Bridge circuit - 5 eqns with 5 unknowns

[skierboy]

Homework Statement

The bridge circuit for this problem:
http://img52.imageshack.us/img52/7366/bridgecircuit.jpg

I have to derive a formula for the equivalent resistance (R_eq) of the bridge circuit shown in the link.

Homework Equations

I've been able to come up with the 5 equations with 5 unknowns using Kirchoff's loop and junction laws. They are as follows:

1) I = I₁ + I₂
2) I₁ = I₃ + I₅
3) I₄ = I₂ + I₅
4) I₁R₁ + I₅R₅ = I₂R₂
5) I₅R₅ + I₄R₄ = I₃R₃

Also, IR_eq = I₁R₁ + I₃R₃

so, R_eq = (I₁R₁ + I₃R₃)/I

The Attempt at a Solution

I am having trouble starting to solve this system of equations. I've tried various substitutions but they have all led me to dead ends.

Based on equation 6, I know that I have to express all the currents across each resistor in terms of 'I', so that 'I' cancels when doing the final substitution in equation 6, leaving only the resistors.

I am not asking for a full derivation, but simply some direction as to how to approach solving this system.

Thank you in advance!

 

[Delphi51]

You also have an equation for the current coming out: 7) I3 + I4 = I.
I would suggest using the relatively simple eqn 3 to eliminate all the I4s. That is, replace all I4 entries with I2 + I5. Likewise, solve eqn 2 for I5 and eliminate all the I5 entries. I'm trying to keep I1 and I3 so you can solve for them and use them in eqn 6. Solve eqn 1 for I2 eliminate that. The next steps, solving for I1 and I3 will be rather messy!