Resolving Multiloop Circuit Configurations with Delta Star Transformation

[nanotubez]

Homework Statement

So, imagine that there are two wires stretched across 2 electrodes crossing over each other, dividing each wire into two pieces at a junction, j. Each wire is connected to two electrodes, one at each end. The pieces have resistances R1, R2, R3, and R4 and the resistance at the junction is Rj.

Homework Equations

Series: Rtot = R1 + R2

Parallel 1/Rtot = 1/R1 + 1/R2

The Attempt at a Solution

Circuit Diagram(attached)

I tried saying R1, Rj, and R4 are in series and are parallel to R2 and R3 and for (1/R2 + 1/(R1+RJ + R4) + 1/R3)^-1, but then you could say that R3, RJ, and R2 are in series and parallel to R1 and R4, but (1/R1 + 1/(R2 + Rj + R3) + 1/R4)^-1 does not equal the same thing. Please help?

Thanks!

 

[berkeman]

Homework Statement

So, imagine that there are two wires stretched across 2 electrodes crossing over each other, dividing each wire into two pieces at a junction, j. Each wire is connected to two electrodes, one at each end. The pieces have resistances R1, R2, R3, and R4 and the resistance at the junction is Rj.

Homework Equations

Series: Rtot = R1 + R2

Parallel 1/Rtot = 1/R1 + 1/R2

The Attempt at a Solution

Circuit Diagram(attached)

I tried saying R1, Rj, and R4 are in series and are parallel to R2 and R3 and for (1/R2 + 1/(R1+RJ + R4) + 1/R3)^-1, but then you could say that R3, RJ, and R2 are in series and parallel to R1 and R4, but (1/R1 + 1/(R2 + Rj + R3) + 1/R4)^-1 does not equal the same thing. Please help?

Thanks!

Welcome to the PF.

What does the problem ask for you to solve? Solve for the equivalent resistance? Or current given some battery voltage?

In the general case, I think the best way to solve this is to use KCL equations at the nodes. In the general case, I'm not sure you can use parallel & series combinations to simplify the circuit.

 

[nanotubez]

Welcome to the PF.

What does the problem ask for you to solve? Solve for the equivalent resistance? Or current given some battery voltage?

In the general case, I think the best way to solve this is to use KCL equations at the nodes. In the general case, I'm not sure you can use parallel & series combinations to simplify the circuit.

Solve for total resistance resistance. No mention of current

 

[CWatters]

Are any of the resistors the same?

If not then I'd number the nodes at each end of Rj and assign them unknown voltages (eg V1 and V2) then write lots of simultaneous equations (eg for the current through each resistor and into and out of the various nodes). Then laborious job of reducing them down to one for the total R (eliminating Vbat, V1 and V2 and all the currents along the way).

If the resulting equation doesn't have a certain symetry about it then it's probably wrong.

 

[pcm]

if you need equivalent resistance, then it can be reduced to series/parallel combination by first using delta star transformation.

 

[Saitama]

As pcm stated, you can use delta star transformation and if the resistors are identical, you can remove RJ because it's a wheat stone bridge then.