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Find the voltmeter reading in a circuit

  1. Sep 29, 2016 #1
    1. The problem statement, all variables and given/known data
    The 4.0 V cell in the circuits shown below has zero internal resistance. An accurately calibrated voltmeter connected across YZ records 1.50 V. Calculate (a) the resistance of the voltmeter, (b) the voltmeter reading when it is connected across Y'Z'.

    d63191dd4fe5.jpg

    What do your results suggest concerning the use of voltmeters?

    2. The attempt at a solution
    (a) I = V / R = (4 - 1.5) / 60 = 0.0417 A
    I = 1.5 / 40 = 0.0375 A
    I that flows in the voltmeter = 0.0417 - 0.0375 = 0.00417 A
    R = V / I = 1.5 / 0.00417 = 360 Ω

    (b) No idea. I did try to some equations like 4 = 600 * I + I R2, but I think they lead into nothing. How can we find the voltmeter reading? It's a parallel circuit but now we don't know neither the V nor the current or the resistance.
     
  2. jcsd
  3. Sep 29, 2016 #2

    berkeman

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    Staff: Mentor

    You know the voltmeter's resistance, so just parallel it up with the 400 Ohm resistor and use the resulting voltage divider to find the voltage.
     
  4. Sep 29, 2016 #3
    You mean 360 Ohm? But it's a different situation (resistors have 600 and 400 Ohm instead of 60 and 40) and it's not stated that 360 Ohm are the same for (b).

    But in that case the calculation is clear: 1 / R = 1 / 400 + 1 / 360, we find R = 189, total R = 189 + 600 = 789 Ohm. I = V / R = 4 / 789 = 5.1 * 10-3. V = 5.1 * 10-3 * 600 = 3.04. V = 4 - 3.04 = 0.96 V.
     
  5. Sep 29, 2016 #4

    berkeman

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    Staff: Mentor

    The question implies it is the same voltmeter that is moved to the 2nd circuit for the 2nd reading, so just keep using 360 Ohms for the meter's internal resistance.
     
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