## A Problem of Resistance

Posted in Cute Problems with tags , on November 29, 2020 by telescoper

Bizarrely, last night I dreamt of this physics problem. This mean that I’ve seen it before somewhere, but if that’s the case then I’ve forgotten where. In the dream the problem of electrical resistance was muddled up with the problem of how to calculate the Euler Characteristic of a structure defined on a grid*, which is something I have used in the past. Anyway, with apologies for the poor quality of the drawing, here is the set up.

Twelve identical resistors R are arranged in four squares with common edges thus:

Yes, they’re meant to be identical squares!

What would be the effective resistance of this circuit measured between A and B?

Please post your answers through the comments box, with appropriate explanations. Bonus marks for elegant (i.e. short) solutions.

(In my dream this problem came up in contrast with the case where the four internal resistors and their connecting wires were absent, so the circuit was just a ring.  The Euler Characteristic of the original connected set of squares is 1 while that of the ring is 0, not that it’s relevant to the problem in hand!)

## A Cube of Resistance

Posted in Cute Problems with tags , , , on September 14, 2017 by telescoper

It has been brought to my attention that I haven’t posted any cute physics problems recently, so here’s one (which involves applying Kirchoff’s laws) that’s a bit harder than A-level standard which might be of interest to students about to begin a degree in physics this month!

The above image, produced using the advanced computer graphics facilities available at Cardiff University’s Data Innovation Research Institute, represents a cube formed of 12 wires each of which has resistance 1Ω.

What is the electrical resistance between: (i) A and G; (ii) A and H; and (iii) A and D?

As usual, answers through the comments box please!