puzzle

[18:25] <ibanezmatt13_> internet failed
[18:26] <eroomde> np
[18:26] <ibanezmatt13_> so yeah, I've tried a few methods and keep getting lost somewhere
[18:26] <ibanezmatt13_> I tried to replace multiple resistors with 1 resistor to narrow it down
[18:27] <eroomde> it's ok, you're doing what everyone does
[18:27] <eroomde> draws a net
[18:27] <ibanezmatt13_> yes
[18:27] <eroomde> but then reaslises that won't work because two end edges of the net are actually electrically connected
[18:27] <eroomde> and wonders how you're meant to deal with things folding back on themselves
[18:28] <eroomde> nd so on
[18:28] <ibanezmatt13_> yep
[18:28] <eroomde> and you'll fill 20 sheets of paper with lots of 1/R crap that isn't getting you an answer
[18:28] <ibanezmatt13_> 3 pages so far
[18:28] <eroomde> ok
[18:28] <eroomde> let's consider ohm's law
[18:28] <eroomde> because it's really powerful
[18:28] <ibanezmatt13_> ok
[18:29] <eroomde> say i have two points on a circuit, some random steady-state circuit
[18:29] <eroomde> they're both at the same voltage
[18:29] <ibanezmatt13_> ok
[18:29] <eroomde> i dunno what this circuit is, say some christmas lights or something
[18:29] <eroomde> doesn't matter
[18:29] <eroomde> you measure the voltage at point a, it's, say, 3V
[18:30] <eroomde> you measure the voltage at point b somewhere else in the circuit, it's at 3V too
[18:30] <eroomde> what would happen if i connected those two points with a wire?
[18:30] <ibanezmatt13_> 0V?
[18:30] <ibanezmatt13_> no
[18:30] <ibanezmatt13_> erm
[18:30] <eroomde> explain
[18:31] <eroomde> don't 'think' so much as use ohms law to tell me exactly
[18:31] <ibanezmatt13_> well I was going to say there's no overall potential
[18:31] <ibanezmatt13_> don't know
[18:31] <eroomde> by 'think' i mean, go on intuition
[18:31] <eroomde> ok, that's a very good start
[18:32] <eroomde> though you should be strict with your terminology and say there's no potential *difference*
[18:32] <eroomde> which is what we define 'voltage' to be
[18:32] <ibanezmatt13_> ok
[18:32] <eroomde> potential difference is the better term for voltage really
[18:32] <eroomde> ok, so there's no potential difference between these two points
[18:32] <eroomde> so what happens if i connect them with a wire?
[18:33] <ibanezmatt13_> err
[18:33] <ibanezmatt13_> nothin
[18:33] <eroomde> why?
[18:33] <eroomde> explain your reasoning with reference to ohm's law
[18:34] <ibanezmatt13_> I can't think how to refer to ohm's law
[18:34] <ibanezmatt13_> like use an equation?
[18:34] <eroomde> yes
[18:34] <eroomde> always yes :)
[18:34] <ibanezmatt13_> ah
[18:34] <ibanezmatt13_> erm
[18:34] <eroomde> equations are fantastic
[18:34] <eroomde> you can prove what you're saying with them
[18:34] <ibanezmatt13_> ok so
[18:35] <ibanezmatt13_> pd = 0, so IR = 0.  Erm, either current or resistance is 0.]
[18:35] <ibanezmatt13_> I don't know
[18:35] <eroomde> yes exactly!
[18:35] <eroomde> now, you know r is never 0 exactly
[18:35] <ibanezmatt13_> no
[18:35] <eroomde> so it must be that I is zero
[18:35] <ibanezmatt13_> oh cool
[18:35] <eroomde> you can disambiguate that by rearranging
[18:35] <eroomde> I = V/R
[18:36] <eroomde> V= 0 there I = 0
[18:36] <eroomde> therefore*
[18:36] <ibanezmatt13_> of course
[18:36] <eroomde> cool
[18:36] <ibanezmatt13_> interview questions? seriously? :)
[18:36] <eroomde> so, a circuit only does things when there's a flow of current
[18:36] <eroomde> that's what a circuit is
[18:36] <ibanezmatt13_> of course
[18:36] <eroomde> no, the resistor cube is the interview question
[18:36] <ibanezmatt13_> right
[18:37] <eroomde> i'm just steering you to the aha moment you need to answer this q
[18:37] <ibanezmatt13_> right, so I should be able to figure this now
[18:37] <eroomde> so, summarise for me, if we connect two pooints on a circuit at the same potential, does it affect the circuit?
[18:37] <ibanezmatt13_> no
[18:37] <eroomde> perfect
[18:38] <eroomde> ok, so now go and tell me the resistence across the cube
[18:38] <ibanezmatt13_> erm
[18:40] <ibanezmatt13_> So I'm working out total R?
[18:40] <eroomde> the R you see from one corner of the cube to the opposite corner
[18:41] <ibanezmatt13_> Assuming what?
[18:41] <eroomde> if you were to put a multimeter across
[18:41] <eroomde> where each edge of the cube is a 1ohm resistor
[18:41] <eroomde> http://www.rfcafe.com/references/electrical/images/resistor-cube-kirt-1.gif
[18:41] <eroomde> R between A and B
[18:42] <ibanezmatt13_> I'm now thinking of how a multimeter actually works, must being straying off topic
[18:42] <eroomde> yep
[18:43] <eroomde> but it works by injecting a known constant current and measuring the voltage between A and B
[18:43] <ibanezmatt13_> oh right, that may help
[18:43] <eroomde> no not really
[18:43] <ibanezmatt13_> oh
[18:43] <eroomde> you don't need to know how it works
[18:43] <eroomde> it just measures the resistence between A and B
[18:43] <eroomde> we want to know what that resitence is
[18:44] <ibanezmatt13_> they have the same PD
[18:44] <eroomde> thing about the discussion we just had. the clue to analysing this circuit is there
[18:44] <ibanezmatt13_> at each point?
[18:44] <eroomde> which points have the same PD?
[18:44] <ibanezmatt13_> one corner to other
[18:44] <ibanezmatt13_> diagonal
[18:44] <eroomde> nope
[18:44] <ibanezmatt13_> oh
[18:45] <eroomde> if i were to put a battery between A and B, it wouldn't be a short circuit
[18:45] <eroomde> so, nope
[18:45] <eroomde> otherwise if A and B did have the same PD, then you could just replace that whole resistor cube with a wire
[18:45] <eroomde> i.e. a short
[18:45] <ibanezmatt13_> ah yes
[18:45] <eroomde> and that clearly isn't the same thing
[18:45] <ibanezmatt13_> of course
[18:46] <eroomde> but keep wondering about which points on that cube are at the same potential
[18:46] <ibanezmatt13_> ok
[18:46] <ibanezmatt13_> none of them
[18:47] <ibanezmatt13_> wait
[18:47] <eroomde> imagine you stick that battery across A and B
[18:47] <eroomde> ok, waiting
[18:47] <ibanezmatt13_> same pd across each resistor?
[18:47] <ibanezmatt13_> as they're identical
[18:48] <eroomde> not necessarily no
[18:48] <ibanezmatt13_> oh
[18:48] <eroomde> depends on how they're all connected up
[18:48] <ibanezmatt13_> oh of course
[18:48] <ibanezmatt13_> if in parallel
[18:48] <ibanezmatt13_> ok erm
[18:48] <eroomde> so imagine this battery we connect to A and B is say 5V
[18:48] <ibanezmatt13_> ok
[18:49] <eroomde> if you get your voltage meter out and randomly probe around, you know you're gonna see voltages between 5 and 0V
[18:49] <eroomde> 5V and A, 0V and B, stuff in between in other bits of the cube
[18:49] <ibanezmatt13_> ok
[18:49] <eroomde> happy with that?
[18:49] <ibanezmatt13_> yep
[18:49] <eroomde> right
[18:50] <eroomde> so, say you're being systematic about it
[18:50] <eroomde> you first probe A, you see 5V
[18:50] <eroomde> what would be the next obvious place(s) to probe?
[18:50] <ibanezmatt13_> B
[18:50] <eroomde> ok, that's 0V
[18:50] <eroomde> where next?
[18:50] <ibanezmatt13_> All branches connected to B?
[18:50] <ibanezmatt13_> no
[18:51] <ibanezmatt13_> wait yes
[18:51] <ibanezmatt13_> across each resistor connected at B
[18:51] <eroomde> ok, so you mean just on the other sides to B of the 3 resistors connected to B?
[18:51] <eroomde> ah good :)
[18:51] <ibanezmatt13_> that's what Imeant
[18:51] <eroomde> and what would you expect those 3 voltages to be like, relative to one another?
[18:52] <ibanezmatt13_> The same
[18:52] <ibanezmatt13_> parallel
[18:52] <eroomde> given the cube is nicely symmetrical
[18:52] <eroomde> yes!
[18:52] <eroomde> so you could connect up those points with your virtual bit of wire
[18:52] <eroomde> and not have the circuit be affected
[18:52] <ibanezmatt13_> which points?
[18:52] <ibanezmatt13_> the three points
[18:53] <eroomde> you tell me
[18:53] <ibanezmatt13_> yes
[18:53] <ibanezmatt13_> the three points
[18:53] <eroomde> yes
[18:53] <ibanezmatt13_> ok
[18:53] <eroomde> so you now have 3 resistors connected to each other at both ends
[18:53] <eroomde> i.e., in parallel
[18:54] <ibanezmatt13_> yes
[18:54] <eroomde> great
[18:54] <eroomde> now spot the symetrry
[18:54] <eroomde> of the cube
[18:54] <ibanezmatt13_> diagonal line
[18:54] <ibanezmatt13_> through
[18:54] <eroomde> and go away for a bit to work out the resistence between A and B
[18:57] <ibanezmatt13_> It doesn't seem to be clicking
[18:58] <eroomde> try and draw it 2d
[18:58] <ibanezmatt13_> the cube net?
[18:58] <eroomde> you've started well by saying the first 3 resistros can be connected in parallel
[18:58] <eroomde> not the cube net
[18:58] <eroomde> the circuit
[18:59] <ibanezmatt13_> oh
[18:59] <ibanezmatt13_> ok
[18:59] <eroomde> using your insight about how you can put in virtual wires
[19:00] <ibanezmatt13_> they're all in parallel
[19:01] <eroomde> no
[19:01] <ibanezmatt13_> oh
[19:01] <ibanezmatt13_> oh of course
[19:01] <ibanezmatt13_> sorry
[19:04] <eroomde> where are you at?
[19:04] <ibanezmatt13_> a very strange diagram that looks kinda good
[19:04] <ibanezmatt13_> let me take a picture
[19:04] <ibanezmatt13_> one sec
[19:06] <ibanezmatt13_> http://sdrv.ms/19Fat79
[19:06] <ibanezmatt13_> three parallel resistors in the middle
[19:06] <ibanezmatt13_> and each ones connects to a further two in parallel
[19:06] <ibanezmatt13_> only 9 there though
[19:07] <eroomde> where the the 3 in parallel?
[19:07] <ibanezmatt13_> right in the middle
[19:07] <eroomde> they don't look in parallel to me
[19:07] <eroomde> you haven't connected the other ends together
[19:07] <ibanezmatt13_> oh
[19:07] <ibanezmatt13_> ah yes
[19:08] <ibanezmatt13_> damn
[19:08] <eroomde> remember, these virtual wires are your friends
[19:08] <eroomde> draw them
[19:08] <ibanezmatt13_> I've not got to that part :/
[19:08] <ibanezmatt13_> oh waity
[19:08] <ibanezmatt13_> think I get what you mean by virtual wires
[19:08] <eroomde> make them real wires
[19:08] <eroomde> imagine soldering them in there
[19:09] <eroomde> then draw *that* circuit
[19:09] <ibanezmatt13_> across each resistor?
[19:09] <ibanezmatt13_> the wires
[19:09] <eroomde> just such that you connect up the points you've identified as being at the same potential
[19:09] <eroomde> which so far iirc is the first 3 corners on the other side of the 3 resistros from B
[19:09] <ibanezmatt13_> yep
[19:09] <eroomde> ok
[19:10] <eroomde> now when i brough up symmetry, think about how it works for A too
[19:10] <ibanezmatt13_> same principle
[19:10] <eroomde> yep!
[19:10] <ibanezmatt13_> still don't know the answer
[19:11] <eroomde> i have drawn something for you
[19:11] <ibanezmatt13_> very kind of you
[19:11] <eroomde> https://www.dropbox.com/s/qe6irwe5pjfk477/2013-10-15%2019.03.49.jpg
[19:11] <ibanezmatt13_> ok so you've labelled the resistors?
[19:12] <eroomde> yes, just so you can see what's going on
[19:12] <eroomde> so the dotted lines are my virtual wires
[19:12] <eroomde> you can see if connected up the 3 points are resistors 1,2,3
[19:13] <eroomde> yep?
[19:13] <eroomde> you can see i've*
[19:13] <ibanezmatt13_> erm one sec
[19:13] <eroomde> after resistors*
[19:13] <eroomde> sorry can't type
[19:13] <ibanezmatt13_> ok yes
[19:13] <eroomde> and i've done the same with dotted lines for the symmetrical case for B
[19:13] <eroomde> 10,11,12
[19:14] <ibanezmatt13_> those dotted lines appear to be connecting 10,11
[19:14] <ibanezmatt13_> sorry
[19:14] <ibanezmatt13_> 10,12
[19:14] <eroomde> oh sorry
[19:14] <eroomde> crap diagram
[19:14] <ibanezmatt13_> 11 to me looks out of the question
[19:15] <eroomde> well, the nodes are 10,11, and 12 are all connected
[19:15] <eroomde> with dotted lines
[19:15] <ibanezmatt13_> oh I see
[19:15] <ibanezmatt13_> I was visualising it wrong
[19:16] <eroomde> cool
[19:16] <eroomde> should have used colour
[19:16] <ibanezmatt13_> I still can't see the point of the wires yet :/
[19:16] <eroomde> look at the diagram on the right!
[19:16] <eroomde> let's start from A
[19:17] <ibanezmatt13_> ok
[19:17] <eroomde> A is connected to resistors 1,2 and 3
[19:17] <ibanezmatt13_> yes
[19:17] <eroomde> we have agreed that the other sides of 1,2 and 3 can all be connected together
[19:17] <eroomde> because that won't affect the circuit
[19:17] <eroomde> yep?
[19:17] <ibanezmatt13_> yes, same pd
[19:17] <eroomde> yep
[19:17] <eroomde> ok, so i draw the first bit of the diagram on the right
[19:18] <eroomde> 1,2 and 3 in parallel
[19:18] <ibanezmatt13_> yes
[19:18] <eroomde> they're basically all the same point now
[19:18] <eroomde> a single node
[19:18] <ibanezmatt13_> ok
[19:18] <eroomde> even though it's actually 3 nodes, you can model it as a single virtual node
[19:18] <eroomde> because we've connected all the nodes up with wires
[19:18] <eroomde> so
[19:18] <eroomde> that's the first bit
[19:18] <ibanezmatt13_> ok
[19:19] <eroomde> now we do the same with the bottom 3 starting from B
[19:19] <eroomde> for 10,11 and 12
[19:19] <ibanezmatt13_> ok
[19:19] <eroomde> and i draw them in parallel at the bottom of the diagram on the right
[19:19] <eroomde> happy?
[19:19] <eroomde> so far...
[19:19] <ibanezmatt13_> I think so yeah
[19:19] <eroomde> so now we have to deal with all the crap in the middle
[19:19] <eroomde> 4,5,6,7,8,9
[19:20] <eroomde> now, look at any of those resistors you like
[19:20] <eroomde> they go from the virtual node on the A side to the virtual node on the B side, i.e. from a point connected by the dotted lines on the A side to a point connected to the dotted lines on the B side
[19:20] <ibanezmatt13_> ok
[19:20] <eroomde> do you see that?
[19:20] <eroomde> from the left hand diagram
[19:21] <ibanezmatt13_> let me have a look
[19:21] <ibanezmatt13_> ah yes :)
[19:21] <ibanezmatt13_> cool
[19:21] <eroomde> so, does the diagram on the right make sense now?
[19:22] <ibanezmatt13_> yes but I'd have never thought of that
[19:22] <eroomde> welcome to interview questions :D
[19:22] <eroomde> don't worry, it seems terrifying now
[19:22] <ibanezmatt13_> I'm gonna become a binman
[19:22] <eroomde> but with practice you start to see how to think about problems better
[19:22] <eroomde> lol
[19:22] <ibanezmatt13_> still not got the total R
[19:22] <eroomde> i nearly cried when i first saw a cambridge exam question in first year
[19:23] <ibanezmatt13_> not surpirsed
[19:23] <eroomde> well, it's 3 in parallel + 6 in parallel + 3 in parallel
[19:23] <eroomde> so 1/3 + 1/6 + 1/3
[19:23] <ibanezmatt13_> Total R = 6/5
[19:24] <eroomde> 5/6
[19:24] <eroomde> 2/6+1/6+2/6
[19:24] <ibanezmatt13_> is that not the reciprocal?
[19:24] <ibanezmatt13_> ie 1/Rtotal
[19:24] <eroomde> so the first bit is 1/Rtot
[19:24] <eroomde> where rtot = 3
[19:24] <eroomde> so the first bit is 1/3
[19:25] <eroomde> it's connected *in series* with the second bit and third bit
[19:25] <ibanezmatt13_> oh
[19:25] <ibanezmatt13_> I see
[19:25] <ibanezmatt13_> total r = 5/6
[19:25] <eroomde> so you have 3 chunks connected in series
[19:25] <eroomde> and within each chunk, they connected in parallel
[19:26] <ibanezmatt13_> well, it all makes sense now I guess. But it wouldn't have got me through the interview!
[19:26] <eroomde> we'll keep practicing random things like that
[19:26] <eroomde> it's 100% practice
[19:27] <eroomde> you'll find you start being able to solve them more easily
[19:27] <ibanezmatt13_> I need to do more of these things
[19:27] <ibanezmatt13_> Can we do one every night?
[19:27] <eroomde> but they're a definite step up from a-level, were it's more knowing how to crank the machine rather than have some insight
[19:27] <eroomde> i'm probably a bit busy for that, but can certainly do them every now and then
[19:27] <ibanezmatt13_> fair enough. Thanks for the help
[19:29] <ibanezmatt13_> This exercise has made me a little more doubtful about whether I'll be able to get half decent grades. :/
[19:29] <eroomde> almost no one can answer that question in the interviews
[19:29] <eroomde> don't worry
[19:30] <ibanezmatt13_> I got an email from a teacher who reviewed my dislexia test. I'm not dislexic apparently, but he said that the test has suggested I will find the majority of my maths course very difficult and that I need to speak to him about it. Bloody marvellous
[19:30] <eroomde> that's vastly harder than anything a-levels would ask of you
[19:31] <eroomde> it's just practice. thinking mathematically is a muscle
[19:31] <ibanezmatt13_> mm
[19:32] <eroomde> i promise
[19:32] <eroomde> in october of first year i tried my first exam question
[19:32] <eroomde> and had a moment like you just had
[19:32] <eroomde> thinking this is so so so so far beyond my powers of thinking
[19:32] <eroomde> and by the summer i could actually do them
[19:32] <eroomde> don't worry about it, we'll just practice
[19:33] <ibanezmatt13_> see, I'm not actually that intelligent. I just have a very good work ethi
[19:33] <ibanezmatt13_> c
[19:33] <eroomde> everyone who did well at cam said the same thing
[19:33] <eroomde> it's totally about consistently plugging away
[19:33] <eroomde> nothing is difficult, it just takes consistent effort ot chip away at it
[19:33] <eroomde> to understand it
[19:34] <ibanezmatt13_> I guess I'll just plod on and see what happens
[19:34] <eroomde> that's all you can do
[19:35] <eroomde> and the right thing to do
[19:35] <ibanezmatt13_> Thankfully, my GCSE results mean I have safely got a place as a bus driver or local class 140 train driver at a push
[19:35] <eroomde> nice to have a backup!
[19:35] <ibanezmatt13_> :)
[19:36] <ibanezmatt13_> You never know, NORB might go global and I'll become Richard Branson of NORB technologies
[19:39] <ibanezmatt13_> eroomde, do you know of any other puzzles like that resistor one that I can look at?
[19:40] <eroomde> nope, wouldn't worry about it though
[19:40] <ibanezmatt13_> ok
[19:49] <eroomde> right, off home
[19:49] <eroomde> bbl