Equivalent Resistance of Figure

[Yealtas]

Homework Statement

https://imgur.com/a/aVCeU

Homework Equations

(1/Req) = (1/Rv1) +(1/Rv2)
Req = Rv1 + Rv2

The Attempt at a Solution

I'm not sure which formula is the correct one to use.So..
I'm absolutely stuck. I tried downloading a bunch of circuit board simulators, but I couldn't find an easy one to use. And googling yields 0 results.

Which formula should I use for the equivalent resistance, and why?

Thank you very much. :)

 

[mfb]

There is a direct cable from one side to the other. What do you expect?

 

[Yealtas]

I would say electrons choose the path of least resistance, and therefor never even attempt to go through the resistances. But I know that's extremely wrong, so I won't say it. In all honesty man, I have no idea.

 

[mfb]

I would say electrons choose the path of least resistance, and therefor never even attempt to go through the resistances.

Correct.

As image:

 

[Yealtas]

Correct.

As image:

View attachment 213652

Hahaha, I want that as a shirt now to be honest!

Alright, i'll give it a better shot tho:

Let's call the wire "Rv3". Rv3 should have 0 resistance. You'd then calculate the equivalent resistance of Rv1 and Rv3 (With the equation for parallel resistances). Let's call this answer Rv4, so that finally Req = Rv2 + Rv4..?

edit: Rv4 would equal Rv1, so that Req is simply Rv1 + Rv2..?

 

[mfb]

What is Rv4?

There is a cable parallel to R1 and one parallel to R2.

 

[Yealtas]

I called the cable in the middle Rv3. Rv3 = 0 (so all current can flow freely). Then I call Rv4 the equivalent resistance of Rv1 and Rv3 (1/Rv4) = (1/Rv1) + (1/Rv3).

I just now realize that what I said earlier doesn't make sense. If Rv3 was infinite I could say that (1/Rv4) = (1/Rv1), but Rv3 is 0...

I have a feeling that Req = Rv1 + Rv2, but I can't explain why. And just the plain answer doesn't satisfy me. I need a method :/

 

[cnh1995]

And just the plain answer doesn't satisfy me. I need a method :/

Think about the image in #4.
Although your statement about current taking the path of least resistance is not accurate, your conclusion below is correct (since the wires are assumed to be ideal).

and therefor never even attempt to go through the resistances

So what does that tell you about the resistance between the two points?

 

[Yealtas]

Think about the image in #4.
Although your statement about current taking the path of least resistance is not accurate, your conclusion below is correct (since the wires are assumed to be ideal).

So what does that tell you about the resistance between the two points?

Sorry, I don't quite understand what you mean. Do you mean the resistance of the wire in the middle..?

 

[cnh1995]

Sorry, I don't quite understand what you mean. Do you mean the resistance of the wire in the middle..?

How many paths can you find to go from the left terminal to the right terminal? Which of them is the path of "least" resistance? How much is that least resistance?

 

[mfb]

Hahaha, I want that as a shirt now to be honest!

It exists as shirt in many places.

If you understand the circuit in #4, you can use it to get rid of R1. And then you can use it to get rid of R2. What is left?

 

[Yealtas]

How many paths can you find to go from the left terminal to the right terminal? Which of them is the path of "least" resistance? How much is that least resistance?

How many paths can you find to go from the left terminal to the right terminal? Which of them is the path of "least" resistance? How much is that least resistance?

4 paths. 2 at the start, and then each path has another 2 'sub-paths'. the least resistance is the path through the wire alone.

 

[cnh1995]

the least resistance is the path through the wire alone.

Yes, and how much is that resistance?

 

[Yealtas]

It exists as shirt in many places.

If you understand the circuit in #4, you can use it to get rid of R1. And then you can use it to get rid of R2. What is left?

See, i don't understand how i can get rid of Rv1 with #4. I'm still stuck on this problem.

The figure is basically just #4 twice. Any more help please?

 

[Yealtas]

Yes, and how much is that resistance?

Speaking in term of ideal circumstances; 0 Ohm.

 

[cnh1995]

Speaking in term of ideal circumstances; 0 Ohm.

Right.

 

[Yealtas]

.

 

[Yealtas]

Right.

Would the equivalent resistance of the Figure simply be 0..?

 

[cnh1995]

Would the equivalent resistance of the Figure simply be 0..?

Yes.

 

[Yealtas]

Yes.

Thanks for the help Sheldon.

:)