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Please Help Looks simple at first but really found it difficult.

  1. Jan 22, 2009 #1
    Two resistors Ra and Rb are connected in series with each other between the terminals of a battery giving a constant pd of 49V. When a voltmeter of 500 ohm resistance is connected across each in turn, the reading are given as Va = 14V and Vb = 28V. Determine the resistance of Ra and Rb..
     
  2. jcsd
  3. Jan 22, 2009 #2
    I'll give you this much: Ra has a lower resistance than Rb. You are going to have to show some work here. What have you determined so far? It's basic algebra which I hate to admit I'm a bit rusty at right now. This should be moved to homework section.
     
  4. Jan 22, 2009 #3
    Do you know the formula to find the parallel resistance (Rp) of Ra and the meter (Rm)? If so, can you rearrange it to find Ra if you know Rp and Rm?
     
  5. Jan 22, 2009 #4
    ((500Ra)/(Ra+500))i = 14
    ((500Rb)/(Rb+500))i = 28

    (Ra+Rb)i = 49

    This what I have come up with but where do I go from here
     
  6. Jan 22, 2009 #5
    Your first mistake is in assuming the battery current is the same in the two cases. You need to rewrite your equations as:

    ((500Ra)/(Ra+500))i1 = 14
    ((500Rb)/(Rb+500))i2 = 28

    You also know that:

    ((500Ra)/(Ra+500))i1 + Rb*i1 = 49
    ((500Rb)/(Rb+500))i2 + Ra*i2 = 49

    You can eliminate I1 between the the first two equations of each pair, and I2 between the second two of each pair.

    This will give you two equations in the two unknowns, Ra and Rb. You should be able to proceed from there.
     
  7. Jan 23, 2009 #6
    Given:
    Vs = 49
    Va = 14
    Vb = 28
    Rm = 500 meter resistance

    V(Ra) = Vs - Vb
    V(Ra) is the voltage across Ra when the meter is across Rb

    V(Rb) = Vs - Va

    V(Rm) = V(Rp)*V(Ra)/(V(Ra) - V(Rp))
    V(Rm) is the voltage across the meter if Ra
    were removed and just the meter were in
    series with Rb.

    Ia = Va(Rm)/Rm
    Ia is current through the meter when it is
    replacing Ra.

    Ib = Vb(Rm)/Rm
    Ib is current through the meter when it is
    replacing Rb.

    Ra = V(Ra)/Ia
    Rb = V(Rb)/Ib
     
    Last edited: Jan 23, 2009
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