# The Naked Scientists Forum

### Author Topic: Physics thought problem  (Read 3753 times)

#### harryneild

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##### Physics thought problem
« on: 05/10/2006 20:12:50 »
We were learning about circuits, and all the laws involved in todays physics and my teacher briefly passed over what she said was a past oxbridge physics problem. I have attempted it but it seems way too hard for me.

The problem was- there is a wireframe cube, with a 10 ohm resistor on each of the edges (therefore 12 altogether). What is the total resistance of the cube when measured from one corner to its opposite?

Any solutions would be appreciated greatly! :)

Thankyou

"Knowledge has to be improved, challenged, and increased constantly, or it vanishes." Peter F. Drucker

#### syhprum

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##### Re: Physics thought problem
« Reply #1 on: 05/10/2006 21:10:10 »
You must re-draw the network in its simplests manner and apply unit voltage to the input, then calculate the voltage and source resistance at each junction hence the current flow for unit voltage from which the resistance can be derived.
I recall this problem being published about 1972 and I very labouriously calculated it by hand but my entry although correct was too late to win the prize.
There are more academicly correct ways of doing it if you have a Phd in electrical engineering!

syhprum

#### Soul Surfer

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• keep banging the rocks together
##### Re: Physics thought problem
« Reply #2 on: 05/10/2006 23:38:25 »
Consider the circuit. there are three ten ohm resistors connected to the input and three ten ohm resistors connected to the output.  the intermediate interconnection level consits of six ten ohm resistors each node splits into two and connects into two out of the three resistors connected to the output.  By symmetry each of the currents splits evenly at the input and output, and at the intermesiate level each of the currents splits evenly at the two resistors  so if the current in one of the resistors connected to the source or the sink is a the current in the intermediate level is a/2  so the total voltage drop across that section is half that across the input and output sections so if there was five volts across the network  two would drop over the input and output and one would drop over the middle section.

It follows that two volts across ten ohms produces 0.2amps times 3 for each of the resistors coneected to the input or output node  so there is a total current flow of 0.6 amps for a 5 volt drop across the whole network  r=v/i  so the total resistance is  5/0.6  =  8.333 ohms

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#### syhprum

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##### Re: Physics thought problem
« Reply #3 on: 07/10/2006 19:10:26 »
I feel you have over simplified the problem, the corner to corner computation is quite complex, I will work on it tomorrow after the Suzuka Grand prix.

syhprum

#### syhprum

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##### Re: Physics thought problem
« Reply #4 on: 13/10/2006 07:33:07 »
I must congratulate Soul Surfer on his analyses of the circuit, it is more simple than it appears at first sight due to the equal value of all the components as there are many nodes that can be joined.
It would be interesting to see the analyses of a similar cube incorporating unequal components and inductors and capacitors, it would certainly be beyond my mathematical skills.
I agree of course with the result of 8.333 Ohms

syhprum

#### The Naked Scientists Forum

##### Re: Physics thought problem
« Reply #4 on: 13/10/2006 07:33:07 »