Help with a resistor network

Discussion in 'Homework Help' started by drao, Mar 11, 2012.

  1. drao

    Thread Starter New Member

    Mar 11, 2012
    Hi guys,
    Im new here and im working for the first time with with these applications.
    So, i have this resistor network :Untitled.png where R1=220 ohm and R2=330 ohm.
    I must find the electrical resistence between pins 1-8, 1-2 and 2-4. They must give me around 92 ohm, 168 ohm and 265 ohm.
    For 1-8 i made (R1+R2)/6=91.66 ohm but for the others i dont know how to solve them. Ill be very glad if you`ll explain me 1-2 or 2-4 to understand how to solve these kind of problems.
    PS: The resistors are not isolated, i also dont know what this means. :(
    Later post: Well, for 1-2 i made ((R1+R2)/5+R1)*R2/(((R1+R2)/5+R1)+R2=165 ohm
    Last edited: Mar 11, 2012
  2. drao

    Thread Starter New Member

    Mar 11, 2012
    Finaly, i solved them with node voltage theoreme :).
    This is the only way of solving irreducible resistor networks???
    This is how i solved:I made pin 1 voltage =0 and i found out the other pin voltage using an 1 amp source between pins.
    And then, the resistence between the 2 pins is |(pin1`s voltage(0)-pin2`s voltage)/1amp|
    Last edited: Mar 11, 2012
  3. mlog


    Feb 11, 2012
    Pins 1-8 is simple. You have six 550-ohm resistors in parallel, which is 550/6 = 91.7 ohms.

    Pin 1-2 is a little more complicated. I used a delta to wye conversion, but first you must recognize that five 550-ohm resistors in parallel, which is 550/5 = 110 ohms. The 110 ohms is one leg of the delta. The other two legs of the delta are 220 ohms and 330 ohms. The 220-ohm leg is between pins 2 & 8. The 330-ohm leg is between pins 1 & 2.

    Now you can covert the delta to the wye configuration. The three legs of the wye, I'll call them RA, RB, and RC, are found as follows:

    RA = 110*330/(110+220+330) = 55
    RB = 220*330/(110+220+330) = 110
    RC = 110*220/(110+220+330) = 36.7

    RA is the wye leg connected to pin 1.
    RB is the wye leg connected to pin 2.
    RC is the wye leg connected to pin 8.

    There is one path from pin 1 to pin 2 and goes through RA and RB. Since we know RA and RB, we find the series resistance to be 55 + 110 = 165 ohms.

    Pins 2-4 is also a bit complicated. Here you must recognize you have four 550-ohm resistors in parallel or 550/4 = 137.5 ohms. And you have another delta to wye conversion.

    The delta terminals are pins 1, 4, and 8. (Pin 2 is not part of the delta or the soon to be wye conversion, but we'll get to pin 2 soon enough.) As above, we'll call the wye legs, RA, RB, and RC, but do not confuse them with the previous problem.

    RA = 137.5*330/(137.5+220+330) = 66
    RB = 220*330/(137.5+220+330) = 105.6
    RC = 137.5*220/(137.5+220+330) = 44

    RA is the wye leg connected to pin 1.
    RB is the wye leg connected to pin 4.
    RC is the wye leg connected to pin 8.

    From pin 4 to pin 2 is RB connected to the center of the wye. The wye branches to RA (66-ohm) and RB (44-ohm). RA is connected to 330 ohm, and RC is connected to the 220 ohm. Thus you have the RA and RB legs connected in parallel between the center of the wye and pin 2. The resistances in parallel are 330+66 = 396 ohms and 220+44 = 264 ohms. 396||264 = 158.4 ohms. Add this to RB and you get 158.4+105.6 = 264 ohms.

    It seems more complicated than it really is. If you draw a sketch for the delta to wye conversion, it makes sense.
  4. jimkeith

    Well-Known Member

    Oct 26, 2011
    While this is an interesting mathematical problem, I believe that the intended application of such a network is being missed.

    To me this appears to be a logic termination network where pin 1 would be connected to common and pin 8 to Vcc. The parallel resistance of each of the 6 terminations are transmission line loads--the two resistors in series reduce supply current, while the parallel resistance is much lower to match the line impedance--yes in this age of gHZ signal processing, each logic line must be treated as a transmission line to control voltage overshoot/undershoot, reflections and signal radiation.
  5. drao

    Thread Starter New Member

    Mar 11, 2012
    Hey, thanks for anwsering mlog. I made them in this morning with traingle-star formula and it was easier and faster. :D
    Wow , thanks for the great informations, jimkeith. I only measured the resisteance between pins in lab and must compare them with the calculated resistence, didint know what it does :).
    Last edited: Mar 12, 2012