Battery connected outside a circuit

[Gabe805]

Homework Statement

How do I get the equivilent circuit in this scenario? The battery is not directly connected within the circuit. I know how to find the equivilent resistance in situations where the battery is "inside" the circuit but I am having a little trouble with this one. The voltage and resistances are given but the current is not. I just want to know how I would deal with the battery using a kirchhoff loop equation.
http://edugen.wileyplus.com/edugen/courses/crs7165/common/art/CMS/image_n/GO_logo_i.png
In Fig. 27-46, http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math340.gif, http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math582.gif, http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math583.gif, and http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math584.gif. What are the potential differences (a) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math585.gif, (b)http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math586.gif, (c) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math587.gif, and (d) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math588.gif?

http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/image_n/w1535-nn.png
Figure 27-46

Homework Equations

1/req = 1/r1 +1/r2 1/r3...
req = r1 + r2 +r3...[/B]

The Attempt at a Solution

I tried inserting the battery in an arbitrary spot and then proceeded to find the equivalent resistances by combining parallel and series resistors into one equivalent resistance. from there I would have had all the relevant data to work backwards. I made an error somewhere and I can only assume it is because i am handling the battery in the wrong way. Any tips or suggestions would be greatly appreciated. By the way the answers at the back of the book are:(a) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math589.gif; (b) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math590.gif; (c) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math589.gif; (d) http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math591.gif

 

[gneill]

None of your images are showing up (at least for me). Can you describe the circuit in more detail, or upload an image (use the "upload" icon to upload an image file)?

 

[Gabe805]

Sorry about that. Here it is.

 

[Gabe805]

 

[gneill]

You'll have to explain what you mean by "equivalent circuit" here. Are you looking for a single resistance value to replace the entire circuit as a load for the battery?

Anyways, as far as loop analysis goes there are three meshes: the upper triangle ABC, the lower triangle BCD and the outer loop with the battery and passing through ACD. You could also circumscribe the circuit with a loop passing through ABD and the battery.

There are other approaches other than loop analysis for a bridge circuit. Sometimes a practical choice can be made if the component values are known and symmetry lends a hand.

 

[Gabe805]

Looking back at my first post, I see that the relevant info was not posted. Emf=12V R1=2000 R2=3000 and R4=4000 ohms. To answer the question in the problem statement, don't I need to first calculate what the current is through the circuit? By equivalent circuit, I meant finding the equivalent resistance. Knowing the equivalent resistance, I can then easilly find current and then work backwards by figuring out the different currents through the various junctions. Then I can use a kirchhoff loop equation. For instance, the potential diffence between A and B would just be current*R1. However I am at a loss as to how deal with the battery when finding the equivalent resistance. Could I just assume It is connected within the circuit instead of the outside and then just find the Req?

 

[CWatters]

The battery _is_ in the circuit. You can't just move it to some other place in the circuit as you propose.

This circuit can't easily be solved by trying to find an equivalent resistance. You have to use the methods others have mentioned. For example you could use KVL to write simultaneous equations and then solve them to find the battery current. That would eventually allow you to work out the equivalent resistance.

 

[gneill]

One method that you might want to investigate which doesn't involve KVL or KCL analysis is Y-Δ and Δ-Y transformations (often called Y-Delta and Delta-Y if you're Googling it). This is a way to convert "Y" shaped ind "Δ" shaped arrangements of resistors back and forth. Often such a conversion on a strategic group of resistors will allow you to proceed with more mundane series/parallel reductions.