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Electricity: shunt calculation for ammeter

  1. Apr 10, 2017 #1
    1. The problem statement, all variables and given/known data
    We have an ammeter with 20Ω resistance and a range of 10mA or 0.01A.
    The different ranges are 3000mA, 300mA, 30mA.
    Calculate the shunt resistors a, b and c.
    Problem.jpg

    2. Relevant equations
    voltage.png
    shunt formula.png
    shunt calculation.png
    formula.png

    3. The attempt at a solution
    Ia = 0.01A ; Ra = 20Ω ; I = 0.03A

    Ua = Ia ⋅ Ra = 0.01A ⋅ 20Ω = 0.2V
    Is = I - Ia = 0.03A - 0.01A = 0.02A
    current flow.jpg

    The multiplication factor:
    m = I / Ia = 0.03 / 0.01 = 3

    I found the equivalent resistance for all shunts:
    Rn = Ra / m - 1
    Rn = 20 / 3 - 1 = 10Ω

    In parallel the voltage is the same in all resistors, but a, b and c are in series and have their own voltages out of our Ua = 0.2V.
    How can I find the voltage for a, b and c?
    Otherwise I can't calculate each resistor.

    The answers on my answer sheet are:
    a = 0.1Ω
    b = 0.9Ω
    c = 9Ω
    So indeed the equivalent resistor is 10Ω.

    I hope someone can help me with this.
     
  2. jcsd
  3. Apr 10, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello again,
    Case m1 is easy, right ? Can peek at the previous thread to help you find Ra+Rb+Rc .

    Case m2: 10 mA through Rc + 20 ##\Omega##, 290 mA through the parallel path of (Ra+Rb). Gets you a ratio.
    Case m3 gets you a ratio too. Two ratios and one sum: means you can solve for the three unknown Rx
     
  4. Apr 10, 2017 #3

    gneill

    User Avatar

    Staff: Mentor

    You'll need to create a set of simultaneous equations to solve. For example, for the first case you found that the sum of all the shunt resistors is 10Ω : ##R_a + R_b + R_c = 10##. You need to find similar equations for the other two cases and solve for the individual resistance values.


    Edit. Ha! I see that BvU beat me to it!
     
  5. Apr 10, 2017 #4
    Okay, so I came up with this:
    Ra + Rb + Rc = 10
    30Rc = 270
    300Rb +300Rc = 2970

    I used the matrix method:

    A
    1 1 1 Ra 10
    0 0 30 ⋅ Rb = 270
    0 300 300 Rc 2970

    Determinant of A = -9000
    -----------------------
    D-Ra
    10 1 1
    270 0 30
    2970 300 300

    Determinant of D-Ra = -900
    --------------------------
    D-Rb
    1 10 1
    0 270 30
    0 2970 300

    Determinant of D-Rb = -8100
    ----------------------------------------
    D-Rc
    1 1 10
    0 0 270
    0 300 2970

    Determinant of D-Rc = -81000
    ------------------------------------------

    Ra = D-Ra / A = -900 / -9000 = 0.1Ω
    Rb = D-Rb / A = -8100 / -9000 = 0.9Ω
    Rc = D-Rc / A = -81000 / -9000 = 9Ω

    So I think I got it right.
    Thanks for your time guys.
     
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