Triangular Resistor Network

An interesting circuit once appeared under this thread:

http://forum.allaboutcircuits.com/showthread.php?t=43005

and I thought I would show how I solved it.

Using just 3 node voltage method equations.

The original problem said: "Find the resistance between points A and B if R=81 Ω.

This is the original circuit, posted by the OP:


All resistors are 81 Ω

Now this is what I did:

1. I re-drew the circuit to make it look neater.
2. I converted the three last resistors into 1.
3. I labeled E1,E2,E3 nodes.
4. I applied Node Voltage method.









And since the voltages E1, E3, are 3.5V, 2.8V, respectively, it follows that:

(3.5V/81) + (2.8V/81) = 77.77mA

Which means that the total circuit resistance is: 90 Ω

----
Thanks to Tony Kuphaltd for his great book.
Thanks to Qucs software for Linux to draw the schematics.
And thank you guys for letting me post this on the forum!

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