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Potentiometer circuit for comparison of two resistances

  1. Sep 15, 2014 #1
    Question :
    Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X.

    Isn't the question wrong?

    I've searched for it everywhere, but didn't get the correct solution.
    i[/COLOR]R/iX = l1/l2
    So, R/X = l1/l2

    How can the current passing through X be equal to that passing through R?
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 15, 2014 #2

    gneill

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    Staff: Mentor

    Your link doesn't take me to a circuit image, but rather to a general home page for the site. The site probably requires a login in order to proceed to the materials. You might want to cut the image out or redraw it and upload it here instead.

    Even without seeing the circuit in question I can tell that this problem will be more suitable in the Introductory Physics forum, so I am moving it there.
     
  4. Sep 15, 2014 #3

    NascentOxygen

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    Last edited: Sep 15, 2014
  5. Sep 15, 2014 #4

    gneill

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    Okay, I grabbed a "snippy" of the image to take a look at the circuit. I don't see how the circuit can function as a bridge since one leg of the Galvanometer appears to have a fixed potential w.r.t. node A set by cell ε regardless of the values of resistors R and X. Also, I don't recognize the components shown as facing arcs in series with the resistors. Some "local dialect" version of a capacitor??? Or perhaps they are push button switches to select one or the other resistor?

    attachment.php?attachmentid=73160&stc=1&d=1410786726.gif

    Also, the problem statement doesn't specify the total length of the resistive wire AB, so what are we to make of the measured values? Are we to assume that the length AB is 1 meter?

    Overall I'm not impressed by the quality of Question 3.23.
     

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  6. Sep 15, 2014 #5

    DEvens

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    If I understand the picture correctly (after another poster gave a corrected link) it looks like R and X are parallel.

    Under what circumstances could the current through parallel resistors be equal? Hint: How does the voltage across R compare to the voltage across X?

    What does the balance point being given in cm mean? What does a potentiometer look like? Hint: Google images for "linear potentiometer."
     
  7. Sep 17, 2014 #6
    They are keys. And the length of the wire is 1 metre. They aren't connected in parallel. We have to calculate the resistance of R and X using the device. When we switch the upper key on, we get a balance point at 58.3 cm and when we switch the lower key on, we get the balance point at 68.5 cm.
    Sorry for that wrong link,
     
  8. Sep 17, 2014 #7

    gneill

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    So the "keys" are switches. Fine. But I don't see how the circuit can function as desired. The voltage source ε places a fixed potential at the lower end of galvanometer G (with respect to node A) regardless of which resistor is switched into the circuit.
     
  9. Sep 17, 2014 #8

    NascentOxygen

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    Q3.24 on that site is illuminating, and suggests that Q3.23 should not be taken in isolation.

    Q3.24 speaks of the internal resistance of the ε volts cell, and so it seems this should feature on the circuit at the centre of this thread!

    All clear now! [PLAIN]http://imageshack.com/a/img29/6853/xn4n.gif [Broken] [Broken] [PLAIN]http://imageshack.com/a/img29/6853/xn4n.gif [Broken] [Broken]
     
    Last edited by a moderator: May 6, 2017
  10. Sep 18, 2014 #9

    gneill

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    Yes, well, I applaud your tenacity and extra effort :approve:
    Given this new information the problem becomes solvable.

    Here's a new depiction of the circuit. I've replaced the "keys" with an SPDT switch to make the selection operation clear, and made visible the internal resistance of the cell ε. We should wait for the OP to comment, see if he can offer an attempt at a solution.

    attachment.php?attachmentid=73270&stc=1&d=1411042571.gif
     

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