1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Simplifying a resistor network using pi-T (Y-delta) conversion

  1. Jul 8, 2012 #1


    User Avatar
    Gold Member

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

    Reduce the resistor network to a single resistor. Go step-by-step and indicate the series or parallel combinations being reduced.


    2. Relevant equations

    For series resistors: [itex]R_T=R_1+R_2+R_3+\cdot \cdot \cdot +R_N[/itex]
    For parallel resistors: [itex]R_T=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\cdot \cdot \cdot +\frac{1}{R_N}}[/itex]

    ∏-T Conversion:

    3. The attempt at a solution

    The first thing I noticed is that RA, RB, and RC are not in series and they're not in parallel. This led me to the ∏-T (Y-Δ) conversion. After the conversion, I was able to make further simplifications in steps (2) and (3).

    In step (4), I get stuck because I don't know how to simplify the circuit given the way R5 is hooked up. Any pointers?
  2. jcsd
  3. Jul 8, 2012 #2


    User Avatar
    Gold Member

    My thinking, assuming I drew everything correctly, is that R5 gets bypassed because a practically resistance-free path exists (the wire on the left-leg of the triangle above R5).

    Therefore the equivalent resistance would be:

    Req=R3+R2||(R1+R4) = 10.57Ω + 58.92Ω ≈ 69.5Ω

    Does this make sense?
  4. Jul 9, 2012 #3


    User Avatar
    Homework Helper
    Gold Member

    Yes. You can also think of the wire as a 0-ohm resistor and use the parallel resistor formula.
  5. Jul 9, 2012 #4
    I guess cable across Rc and R4
    So mark all the points as zero voltage.
    Now we have a parallel circuit of
    1. Ra-150Ω
    2. Series of Rb and parallel resistors of Rc and R4-129Ω

    Equivalent resistance=69.35Ω
    Last edited: Jul 9, 2012
  6. Jul 9, 2012 #5


    User Avatar
    Gold Member

    This makes sense.

    So, [itex]R_T=\frac{1}{\frac{1}{\sim 0 \Omega }+\frac{1}{220\Omega }}\approx 0 \Omega [/itex]

    Thanks lewando.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook