The "Cubic" ohm question.?

Question

I have 12 off 1 ohm resistors.

They are all connected to form a cube, which means that each corner of the cube is formed by 3 ends of 3 resisters being connected.

The question is :- If you were to measure the resistance value of the cube from the "cape and corner" points of the cube, what would be the eqivalent resistor value ?

The "cape & corner" points are "top far away point" to "bottom near point".

Answer 1

There are essentially 3 sections to consider. As others have pointed out the first and last section have 3 equal paths of 1 ohm so each will contribute 1/3 ohm to the through path resistance. The difficult part is in the middle it seems there are actually 6 resistors in parallel giving 1/6 ohm. So I think the resistance from corner to corner is 5/6 ohm.

Answer 2

The easiest way to look at this is to use Kirchovs laws.

Imagine sending 3 amps through the cube. At the corner the current can go into 3 1 ohm resistors, and as this is a symmetric set up 1 amp goes through each. Similarly at the other end the current arrives equally, 1 amp through each of 3 1 ohm resistors.

Now follow any one path through the cube and add up the voltage dropped. It is 1 Volt across the first resistor and 1 Volt across the second and 1 Volt across the thirs. So there are 3 Volts from corner to corner for a 3 Amp current.

Hence the resistance is 1 Ohm.

Now imagine an infinite square grid of 1 ohm resistors and use the same idea to calculate the resistance diagonally across any square in the grid.

Answer 3

I recall the answer to this one.

First, there is a three-way symmetric split. Then for each of these three paths there is a two-way symmetric split. Then there are two-way and three-way joins.
Suppose you are sending 1 Amp through the resistor cube. At the first split, you get 1/3 Amp through each R. After the two-way split, you get 1/6 amp through each of those R's. Then back to 1/3, and all the current comes out the other corner.

The voltage drop for a 1 Ampere current along any path through the cube is 1Amp*(R/3+R/6+R/3)=1Amp*5R/6. But voltage per Ampere is the definition of equivalent resistance. So the answer is 5/6 Ohm.

Answer 4

my god.
I actually had to draw this one out first.
simply, the answer is...1/6 of 36, which equals 6ohms
from the first point, there is 6 ways without backtracking to travel.
so there is the 1/6. and each path goes through 3 resistors of 12 ohms each. so there is the 36. make it and see

Answer 5

Without looking closer to the problem, I'd say the value is 1 Ohm.

Answer 6

5/6 ohm

Answer 7

you'de have to do a massive matrix to solve this one, it would be a disaster! trick question,, looks simple...