Resistor bridge calculations ?

Discussion in 'Homework Help' started by curry87, Dec 22, 2010.

  1. curry87

    Thread Starter Member

    May 30, 2010
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    Need some help to solve the following resistor problems.
    First for resistor map 1(first figure)

    How do i calculate the current going though r5 ?
    So far i know the voltage between:
    vr13 is 5.5v
    vr24 is 1.7v

    For resistor map 2 (second figure)
    What steps are reqired to calculate the current going though r5 or r6 or r7 and the equivalent resistance?
     
  2. Jony130

    AAC Fanatic!

    Feb 17, 2009
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  3. Jony130

    AAC Fanatic!

    Feb 17, 2009
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    And of course you could use nodal analysis.

    (Vcc - Va) /R1 = (Va - Vb) / R5 + Va/ R3 (1)

    (Vcc - Vb) / R2 + (Va - Vb) / R5 - Vb/ R4 = 0 (2)

    IR5 = (Va - VB)/ R5

    IR5 = 393.30633uA
     
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  4. curry87

    Thread Starter Member

    May 30, 2010
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    A little lost in the calculations for va and vb on figure 1 can you please break them down and explain exactly how to calculate them step by step my electrical theory knowledge is limited?


    If i find the voltage at node a and node b using the voltage divider calculation (r2/r1+r2)*vcc then subtracting b from a and dividing that by r5 why doesnt it come up with the same answer as using nodal analysis to find current though R5 ?
     
  5. Jony130

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    Feb 17, 2009
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    OK, let's try something simpler Thévenin's theorem

    http://en.wikipedia.org/wiki/Thévenin's_theorem

    So first step is to find Vth ( Va - Vb ) without R5

    [​IMG]

    Va = Vcc * R3 / (R1 + R3) = 5.53846154V

    Vb = Vcc * R4 / (R2 + R4) = 1.7027027V

    So Vth = ( Va - Vb) = 3.83575884V

    The next step is to find Rth looking into Va; Vb

    Rth = R1||R3 + R2||R4 = 3.07692308KΩ + 5.67567568KΩ = 8.75259876KΩ

    [​IMG]

    So finally we end with this simple diagram
    [​IMG]

    IR5 = Vth/(Rth + R5) = 392uA

    And if you add R6 and R7 there is now problem becaues those resistor are connect parallel to R1 and R7 parallel to R4.

    So when finding Vht then
    R1 = R1||R6
    R4 = R4||R7

    And of course you can directly determine IR5 from nodal analysis

    [​IMG]

    I use Mathematica software to do all the math for me.
     
  6. curry87

    Thread Starter Member

    May 30, 2010
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    How do you find Ir1,Ir2 when r5 is connected ive tried (vcc-va)/r1 and (vcc-vb)/r2 but doesn't give me the values that the simulation comes up with ?

    Is IT= ir1 + ir2 or ir3 +ir4 ?
     
  7. Jony130

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    Witch equation you use to find Va and Vb ?
     
  8. curry87

    Thread Starter Member

    May 30, 2010
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    The voltage divider eq for r1,r3 then r2,r4 .
     
  9. Jony130

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    Feb 17, 2009
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    You must understand that this equations

    Va = Vcc * R3 / (R1 + R3) = 5.53846154V


    Vb = Vcc * R4 / (R2 + R4) = 1.7027027V

    Holds only when R5 is disconnect form the circuit.
    And I use this equations only for find Thevenin equivalent circuit (Vth).
    Becaues there is no simply way to find IR5 current.

    And I give you equations for Va, Vb and I5 when R5 is connect to the circuit.
    http://images.elektroda.net/54_1293045055.png

    And of course you could use Δ-Y transform to find Va and Vb
     
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