1. Midnight Oil

    Midnight Oil Guest

    I am new to electronics, and I've been learning the basics of ohm's
    law. I ran into the formula for finding the total resistance in a parallel
    circuit, struggled with it's meaning...and I want to be sure I understand
    the formula:

    R(tot) = 1
    1 + 1 + 1
    -- -- --
    R1 R2 R3

    I broke the formula down like this:

    R(tot) = 1 <--- E (volts)
    1 + 1 + 1
    -- -- -- <--- I (amps)
    R1 R2 R3

    In other words, the addition of 1/R1, 1/R2, and 1/R3 reveals the
    current when 1 volt is applied to the circuit (E/R). Then, once we know
    the current, we can divide the 1 volt by the current to reveal the total
    resistance R= (E/I).

    In other words, 1/Rx reveals the amount of current in one branch of the
    parallel circuit, and adding these together gives us the total current in
    the circuit when 1 volt is applied. If we divide 1 volt by that value, we
    get the resistance in the circuit when one volt is applied.

    Is my understanding of the equation correct?

    I thought it was, until I read further in the book. It explained that
    the reason for the 1/Rx was because it is expressing conductivity rather
    than resistance.

    I thought it was interesting that 2 interpretations of the formula
    could co-exist...or was my own interpretation of the formula wrong?

    Is it just a coincidence that the amount of conductance is equal to the
    amount of current flowing when 1 volt is applied?


    - Jamie

    The Moon is Waxing Crescent (7% of Full)
  2. Tom Biasi

    Tom Biasi Guest

    Yes Jamie,
    It can be confusing.
    If you can use your algebra ( a must in this field) you may better
    understand the concept if you consider only two resistances in parallel.

    With manipulation you will arrive at the - product over sum - formula. R1 x
    R2/(R1 + R2) You can do two resistors (resistances), come to a conclusion,
    use the result to combine the other one in the pair.

    Then you will appreciate the - one over, one over formula. Yes they are
    conductance's. As for you coincidence: is 2+2 the same as 2 squared? Is 4+4
    the same as 4 squared?

    Review the algebra.
    Best Regards,
  3. I think so. At least you seem to be getting that an ohm is just
    another way of saying 1 volt per ampere. Another way to look at the
    parallel resistance formula is that you convert the resistances to
    conductances (amperes per volt, as you have figured out, but now you
    have a word that names that ratio). Then, after adding the
    conductances together to get a total conductance you convert that
    conductance back to a resistance by taking the inverse (flipping the
    amperes in the numerator with the volts in the denominator to get back
    to volts per ampere.
    Exactly. Conductance (a bit different than conductivity, which is a
    property of a bulk material) is the name for the ratio of amperes per
    Not wrong, just sticking to the more fundamental units.
    It is the definition of conductance.
  4. Tim Williams

    Tim Williams Guest

    Incorrect: the ones do not represent any units, so the only thing you'll get
    out is what you put in - in this case, ohms. The intermediate step of
    reciprocal resistance in ohms (which is conductance in mhos) follows from
    the nature of the circuit.

    Aside from the confusion on units ...

    What you are imagining is equivalent to the mathematical technique of
    testing a "well-behaved" function at a convienient value like x = 1 and
    extrapolating or proving other values based on this.

    Given nice ohmic devices, the exact same behavior applies, as a matter of
    fact, so it is true you can test and prove it in this way.
    Only as I mentioned above. Gotta watch units in equations. :)
    Nope, it's by definition in fact :)

  5. redbelly

    redbelly Guest

    That's not a bad way to interpret what's going on. But, to make the
    units work out properly, we could multiply the expression by 1V/1V
    (since that equals 1 and multiplying by 1 is allowed), then manipulate
    things like this:

    1 1V
    R(tot) = ---------------- x ----
    1 1 1 1V
    -- + -- + --
    R1 R2 R3

    1V <--- E (volts)
    = ----------------
    1V 1V 1V
    -- + -- + -- <--- I (amps)
    R1 R2 R3

    So each resistor has 1V across it, and has (1V/Rx) current flowing
    through it.



    Hmmmm. Years ago I had DOS version of that program. Is there
    something available for Windows these days?
  6. Pooh Bear

    Pooh Bear Guest

    Think of it as the sum of conductances. It's simple then.

  7. Jasen Betts

    Jasen Betts Guest

    you are measuring conductance if you put 1 volt across a resistor and
    measure the current it passes.

    I would say that both interpretations are equivalent.

  8. Rich Grise

    Rich Grise Guest

    I saw this derived from the sum of conductances:

    G(tot) = G1 + G2 + G3

    Since conductance is the reciprocal of resistance,

    G(tot) = 1 / R(tot)
    G1 = 1 / R1 etc


    1 / R(tot) = (1 / R1) + (1 / R2) + (1 / R3)

    Multiply through by R(tot)

    1 = R(tot) * ((1 / R1) + (1 / R2) + (1 / R3))

    Divide through by ((1 / R1) + (1 / R2) + (1 / R3))

    1 / ((1 / R1) + (1 / R2) + (1 / R3)) = R(tot)

    QED. (I've always wanted to be able to say that! :) )

  9. Jasen Betts

    Jasen Betts Guest

    The Moon is Waxing Crescent (7% of Full)
    it looks like the output from "pom" the bsd "phase of moon" program

    The Moon is Waxing Crescent (23% of Full)

    C source is available from

    winzip (etc) should be able to open that file, and pretty much any C compiler
    should be able to produce a working executable from the source. some of the
    other "games" in the package may not compile for windows as easily.


    Today is Sweetmorn, the 62nd day of Bureaucracy in the YOLD 3171
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