In Cube of resistances how to calculate current in one edge?

[agoogler]

Homework Statement

Twelve resistors of equal resistance are connected so as to form a
cube ABCDEFGH shown. Equivalent resistance between points A
and G is 5/3 ohm. If a battery of voltage 100 V is connected across
the points A and G, find the current (in ampere) flowing through the
resistor CD.

Homework Equations

V=IR
1/R_parallel = 1/R₁ + 1/R₂ + ...
R_series = R₁ + R₂ + ...

The Attempt at a Solution

V=IR
So 100=i*5/3 ( between A and G )
So current between A and G is i=60 .
But what now ? How to calculate current between C and D ?

 

[ehild]

Use the symmetry and use KCL. I=60A current flows into A. It has three equivalent ways to flow: Towards B, D, and E.

The current flowing into D has two choices to flow further...ehild

 

[agoogler]

Use the symmetry and use KCL. I=60A current flows into A. It has three equivalent ways to flow: Towards B, D, and E.

The current flowing into D has two choices to flow further...


ehild

Whats KCL? Also by symmetry do you mean that some of the currents are equal or what ?

 

[ehild]

Whats KCL? Also by symmetry do you mean that some of the currents are equal or what ?

KCL is Kirchhoff's Current Low. By symmetry, I mean that equal currents flow along equivalent paths.

ehild

 

[CWatters]

KCL = kirchhoff current law.

I would draw the equivalent circuit first. Do you know how to calculate the equivalent resistance between A and G? if you do then it might be easier.

 

[agoogler]

KCL = kirchhoff current law.

I would draw the equivalent circuit first. Do you know how to calculate the equivalent resistance between A and G? if you do then it might be easier.

Nope I don't know how to find equivalent resistance between A and G . Also by drawing equivalent circuit do you mean to convert this 3d cube into 2d circuit ? If so how to do that ?

 

[ehild]

Nope I don't know how to find equivalent resistance between A and G . Also by drawing equivalent circuit do you mean to convert this 3d cube into 2d circuit ? If so how to do that ?

It is not needed. You are given the equivalent resistance. So you know the current flowing into the node A. How much current flows out of A along each resistor connected to A?

ehild

 

[Chestermiller]

Follow Echild's advice. 60 amps flow out of node G and 60 amps flows into node A. By symmetry, the current flowing out of node G splits evenly between legs GH, GC, and GF. Also, by symmetry, the same 60 amp current converges evenly from BA, DA, and EA into node A. So, the current in all 6 of these legs is 20 amps. Now all you need to do is to use symmetry to figure out how the 20 amp current coming into node C from node G splits between legs CB and CD.

Chet

 

[agoogler]

Follow Echild's advice. 60 amps flow out of node G and 60 amps flows into node A. By symmetry, the current flowing out of node G splits evenly between legs GH, GC, and GF. Also, by symmetry, the same 60 amp current converges evenly from BA, DA, and EA into node A. So, the current in all 6 of these legs is 20 amps. Now all you need to do is to use symmetry to figure out how the 20 amp current coming into node C from node G splits between legs CB and CD.

Chet

So the current splits evenly between CB and CD and so the current through CD is 10 amps . The answer is right but can you link me to a good online video/tutorial/guide/book which explains this "symmetry " thing ?

 

[ehild]

Try:

http://physicstasks.eu/uloha.php?uloha=285

and you can follow the thread in Physics Forums from post #6

https://www.physicsforums.com/showthread.php?t=557461

ehild

 

[CWatters]

The traditional way to solve the resistor cube problem by applying symmetry...

http://www.rfcafe.com/miscellany/factoids/kirts-cogitations-256.htm#Traditional_Method

Also has other methods.

 

[agoogler]

Thanks for the links guys !

 

[cabraham]

For a cube with 12 identical resistors on each edge, I remember the resistance across corners as (5/6)*R, not (5/3)*R.

Claude

 

[ehild]

Claude,

The equivalent resistance was said 5/3 ohm, not 5/3 R. ehild

 

[cabraham]

Well, if the edge resistance is R, then the diagonal resistance is 5/6 of R. With 1.0 ohm resistors on each edge, the catecorner resistance should be 5/6 ohm, not 5/3 ohm. I'm pretty sure I remember it right.

Take the 1st corner, draw a shorting plane through the vertices of the adjacent corners. Do the same at the diagonally opposite corner. What is the net resistance. If one corner is A, the other G, we compute Rag as follows. From A to plane 1 we have 3 edges in parallel for 1/3 ohm. From plane 1 to plane 2 we have 6 edges in parallel for 1/6 ohm. Then from plane 2 to G we have 3 edges in parallel for 1/3 ohm.

Rag = (1/3) + (1/6) + (1/3) = 5/6 ohm.

Claude

 

[nasu]

Where does it say that the resistors are 1 Ohm?

 

[cabraham]

Where does it say that the resistors are 1 Ohm?

The OP stated that all 12 edges were equal in resistance. Call this value "R". I stated that the value of Rag = (5/6)*R. Then I was told that it was 5/3 ohm, which is incorrect. If each edge has R= 1.0 ohm, then Rag = (5/6) ohm.

You're right, 1.0 ohm is not stated in the OP. It is merely 12 edges of equal value "R". So the diagonal resistance Rag would be (5/6)*R. Is this clear?

Claude

 

[nasu]

The OP stated that all 12 edges were equal in resistance. Call this value "R". I stated that the value of Rag = (5/6)*R. Then I was told that it was 5/3 ohm, which is incorrect. If each edge has R= 1.0 ohm, then Rag = (5/6) ohm.

You're right, 1.0 ohm is not stated in the OP. It is merely 12 edges of equal value "R". So the diagonal resistance Rag would be (5/6)*R. Is this clear?

Claude

Clear, bot not relevant for this problem.
The problem states that the resistance is 5/3 ohm. So you don't need the general formula.

An interesting results to remember, though.

 

[dauto]

Clear, bot not relevant for this problem.
The problem states that the resistance is 5/3 ohm. So you don't need the general formula.

An interesting results to remember, though.

Yes, but why remember it when it's so easy to calculate it?

 

[cabraham]

Clear, bot not relevant for this problem.
The problem states that the resistance is 5/3 ohm. So you don't need the general formula.

An interesting results to remember, though.

So am I correct in understanding that 12 edges have identical R, with the diagonal value Rag being 5/3 ohm? Is that right?

Just for the record, in that scenario, the R value for each edge would be 2.00 ohms. Then 5/6 of 2.00, gives 10/6 ohm, or equivalently 5/3 ohm.

Claude

 

[ehild]

Read the first post :

Twelve resistors of equal resistance are connected so as to form a
cube ABCDEFGH shown. Equivalent resistance between points A
and G is 5/3 ohm.

ehild