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What is the resistance of a cube

Discussion in 'Electrical Engineering' started by Kilowatt, Nov 10, 2004.

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  1. Kilowatt

    Kilowatt Guest

    What is the resistance of a cube that has a 1 ohm resister on each side
    measured between opposite corners?
     
  2. krw

    krw Guest

    Flatten out the cube. Assume your two corners are 'X' and 'Y', and the
    corners that are attached to 'X' through one resistors are 'A', 'B',
    and 'C'. The corners thusly connected to 'Y' are 'D', 'E', and 'F'.
    You then have three resistors XA, XB, and XC and three symmetrical at
    the other corner: YD, YE, and YF. Inbetween there are six resistors;
    AD, AE, BD, BF, CE, and CF. By symmetry we can see that the voltage at
    A=B=C and D=E=F, so we can consider all the resistors in these three
    sets in parallel. Thus the total resistance is (XA||XB||XC)+
    (AD||AE||BD||BF||CE||CF)+(YD||YE||YF), or 1/3 + 1/6 + 1/3.
     
  3. John McGaw

    John McGaw Guest

    Gawd! Is that one still floating around? That was one of the questions given
    in the early stages of the basic electronics course in my junior year of HS
    back in 1963...
     
  4. Jimmie

    Jimmie Guest

    Seems it never goes away. When I first saw it in the late 60's it was
    presented to me and a friend of mine by a retired engineer from GE. My
    friend who was in college at the time took about 2 days and several sheets
    of paper to work it out. I was a junior in HS and worked it out in my head
    in about fifteen minutes. Not bragging, I saw the symetry and the easy way
    to work it. My friend attacked it in a way that did not depend on the
    symetry of the network.I am sure his better understanding of networks led
    him in the direction he went and my ignorance in mine.
     
  5. Sylvia Else

    Sylvia Else Guest

    Why?

    When considering tolerances, one isn't interested in a design that will
    probably work given the distribution of component values within their
    tolerance limits. One wants a design that definitely will work even if
    all the components are at their worst case permitted values.

    So the tolerance of the cube made of 10% resistors (of the same nominal
    value) is still 10% isn't it?

    Sylvia.
     
  6. daestrom

    daestrom Guest

    But I think his point is more about how 'balanced' it will be. Presumably
    the cube is used instead of a single resistor for a reason. If some
    resistors are high, while others low, how will the imbalance affect some of
    the current distribution. Will the non-uniformity upset the current balance
    enough to dissipate too much power in some resistors?

    Admittedly, it is a 'contrived' problem, but it does illustrate that "things
    are not always what they seem..."

    daestrom
     
  7. Sylvia Else

    Sylvia Else Guest

    No, sorry, I don't get this. If a design might not work properly when
    some components are at the limit of their tolerance, then the design
    should specify components with closer tolerances.
     
  8. Sylvia Else

    Sylvia Else Guest

    I do not dispute that, but I cannot see its relevance.

    What I should probably have asked is what you actually mean by the
    "tolerance" of the effective network.

    When we say that a resistor has a tolerance of 10%, we mean that its
    true value may differ from its nominal value by up to 10% (of its
    nominal value). The obvious meaning of the tolerance of the network is
    therefore the extent by which its true value may differ from the value
    calculated using the nominal value of its resistors. You introduced the
    issue of the distribution of values, but there's no way of using that
    concept in calculating the tolerance of the network according to the
    usual meaning, so you presumably meant something else.

    What?

    Sylvia.
     
  9. daestrom

    daestrom Guest

    Yes, but how do you know, "If a design might not work properly when ...."?

    You have to do the analysis with the various components at their limits and
    understand what happens if a certain one is at its high limit while another
    is at its low limit. That's all, just saying such analysis is an
    'interesting' problem.

    If it turns out that it won't work under such circumstances, then you're
    absolutely right. Time to change the design and/or specs. But, "How do you
    know?"

    daestrom
     
  10. Sylvia Else

    Sylvia Else Guest

    I have no disagreement with that, but that's not what the proposed
    modified question required. There was talk about a distribution of
    values, not worst case scenarios.

    Sylvia.
     
  11. daestrom

    daestrom Guest

    Perhaps I was reading it differently. I'm thinking more of 'works' includes
    getting a certain voltage division between vertices, or the total resistance
    is 5/6 ohm with a certain confidence when the thing is constructed of
    individual parts whose tolerances are spread with a certain distribution.
    Kind of like making them on an assembly line and you want to know how many
    will pass a test that measures the voltage between two vertices. Using just
    standard 10% components, if the distribution of values is 'normal', or
    'flat', or'chi', or whatever, what would be the variation in performance.
    (i.e. how many will fail the QC test and have to be re-worked).

    After all, if building up a resistor network to make one 'composed resistor'
    with 10% tolerance parts, given enough individual parts, the variations
    *should* cancel out in the overall system and give you a 'composed resistor'
    with even better tolerance than the parts. And how will the variation of
    such a resistor network be distributed compared the distribution of
    variation in the individual components.

    daestrom
     
  12. Sylvia Else

    Sylvia Else Guest

    Such calculations are certainly possible. I'd question whether it would
    be a realistic approach to production.

    As something of an aside, I think it used to be the case that resistors
    were marked according to the actual tolerance they achieved. That is,
    you made bunch of resistors, then measured them. The ones within 1% were
    marked accordingly, and sold at a high price. Next came the 5% ones, at
    a lower price, then the 10% ones, and finally, the 20% ones (no
    tolerance band). So if I bought 10% resistors, the one thing I could be
    sure about was that they were not within 5% of their nominal value.

    I doubt it's still true, though.

    Sylvia.
     
  13. Sylvia Else

    Sylvia Else Guest

    That's a good question.

    No market? I suppose it's a form of yield management.

    Those designs that require 1% resistors would mostly be because they
    needed a consistency in value, wouldn't they, rather than because they
    need to be able to choose a value? I don't remember seeing many very odd
    valued 1% resistors. Typically, more like the values in the 5% range,
    just with 1% tolerance.

    I did once come across 1% resistors that had an extra band, and the next
    lower multiplier. I don't know about others, but over time I've tended
    to have the colour combination for common resistor values in my head, so
    I recognise them directly, without having to decode them. The extra band
    and lower multiplier was a damned nuisance.

    Sylvia.
     
  14. daestrom

    daestrom Guest

    Reminds me of the story about the old 'Double-Sided' vs 'Single-Sided'
    floppy disks. Supposedly all manufactured the same way, those that passed
    on both sides were labeled 'Double-Sided' and sold for a higher price than
    those that failed one side and were thus labeled 'Single-Sided'.

    daestrom
     
  15. Sylvia Else

    Sylvia Else Guest

    I think it is still true of CPUs. They're all made the same way, then
    tested. The ones that perform properly at the higher clock rates are
    then labelled that way, and sold at the higher prices.

    BTW, who are the people who pay top dollar for today's top of the range
    speed, that becomes tomorrows totally obsolete version?

    Sylvia.
     
  16. Sylvia Else

    Sylvia Else Guest

    I've just decided upgrade from a P3 600 to an P3 866 which I've bought
    second hand for $50. Mainly because the 600 only has a 100Mhz FSB, and I
    need a memory upgrade (Java is so memory thirsty). Turns out that buying
    a processor with a 133Mhz FSB means I save on the memory upgrade -
    100Mhz memory is difficult to get now, and priced accordingly.

    No doubt someone will tell me I could have underclocked the 600 clock,
    but overclocked its FSB. I wasn't sure that that would work, of if it
    did, that it'd be reliable.

    Not that any of you wanted to know that.

    Sylvia.
     
  17. krw

    krw Guest

    It's more or less still true, though with more twists. One can tweak
    the processing to produce higher yields at lower speeds, or more higher
    speed units at a reduced yield. One can similarly tweak the process to
    optimize for power and speed. If customers are ordering higher speed
    parts than your process wants to make, turn the knobs to produce what
    the customer wants. Productivity may suffer, but it beats having a lot
    of parts that no one wants.
    The same ones that will buy tomorrow's "top of the range" part. ;-)
     
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