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An infinite ladder of resistors

  • Thread starter phys121
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  • #1
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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:

Answers and Replies

  • #2
318
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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.
 
  • #3
jambaugh
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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.
 
  • #4
jambaugh
Science Advisor
Insights Author
Gold Member
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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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