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Circuit Problem involving resistors and a switch

  1. Oct 20, 2013 #1
    1. The problem statement, all variables and given/known data

    When switch S in the figure below is open, the voltmeter V of the battery reads 3.68 V. When the switch is closed, the voltmeter reading drops to 3.50 V, and the ammeter A reads 1.80 A. Assume that the two meters are ideal, so they don't affect the circuit.

    Find the emf of the battery.

    Find the internal resistance of the battery.

    Find the circuit resistance R.

    26-29.gif


    2. Relevant equations
    V=IR
    Resistors in series: Req=R1+R2+R3...


    3. The attempt at a solution

    I found the emf of the battery to be 3.68 V, because it is the only voltage source being read by the voltmeter when the switch is open.

    I am not sure how to find the resistance.
    I have come up with this:
    Req = r + R
    Vtotal = I*Req ==> Req = Vtotal/I = 3.5/1.8 = 1.944 Ω

    1.944 = r + R

    I am not sure where to go from here.
     
  2. jcsd
  3. Oct 20, 2013 #2

    rude man

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    Right.
    What's the voltage read by the voltmeter after the switch is closed?
     
  4. Oct 20, 2013 #3
    It will be 3.5 V according to the problem, which I tried using in my calculations. I'm still confused.
     
  5. Oct 20, 2013 #4

    rude man

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    OK, so how about you write an equation relating that 3.5V with the current of 1.8A, the battery voltage E and the unknown resistor r?

    Then, do you have 2 equations with 2 unknowns (r and R)?
     
  6. Oct 22, 2013 #5

    epenguin

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    The emf of the battery is 3.68 V. If you could connect the voltmeter to the right of r it would still read that when current is flowing. But connected to the left there is a voltage drop across r. How much is it?

    When you know that, since you know the current through r, you can calculate r.

    You will also know the voltage drop across R, the current is the same and known so you can calculate R.
     
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