Resistor Pyramid

Electricity and Magnetism Level 3

Jo has 8 identical resistors with resistance r r . He decides to build a Resistor Pyramid for his Physics project. Being a curious boy, he tries to find out the equivalent resistance between A A and B B using his ohmmeter. Find the equivalent resistance that the ohmmeter shows up when r = 1 Ω r = 1 \Omega .

If the resistance can be expressed in the form of α β \dfrac{\alpha}{\beta} , where α \alpha and β \beta care coprime positive integers, submit your answer as α + β \alpha + \beta .


The answer is 23.

Swapnil Das by Swapnil Das , 20, India

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2 solutions

Relevant wiki: Series and parallel resistors

Let's take a top view of the pyramid,

Now, since the connections are symmetric about ℓ \ell , we can split the connections at point E E to give,

Now it's a simple circuit, which after computing the net resistance gives R e q = 1 1 + 1 2 + 1 2 + 1 1 + 1 2 = 8 15 R_{\mathrm{eq}} = \dfrac 1{1+\dfrac12+\dfrac1{2+\dfrac1{1+\dfrac12}}}=\boxed{\dfrac8{15}}

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Moderator note:

Always best to let a well made figure do the talking. This is exceptionally clear.

Thanks! That's very clearly presented :)

Calvin Lin Staff - 5 years ago

Very nicely done :)

Abhay Tiwari - 5 years ago
Swapnil Das
May 27, 2016

The very resistor pyramid can be transformed to the following, and then easily evaluated by the disconnection method.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Did the exact same

Aditya Kumar - 5 years ago

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