How to redraw circuits in this problem to see series/paralle

[LongApple]

Homework Statement

See pic for problem statement and diagram (we are dealing with the diagram on the right)
http://i.imgur.com/Uv7Ikma.png
I'll rewrite the problem statement here if that helps: Find R_T in the diagram for the cases where ab is open circuited and short circuited.

And its solution in the textbook: The first part of is part a) the second part b)
http://i.imgur.com/yYLGoFE.png

Why is it that after combining the top two resistors and combining the bottom two resistors in the picture that the two resulting series combinations are parallel to each other?

Homework Equations

None, this is conceptual

The Attempt at a Solution

part a)
I drew what I think combining the top two and bottom two resistors would look like here in part a for the open circuit case:
http://i.imgur.com/Uv7Ikma.png
In the pic with the shadow of the hand below, I draw more pictures and I dont' see why the circuit has anything parallel
http://i.imgur.com/azqgWwD.png
The picture drawn on the right labeled "parallel" was just for me to visually compare the left to see where the "two series combinations are in parallel" in the part a) solutions

but I don't see how it leads to the statement in the solutiosn "The two series combinations are in parallel" for part a) which is the first solution in the solution imgur linkIn part b) the short circuited case, I have also drawn what I believe to be equivalent circuits in the short circuited case but don't understand why the 40/60 combo and 90/10 combo mentioned in the solutions are in series
http://i.imgur.com/h4X5Dcn.png

What are some smarter ways to draw the circuits to better see why certain combinations are in parallel or series?

 

[BvU]

What are some smarter ways to draw the circuits to better see why certain combinations are in parallel or series?

To avoid errors like your last picture (*), you can flip the 90 Ω and 10 Ω resistors from left to right with the line ab as axis. The it becomes clear that 40 and 90 are in series, as are 60 and 10 (case ab open).



(*) you draw a circle around a non-connection and move it to the top left as if that were short-circuited too (that would yiled R_T=0 !)

By te way, PF guidelines don't appreciate this way of posting with a lot of links. How long will the imgur pictures be available ?

I see in another thread you started that you might even be in favour of expiring links to avoid copyright problems. But PF aims to build up a long-lasting 'database' of re-usable threads. One more reason to use picture uploads (preferable) and picture links only as a supplement, not as a substitute.

 

[ehild]

https://www.physicsforums.com/attachments/77023

You can walk from c to a and then from a to d (blue path). If nothing else is connected to a, the 40 Ω and 90 Ω resistors are connected in ?
You can also reach from c to d along the green path. If noting is connected to b the 60 Ω and the 10 Ω resistors are connected in ?
So you can redraw the circuit as in the picture on the right.
What happens if a and b are short-circuited?

 

[LongApple]

https://www.physicsforums.com/attachments/77023

You can walk from a to c and then from c to b (blue path). If nothing else is connected to c, the 40 Ω and 60 Ω resistors are connected in ?
You can also reach from a to b along the green path. If noting is connected to d the 90 Ω and the 10 Ω resistors are connected in ?
So you can redraw the circuit as in the picture on the right.
What happens if c and d are short-circuited?

I just want to confirm that the intersection X of blue and green and in circuit diagrams in general does not mean there is a physical intersection. Am I correct?
So like the blue could come out of the page and the green could go under the page?

 

[BvU]

I just want to confirm that the intersection X of blue and green and in circuit diagrams in general does not mean there is a physical intersection. Am I correct?
So like the blue could come out of the page and the green could go under the page?

Yes

@ehild: the exercise wants R_T, not R_ab

 

[ehild]

I just want to confirm that the intersection X of blue and green and in circuit diagrams in general does not mean there is a physical intersection. Am I correct?
So like the blue could come out of the page and the green could go under the page?

There is no physical intersection in the middle of the drawing. If it was, it would be drawn by a circle, as it would be a node.
Yes, the lines can go one above and the other below the paper.

 

[ehild]

Yes

@ehild: the exercise wants R_T, not R_ab

Sorry, I misread ...I attached a corrected picture. I hope, it i right now.

 

[LongApple]

https://www.physicsforums.com/attachments/77023

You can walk from a to c and then from c to b (blue path). If nothing else is connected to c, the 40 Ω and 60 Ω resistors are connected in ?
You can also reach from a to b along the green path. If noting is connected to d the 90 Ω and the 10 Ω resistors are connected in ?
So you can redraw the circuit as in the picture on the right.
What happens if c and d are short-circuited?

I just want to make sure I understand the problem statement

http://i.imgur.com/Uv7Ikma.png

In part b) when they say short circuited they mean connecting terminals a and b, correct? Or is it c and d?

 

[ehild]

Sorry, I misread the problem. I corrected my original post and picture. The problem means a and b short-circuited. You have to find how the resistors are connected with respect to the terminals c and d.

It is very important that you write the problem statement in your post. People can misread and forget what the question was, when the question is not in front of their eyes.

 

[ehild]

I just want to make sure I understand the problem statement

http://i.imgur.com/Uv7Ikma.png

In part b) when they say short circuited they mean connecting terminals a and b, correct? Or is it c and d?