How many pure serial, pure parallel and combined did you get?
How many pure serial, pure parallel and combined did you get?
I found 17. Of the combined s-p I got 3 par. within ser. 3 ser within par. and 3 par within par. Maybe one is redundant.
You are right, they are not different, and the resistance is the same (0.977 Ohm) when calculated separately in spite of the extra junction. Then I get 14 possibilities as well. A good thing I did not choose electronic engineering.
Last edited by Timoleon of Korinthos; February 06, 2013 at 03:24 PM.
"Blessed is he who learns how to engage in inquiry, with no impulse to hurt his countrymen or to pursue wrongful actions, but perceives the order of the immortal and ageless nature, how it is structured."
Euripides
"This is the disease of curiosity. It is this which drives to try and discover the secrets of nature, those secrets which are beyond our understanding, which avails us nothing and which man should not wish to learn."
Augustine
You are right, they don't have an equivalent because they involve three terminals, not two. I can't think of another 2 combinations though, I also get 14. Unless you count each resistance by itself as a combination, in which case you would have 17. Do you need to calculate equivalent resistances or just draw the different combinations?
Last edited by Timoleon of Korinthos; February 06, 2013 at 03:50 PM.
"Blessed is he who learns how to engage in inquiry, with no impulse to hurt his countrymen or to pursue wrongful actions, but perceives the order of the immortal and ageless nature, how it is structured."
Euripides
"This is the disease of curiosity. It is this which drives to try and discover the secrets of nature, those secrets which are beyond our understanding, which avails us nothing and which man should not wish to learn."
Augustine
I tried with a =0, the result is (a,b,c,d)=(0,1/2,2/3,-1/6), I found it weird to have a negative probability though.
then with a=1, the result is (a,b,c,d)=(1, -1/2,-1/3,5/6), weirder...
Seems there are infinate solutions, but you want the one with all 4 being positive. I can't help you more.
This is a linear system of equations. The simplest treatment for such problems is the Gaussian elimination.
The issue in this case is that after the first steps you end up with the following equivalent system:
1a + 1b + 0c + 0d = 1/2
0a + 1b + 0c + 1d = 1/3
0a + 0b + 1c + 1d = 1/2
0a + 0b + 1c + 1d = 1/2
This shows that essentially you have 4 unknowns but only 3 linearly independent equations, consequently one degree of freedom, so if you want a solution you have to choose a value for one of the unknowns yourself, plug it in the equations and solve for the other three. This means of course that you can obtain infinite sets of solutions, as your parameter can take an infinite number of values.
Your physical constraints are that since a,b,c,d represent probabilities, the value of each of them must lie between 0 and 1. So one pretty straightforward solution is to set c=1/3, which will bring about d=1/6, b=1/6 and a=1/3. All of them within the [0,1] range, therefore having a physical meaning. I suspect that this is what your teacher expects.
At this point I want to ask, have you been taught linear algebra in your course, or are you supposed to be familiar with it? If no, skip the rest. If yes, the fact that there is no unique solution can be proven:
In your system A = [1 1 0 0; 0 0 1 1; 1 0 1 0; 0 1 0 1;]
and b = [1/2 1/2 2/3 1/3]T
You will note that m=n=4, det(A)=0 and rank(A)=rank([A b]) = 3, so a solution exists and depends on n-rank = 4 -3 = 1 parameters
Last edited by Timoleon of Korinthos; February 10, 2013 at 10:02 PM.
"Blessed is he who learns how to engage in inquiry, with no impulse to hurt his countrymen or to pursue wrongful actions, but perceives the order of the immortal and ageless nature, how it is structured."
Euripides
"This is the disease of curiosity. It is this which drives to try and discover the secrets of nature, those secrets which are beyond our understanding, which avails us nothing and which man should not wish to learn."
Augustine
I had better luck in the begining trying with b=0 as well as d=0 getting (1/2,0,1/6,1/3) and (1/6,1/3,1/2,0)
I did the Gaussian elimination and with one more step I got
1a + 0b + 0c - 1d = 1/6
0a + 1b + 0c + 1d = 1/3
0a + 0b + 1c + 1d = 1/2
0a + 0b + 1c + 1d = 1/2
If I put d=t it leads to
a = 1/6 + t
b = 1/3 - t
c = 1/2 - t
d = t
From here I can only make the constraint 0 ≤ t ≤ 1/3 and I guess that's the most I can get out of it.
This is only part of an exercise, another part implies that d = 1/3 and since that is one possible solution I believe it is solved.
Well, I don't know, yes, if you need to find a set of specific figures go for d=1/3 or whatever makes sense in the context of the exercise.
But I would say that the way you have expressed every unknown as a function of t would be the best way to formulate the solution in the general case, because it displays the parametric dependence from the outset as well as making obvious the range of values that your parameter can take in order for the physical constraints of the problem to be respected.
"Blessed is he who learns how to engage in inquiry, with no impulse to hurt his countrymen or to pursue wrongful actions, but perceives the order of the immortal and ageless nature, how it is structured."
Euripides
"This is the disease of curiosity. It is this which drives to try and discover the secrets of nature, those secrets which are beyond our understanding, which avails us nothing and which man should not wish to learn."
Augustine
Yo!
What raw materials are used to make USB flash drives? Its a pain in the ass, i searched whole internet but didnt find anything..
Magic.
Probably a stupidly obvious chem question which I have trouble answering.
"Separate samples of a solution of an unknown soluble ionic compound are treated with KCL, Na2SO4, and NaOH. A precipitate forms only when Na2SO4 is added. Which cations could be present in the unknown soluble ionic compound?"
I don't really need an answer, just an explanation of how to progress through this problem would be greatly appreciated.
A People, but a Nation? A Louisiana AAR [Startpos mod] (updated June 13)
Look up which ions would make precipitations (look for numbers for solubility) with KCl (not many if any) and NaOH (some here). Precipitations are expected if the solubility of any new possible species is lower than those already in solution. The cations forming precipitations with Cl+ and/or OH- is not expected to be present in the solution. Then look up which sulphate salts that have a low solubility and discard those not having high solubilities as hydroxides or chlorides.
Edit: If this was unclear then please let me know, and I will try to give a better explanation.
Last edited by Logios; February 20, 2013 at 06:45 AM.
Could somebody help me with my electricity & magnetism homework?
Question 1:
Two condensers connected in series will be charged such that one gets +Q charge on one of its plates, and the other -Q.
Schematic: ------(-Q)| |(a)------(b)| |(+Q)-------
Can somebody prove (or at least show) intuitively to me why the plate "a" gets a +Q charge, and the plate "b" -Q? Ie, why do the inner plates have charges equivalent to the outer ones?
Question 2:
A dialectic of length d is inserted into a condenser made up of two plates a distance D apart (d<D). Afterwards, the condenser acts like it is two condensers connected in series. Why?
Last edited by Nikitn; February 24, 2013 at 03:02 AM.