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Calculating voltmeter resistance in DC circuit

  1. Mar 7, 2016 #1
    1. The problem statement, all variables and given/known data
    initial problem: A 228 −Ω resistor and a 586 −Ω resistor are connected in series across a 90.0−V line.
    A voltmeter connected across the 228 −Ω resistor reads 24.0 V . Find the voltmeter resistance.



    For Req, i got Req=228R/(2+228), R being the resistance of the voltmeter.
    But after that, I'm stuck. How do I find the necessary I(current) in order to calculate the R (resistance of voltmeter).?

    2. Relevant equations
    V=IR
    1/Req=1/R1 +1/R2

    3. The attempt at a solution
    For Req, i got Req=228R/(2+228), R being the resistance of the voltmeter.
    But after that, I'm stuck. How do I find the necessary I(current) in order to calculate the R (resistance of voltmeter).?
     
  2. jcsd
  3. Mar 7, 2016 #2
    The total current is going to be given by V = IR

    They give you the total voltage and they give you the resistors. To find the total resistance you have to find the equivalent resistance. The resistors are connected in series, not in parallel, so what does that tell you about how to calculate the equivalent resistance?

    Once you solve for the equivalent resistance and find the total current, you can use Ohm's law again and find the resistance with the voltmeter. The resistance of the voltmeter itself will then be the difference between the value of the resistance with it and the value without it.
     
  4. Mar 7, 2016 #3
    normally a voltmeter does not disturb a circuit parameters - but suppose it draws a current say( Iv) then the current in 228 ohm resistance will be reduced by Iv so you have two loops one smaller one through voltmeterand the 228 ohm. a larger loop is current flowing through the two resistances- one can apply Kirchhoff's loop equations to relatecurrent and voltage and resistances. that should solve your problem
     
  5. Mar 7, 2016 #4
  6. Mar 7, 2016 #5
    The first calculation is simply a voltage divider where you can determine the resulting resistance after puting the voltmeter across R1 => Rx.
    Then take Rx and calculate back using the formula you use when you have two resistors in paralell and wanna know the total resistance.
    you don't need a current to find Rv.
    except you have to calculate them. then just use the total resistance without the voltmeter and then with the voltmeter...where R1 changes to Rx.

    br Chris
     
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