Find Current I: 2 R & V Short Circuit

[Gbox]

Homework Statement

All resistors have resistance of R and all voltage sources have voltage of V, Find the current I

Homework Equations

The Attempt at a Solution

At the leftmost corner I can connect the two resistors in parallel, but what should I do with the short on the top right?

 

[.Scott]

I would do this one voltage source at a time - and then add the results up.
You have three resistors in parallel at the top left and two in parallel at the top right.

 

[Gbox]

What does it mean each "voltage source at a time"?

in the top left I can see just 2 resistor in parallel and so in the right:

 

[CWatters]

or even...

 

[azizlwl]

Just remove the short-cicuited resistors(series resistors). No current flow through them.

 

[Gbox]

Just remove the short-cicuited resistors(series resistors). No current flow through them.

Why can I remove it? there is current there, here is what I got:

 

[azizlwl]

There is no potential difference between both end of the conductor, thus no current flow across resistors parallel to it. Likewise no current flow up to the middle of the shorted resistors since no potential difference between them. If you say X volt on the right side, it will the same at the middle, which in turn equal to the right side of the lower resistor.
If you have a conductor carrying current, will there any difference to the circuit if you touch both ends of resistor to it.
It will be helpful if you could name all the resistors.

 

[Gbox]

From the current point of view (the arrows I added) this is what you mean? therefore where there is no current I can remove those resistors?

 

[haruspex]

Just remove the short-cicuited resistors(series resistors). No current flow through them.

Are there any short-circuited resistors?
Numbering the resistors from 1, top to bottom, left to right within a horizontal: 3 , 4 and 5 are in parallel, but not short-circuited. Likewise 1 and 2. See CWatters' diagram.

 

[azizlwl]

From the current point of view (the arrows I added) this is what you mean? therefore where there is no current I can remove those resistors?

One correction. There is current flow in the lower right resistor.

 

[Gbox]

Are there any short-circuited resistors?
Numbering the resistors from 1, top to bottom, left to right within a horizontal: 3 , 4 and 5 are in parallel, but not short-circuited. Likewise 1 and 2. See CWatters' diagram.

So my diagram after azizlwl comment is ok?

 

[gneill]

Color or otherwise identify the relevant nodes in your circuit to begin with. Any components that connect to the same two nodes (colors) must be in parallel.

There's a parallel bonanza there!

 

[azizlwl]

Color or otherwise identify the relevant nodes in your circuit to begin with. Any components that connect to the same two nodes (colors) must be in parallel.

View attachment 92415

There's a parallel bonanza there!

I think the color between the resistors should be red too, no current flow thus no p.d.

 

[Gbox]

Color or otherwise identify the relevant nodes in your circuit to begin with. Any components that connect to the same two nodes (colors) must be in parallel.

View attachment 92415

There's a parallel bonanza there!

So which equivalent diagram is right this:

or this (although I am not sure as I removed short circuit cords):

 

[gneill]

I'm not liking either of them.

If you look at the colored diagram that I posted, all of horizontal resistors connect to the same pair of colors. That is, they all connect to the same two nodes. That is, they are ALL in parallel. So erase all but one and label it with the correct resistor value. Personally I'd choose to keep the one at the bottom right, just to clean up the diagram.

 

[SammyS]

I think the color between the resistors should be red too, no current flow thus no p.d.

@azizlwl

There is current flow through each and every resistor in this circuit.

Your attempts at being helpful are not really helping.

(gneill has this covered very well..)

 

[Gbox]

I came to this $I=\frac{21V}{2R}$

 

[SammyS]

I came to this $I=\frac{21V}{2R}$
[ IMG]http://i.imgur.com/pXELuJ3.jpg[/PLAIN]

[ IMG]http://i.imgur.com/q0miIhP.jpg[/PLAIN]

Looking back at post #12, there are 5 resistors in parallel. Right ?

Otherwise, this is correct.

Added in Edit:
Well, the method is correct. The fraction addition is not.

 

[Gbox]

Looking back at post #12, there are 5 resistors in parallel. Right ?

Otherwise, this is correct.

Yes it should be 5, Thanks!

 

[SammyS]

Yes it should be 5, Thanks!

By the way, even though the R/4 isn't correct, you should know that $\displaystyle \ \frac{R}{3}+ \frac{R}{4}\neq \frac{R}{7}\$.

 

[Gbox]

By the way, even though the R/4 isn't correct, you should know that $\displaystyle \ \frac{R}{3}+ \frac{R}{4}\neq \frac{R}{7}\$.

I have wrote this?

 

[SammyS]

I have wrote this?

Maybe not explicitly, but you have R/3 and R/4 in series with a result of R/7 .

 

[Gbox]

Ahh so it a mistake, I connected them in parallel

 

[Dopplershift]

It's always best to simplify the circuit step by step. Take all the resistors in series and add them together and label it as one resistor. Then worry about the ones in parellel and use the inverse for each of them.