3 Kirhoff laws is all you need. Странно, в мое школьное время (начало 80-х) такие задачки были хлебом в 9-м и 10-м классе мат-школ. Чего такого заслуживающего в ней??

True, the CAPTCHA is probably there to filter out those pesky mathematicians, botanists and other non-physicists.

You can derive it directly from 2 Kirchhoff's laws (voltage around every loop is 0, net current at every node is 0), but it gets a bit messy. section 2.1 of Bollobas' "Modern Graph Theory" works out a simple example in detail using this method.

Most practical method is probably to use a CAS and a formula for 2-point resistance of general graphs (formula 2 of http://www.springerlink.com/content/ehddhc1cl2078cfa/), also see http://www.citeulike.org/user/yaroslavvb/article/1611063 for derivation

Without CAS, you could use parallel (conductances add), series (resistances add) and star-triangle laws (see Bollobas 2.1) to simplify the network into a single resistor

There are some interesting connections between theory of resistor networks and partition functions of statistical models. Alan Sokal (same one as the Alan Sokal hoax) shows that partition function of Potts model has equivalents of parallel/resistance laws of electrical networks http://arxiv.org/abs/math/0503607

Also, there's a 1-1 correspondence between electrical networks and reversible Markov chains (ie, http://www.citeulike.org/user/yaroslavvb/article/2081200), so you could potentially use theory of Markov Chains to solve this problem as well

Do you think one day the author of this forum will not be able to solve the circuit theory problem and hence be unable to enter?

I am speculating that he will forget to solve it soon after his 80th birthday. I hear thats when the resistance of the neuron sheaths breaks down and the charge carrying capacity comes down drastically.

## 5 comments:

3 Kirhoff laws is all you need.

Странно, в мое школьное время (начало 80-х) такие задачки

были хлебом в 9-м и 10-м классе мат-школ. Чего такого заслуживающего в ней??

Чего заслуживающего в этой задаче будет ясно из следующего поста :)

Interesting. Seems like they are filtering more than just spambots.

True, the CAPTCHA is probably there to filter out those pesky mathematicians, botanists and other non-physicists.

You can derive it directly from 2 Kirchhoff's laws (voltage around every loop is 0, net current at every node is 0), but it gets a bit messy. section 2.1 of Bollobas' "Modern Graph Theory" works out a simple example in detail using this method.

Most practical method is probably to use a CAS and a formula for 2-point resistance of general graphs (formula 2 of http://www.springerlink.com/content/ehddhc1cl2078cfa/), also see http://www.citeulike.org/user/yaroslavvb/article/1611063 for derivation

Without CAS, you could use parallel (conductances add), series (resistances add) and star-triangle laws (see Bollobas 2.1) to simplify the network into a single resistor

There are some interesting connections between theory of resistor networks and partition functions of statistical models. Alan Sokal (same one as the Alan Sokal hoax)

shows that partition function of Potts model has equivalents of parallel/resistance laws of electrical networks

http://arxiv.org/abs/math/0503607

Also, there's a 1-1 correspondence between electrical networks and reversible Markov chains (ie, http://www.citeulike.org/user/yaroslavvb/article/2081200), so you could potentially use theory of Markov Chains to solve this problem as well

Do you think one day the author of this forum will not be able to solve the circuit theory problem and hence be unable to enter?

I am speculating that he will forget to solve it soon after his 80th birthday. I hear thats when the resistance of the neuron sheaths breaks down and the charge carrying capacity comes down drastically.

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