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Resistance - Length Graphs

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    Hi.

    I've got a question on Resistance-Length graphs:

    If you had resistance on the y axis, and length on the x axis, and you had a material such that decreasing its length will increase its resistance, (so you would have a straight line graph with negative gradient), what would happen to the gradient of the graph if the resistance increased, but the length remained constant?

    Thanks...
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    If resistance changes while length is constant on a resistance(y) - length(x) graph, you get a vertical straight line.
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    Thanks for you response, but sorry I guess I didn't make the question clear... I meant that the resistance would change for each length of the material so for example:

    Resistance/ohms 100 92 84

    Length/cm 10cm 20 cm 30cm

    And then if the resistance increases, and your results become:

    Resistance/ohms 200 184 168

    Length/cm 10cm 20 cm 30cm

    Here I've doubled the resistance just as an example, but presuming that it's not directly proportional, what would happen to the gradient of the graph?
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    (Original post by Stonebridge)
    If resistance changes while length is constant on a resistance(y) - length(x) graph, you get a vertical straight line.
    Sorry forgot to quote you in my reply.
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    (Original post by justanotheruser)
    Thanks for you response, but sorry I guess I didn't make the question clear... I meant that the resistance would change for each length of the material so for example:

    Resistance/ohms 100 92 84

    Length/cm 10cm 20 cm 30cm

    And then if the resistance increases, and your results become:

    Resistance/ohms 200 184 168

    Length/cm 10cm 20 cm 30cm

    Here I've doubled the resistance just as an example, but presuming that it's not directly proportional, what would happen to the gradient of the graph?


    In the example you have given the negative gradient has doubled because the change in resistance has doubled for the same change in length.

    The easiest way to answer the question would be to plot the values and see for yourself.
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    (Original post by Stonebridge)
    In the example you have given the negative gradient has doubled because the change in resistance has doubled for the same change in length.

    The easiest way to answer the question would be to plot the values and see for yourself.
    Ah! So an increase in resistance will cause the gradient of the line to increase (and thus get steeper) because there has been the change in length has remained constant?
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    (Original post by justanotheruser)
    Ah! So an increase in resistance will cause the gradient of the line to increase (and thus get steeper) because there has been the change in length has remained constant?
    Part of your sentence is missing, I think.

    Yes. Because there has been an increase in the change of resistance for the same change in length.
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    (Original post by Stonebridge)
    Part of your sentence is missing, I think.

    Yes. Because there has been an increase in the change of resistance for the same change in length.
    Yep, apologies, and thanks.
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    (Original post by justanotheruser)
    Hi.

    I've got a question on Resistance-Length graphs:

    If you had resistance on the y axis, and length on the x axis, and you had a material such that decreasing its length will increase its resistance, (so you would have a straight line graph with negative gradient), what would happen to the gradient of the graph if the resistance increased, but the length remained constant?

    Thanks...
    (Original post by Stonebridge)
    If resistance changes while length is constant on a resistance(y) - length(x) graph, you get a vertical straight line.
    isnt a resistance against length graph always meant to be of positive gradient?

    Also what could the gradient of the graph represent?
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    Yes.
    I can't think of a reason why the resistance of something would decrease as you increased its length.

    Refer to the equation R=ρL/A
    R and L are directly proportional.
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    (Original post by Stonebridge)
    Yes.
    I can't think of a reason why the resistance of something would decrease as you increased its length.

    Refer to the equation R=ρL/A
    R and L are directly proportional.
    but what if you didnt know what ρ or A was and you didnt measure it. If you just measured the resistance of an unknown material across its length and then asked to calculate the gradient, what could the gradient represent?
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    (Original post by arnab)
    but what if you didnt know what ρ or A was and you didnt measure it. If you just measured the resistance of an unknown material across its length and then asked to calculate the gradient, what could the gradient represent?
    Compare the equation RL/A with
    y = mx + c
    If you plot R (y) against L (x) what does the gradient equal?
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    (Original post by Stonebridge)
    Compare the equation RL/A with
    y = mx + c
    If you plot R (y) against L (x) what does the gradient equal?
    errm the gradient represents the resistivity of the unknown material, divided by the cross-sectional area of the material?
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    (Original post by arnab)
    errm the gradient represents the resistivity of the unknown material, divided by the cross-sectional area of the material?
    Yes. Gradient=ρ/A
    That's as far as you can go if you know neither of those. If you know one you can find the other.
    In an experiment you can measure A
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    (Original post by Stonebridge)
    Yes. Gradient=ρ/A
    That's as far as you can go if you know neither of those. If you know one you can find the other.
    In an experiment you can measure A
    ahh cool. I get it now. So am i right in thinking that if the Width of the material decreased the resistance could increases, due to the formula of R = (P x L) / A?

    Also if the Width of the material Decreased, the gradient of the graph will also decrease?
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    (Original post by arnab)
    ahh cool. I get it now. So am i right in thinking that if the Width of the material decreased the resistance could increases, due to the formula of R = (P x L) / A?

    Also if the Width of the material Decreased, the gradient of the graph will also decrease?
    Yes, for the first.
    If the width decreases, so does A.
    If A decreases and the gradient is p/A then gradient will increase.

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