Determine resultant resistance in network (Thévenin)

[Twinflower]

Homework Statement

I need to calculate the resultant resistance between points A and B
The |-| parts are short curcuited ideal DC power supplies (illustration only)

This is the circuit:

Homework Equations

[tex] R_P = \frac{1}{\frac{1}{R1}+\frac{1}{R3}+\frac{1}{Rn}}[/tex]
[tex]R_S = R_1 + R_2 + R_N[/tex]

The Attempt at a Solution

I can't find any pure series or pure parallel resistance, so I really do not know where to start at this.
Simulation in Multisim gives me a resistance at 5.7 Ohm.

 

[The Electrician]

This is a Wheatstone bridge: http://en.wikipedia.org/wiki/Wheatstone_bridge

Search the web and you'll find a lot of analysis of this circuit.

 

[Twinflower]

Thank you.
Also, someone whispered that i had to transfer the two deltas to star-networks, so I am working on that one now.

 

[uart]

Thank you.
Also, someone whispered that i had to transfer the two deltas to star-networks, so I am working on that one now.

It's sufficient to just transform one of the star networks (eg the 4.5, 5, 6 ohms) to delta.

Other ways are to insert a 1 amp current source between A and B and to use nodal analysis to find the input voltage (which is numerically equal to the input resistance) or to insert a 1 volt voltage source between A and B and use mesh analysis to find the input current (which is numerically equal to the input conductance).

 

[Twinflower]

TADA

 

[gneill]

Nicely done. If you ever find yourself in a situation where you would need to use Y-Delta conversion to simplify a network and can't remember the formulas you can always slap a 1V voltage source on the network (across AB) and use mesh analysis (or your own favorite method) to find the current, I, that this source will be driving into the network. The network resistance is then given by R = V/I.

 

[Twinflower]

Thank you gneill :)

I have a further question about this problem as I am stuck with finding the thévenin voltage of the network, but I haven't found the time to create a new post showing my attempts yet.

stay tuned

 

[Twinflower]

Ok, I solved that issue using mesh current analysis. No further assistance needed from my part in this thread :)