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Equivalent Resistance

  1. Jan 30, 2013 #1
    http://img7.imageshack.us/img7/6238/capturealh.png [Broken]

    My gut tells me that these resistors are in parallel. However something tells me that it might be more complicated but I'm not sure.

    Do I find the equivalent resistance by just simply adding them together as if they were in parallel to each other.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 30, 2013 #2

    gneill

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    Can you find a path from A to B that doesn't pass through any resistor?
     
  4. Jan 30, 2013 #3
    Ya I can so what exactly does that mean though in terms if it's in series or parallel or neither?
     
  5. Jan 30, 2013 #4
    Try redrawing the circuit
     
  6. Jan 30, 2013 #5

    gneill

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    If two points are connected by a wire, what's the resistance between those two points?
     
  7. Jan 30, 2013 #6
    Well their would be zero potential difference between the two points, there would therefore be no current that could flow through it either. I'm not sure about the resistance though.
     
  8. Jan 30, 2013 #7
    Try redrawing the circuit with a straight center wire.
     
  9. Jan 30, 2013 #8

    gneill

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    You could say the same for every wire in a circuit, yet current flows through them.

    Ideal wires, having no resistance, conduct current without losses (potential drop or power dissipated). Think of a wire as a zero ohm resistor. Place a zero ohm resistor in parallel with any other resistor and what's the resulting resistance?
     
  10. Jan 30, 2013 #9
    If you put a zero ohm resistor in place of the wire you would have three resistors in parallel. If you did this in the circuit above you would have an infinite resistance?

    (1/0 + 1/8 + 1/8)^-1 = inf
     
  11. Jan 30, 2013 #10

    gneill

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    Nope. You'd want to evaluate that expression using limit theory. Or for the faint of math, just call the "zero" resistor Rz and reduce algebraically before substituting Rz=0.
     
  12. Jan 30, 2013 #11
    So the equivalent resistance is then zero?
     
  13. Jan 30, 2013 #12

    gneill

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    Certainly. A wire is a zero resistance path. Nothing put in parallel with it can change that.
     
  14. Jan 30, 2013 #13
    What's ∞^(-1), you did not take the reciprocal.
     
  15. Jan 30, 2013 #14
    Oh ya think I forgot about that but that make since as well.

    Is an ideal current source sitting on a shelf like so

    |
    O
    |

    A valid circuit?

    The current has no were to go so isn't it invalid?
     
  16. Jan 31, 2013 #15

    CWatters

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    Just because there is zero potential difference doesn't mean the current would also be zero.
     
  17. Jan 31, 2013 #16

    CWatters

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    Depends what you mean by invalid. Can you actually make an ideal current source anyway?

    Lets say there was a 1K resistor across the output. What happens to the voltage if the resistor value is gradually increased to ∞ Ohms. Could you design a circuit to do that?

    At the end of the day "ideal" anythings are just a useful approximation to what goes on in the real world.
     
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