How Does Circuit Resistance Change with Increasing Triangle Numbers?

AI Thread Summary
The discussion revolves around determining how circuit resistance changes with increasing triangle numbers in a circuit composed of resistors. The circuit's resistance is calculated for n = 1, 3, and 6 triangles, but the user struggles with n = 10. The user notes that the circuit has vertical symmetry, allowing for simplifications by connecting points with the same potential. They seek advice on techniques to simplify the circuit further to derive a function for resistance as a function of n. The user emphasizes the importance of resolving this problem for their understanding.
Petrulis
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Homework Statement



First of all, there is an an attachment called EXPLANATION which shows the situation and what I have done so far.

So we have got some circuits which are made of triangles (each triangle is made of three resistors (resistors here are shown as rectangles)). The resistance of each resistor is R. The shown part of the circuit is connected to the source with points A and B.

We increse the number of triangles. The first circuit is made of n = 1 triangle, the second circuit has got n = 3 triangles and so on (so n can be equal to 1;3;6;10;15;21...).

I need to find out how the resistance of the circuit depends on n. So I really have to find out the function
(resistance of the circuit) = f(n).

So as you see I can calculate the resistance when n =1;3 and 6, but I stop when I reach n=10.


Homework Equations



Each circuit has got vertical symmetry axis (it is the grey line in the EXPLANATION drawing. This grey line is not the part of the circuit). So the points a, b, c, d, e has got the same potentials, and when we draw the equivalent circuit, we can connect these points with a wire.


The Attempt at a Solution



So I can't draw the equivalent circuit when n = 10, and I can't find out how the resistance of the circuit depends on n.
Maybe I should use other techniques for simplifying the circuit?

Thanks in advance.
 

Attachments

  • EXPLANATION.JPG
    EXPLANATION.JPG
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Pleas someone have a look at this problem. It is very important for me.
 
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