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Bridge circuit - 5 eqns with 5 unknowns

  1. Nov 8, 2009 #1
    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.

    Thank you in advance!!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 8, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    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!
     
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