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Resistance of the voltmeter

  1. Oct 3, 2016 #1
    1. The problem statement, all variables and given/known data
    A battery is known to have an EMF of 5.0 V but when a certain voltmeter is connected to it the reading is 4.9 V. The battery can deliver a current of 0.40 A when connected to a resistance of 12 Ω. What is the resistance of the voltmeter?

    Answer: 24.5 Ω.

    2. The attempt at a solution
    Let's find the internal resistance first: E = I (r + R) → 5 = 0.40 = (r + 12) → r = 0.5 Ω.

    Then we have 4.9 = 5 - I r → I = 0.2 A and the resistance is R = V / I = 4.9 / 0.2 = 24.5 Ω.

    Is this correct? I am mostly unsure why do we look for current in here 4.9 = 5 - I r. The internal resistance is in series with the battery and the current is equal to 0.4 A.
     
  2. jcsd
  3. Oct 3, 2016 #2

    gneill

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    Staff: Mentor

    The current is not 0.4 A when it's just the meter attached to the battery. The 0.40 A occurs when the 12 Ω resistor is connected to the battery. They are two separate experiments.

    upload_2016-10-3_10-9-16.png
     
  4. Oct 3, 2016 #3
    Case 2 is the original case, right?
     
  5. Oct 3, 2016 #4

    gneill

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    Staff: Mentor

    What do you consider to be the original case?
     
  6. Oct 3, 2016 #5
    E = 5 V, I = 0.4 A, R = 12 Ohm.
     
  7. Oct 3, 2016 #6

    gneill

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    Staff: Mentor

    Then yes, that's what's depicted in Case 2.
     
  8. Oct 3, 2016 #7

    David Lewis

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    Gold Member

    A simplifying assumption was made that battery source impedance is invariant with respect to current.
     
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