Simplifying a resistance circuit

[GBA13]

Homework Statement

Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution

Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.

 

[gneill]

Homework Statement

Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution

Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.

The two 1 Ohm resistors do indeed share the same nodes; That makes them parallel connected, not serial.

 

[GBA13]

Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..

So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?

Thanks for the help!

 

[gneill]

Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..

As long as two components share two nodes they are parallel-connected regardless of what other components may also connect to those nodes. It's series connections that are finicky that way -- components that are in series must be the "sole proprietors" of the node that they share.

So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?

Ah, so close. Two 1 Ohm resistors in parallel is how many Ohms?

 

[GBA13]

Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)

 

[gneill]

Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)

Ta da! Yup.

 

[GBA13]

Yay! Thanks very much, you've been really helpful! :)