text: # Homework Help: Electricity: shunt calculation for ammeter
  
  Tags:
  1. Apr 10, 2017
  
  ### Epoch
  
  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.
  
  2. Relevant equations
  
  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
  
  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. Apr 10, 2017
  
  ### BvU
  
  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
  
  3. Apr 10, 2017
  
  ### 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!
  
  4. Apr 10, 2017
  
  ### Epoch
  
  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.
  
  Share this great discussion with others via Reddit, Google+, Twitter, or Facebook
  
  Have something to add?
  Draft saved Draft deleted
explanation: The document is a homework help post about calculating shunt resistors for an ammeter. It contains a detailed problem statement, relevant equations, and an attempt at a solution. The post also includes the correct answers from an answer sheet and a step-by-step solution provided by the user. The document contains both a question and an answer.
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distilabel_metadata.content: # Homework Help: Electricity: shunt calculation for ammeter
  
  Tags:
  1. Apr 10, 2017
  
  ### Epoch
  
  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.
  
  2. Relevant equations
  
  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
  
  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. Apr 10, 2017
  
  ### BvU
  
  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
  
  3. Apr 10, 2017
  
  ### 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!
  
  4. Apr 10, 2017
  
  ### Epoch
  
  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.
  
  Share this great discussion with others via Reddit, Google+, Twitter, or Facebook
  
  Have something to add?
  Draft saved Draft deleted
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a homework help post about calculating shunt resistors for an ammeter. It contains a detailed problem statement, relevant equations, and an attempt at a solution. The post also includes the correct answers from an answer sheet and a step-by-step solution provided by the user. The document contains both a question and an answer.
  
  Label: question-and-answer