# Homework Help: Bridge circuit - 5 eqns with 5 unknowns

1. Nov 8, 2009

### skierboy

1. The problem statement, all variables and given/known data

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

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

2. Relevant 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, IReq = I1R1 + I3R3

so, Req = (I1R1 + I3R3)/I

3. 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.