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An infinite ladder of resistors

  1. May 18, 2009 #1
    The network of resistors shown extends off to infinity. The resistors on the
    sides of the “ladder”, RS, are equal to each other,but different from the resistors in the center of the ladder,Rc

    ..............Rs..............................Rs.........................Rs
    a------^^^^^------c---------^^^^^------------^^^^^------------etc.
    ............................>...............................>........................>
    ............................<...............................<........................<
    ............................>Rc............................>Rc.....................>Rc
    ............................<...............................<........................<
    ............................>...............................>........................>
    b------^^^^^------d---------^^^^^------------^^^^^------------etc.
    ..............Rs................................Rs..........................Rs

    1) find a general expression for the resistance RT between points a and b.

    2) find a general expression for the potential difference between points c and d in
    terms of the Rs , Rc , Rt , and the potential difference between points a and b, Vab .


    Any Help would be very much appreciated. have been sitting her for many hours now just stuck!

    Ps. Please ignore all the full stops, it was the only way to make the circuit look like it should. So they actually mean nothing.
    Between the two 'ladder' sides there is a resistor Rc just in case its not 100% clear. thanks in advance
     
    Last edited: May 18, 2009
  2. jcsd
  3. May 18, 2009 #2
    Well this could have been a classic sum had been an infinite maze. But its quite easy as it s a ladder. The thing you have to note is that this is an infinite arangement.Lets say that the resisatnce betwen a and b is R. Then you can assume that after the c d branch you can replace the remaining ladder with R.
     
  4. May 18, 2009 #3

    jambaugh

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    Science Advisor
    Gold Member

    I suggest you work out the resistance for a couple of finite ladders to see if there is a general formula to which you can apply a limit.
     
  5. May 18, 2009 #4

    jambaugh

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    Science Advisor
    Gold Member

    On second thought you can use a recursion relationship. Remember that the whole ladder is one rung plus another identical infinite ladder.
     
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