resistivity formula

Discussion in 'Homework Help' started by mac_mula, Jan 25, 2012.

  1. mac_mula

    Thread Starter New Member

    Jan 25, 2012
    2
    0
    i am a first year electrician in school and was taught the resistivity formula over the past couple days but i am having a hard time wrapping my head around it and was wondering if some one could help.

    R in (Ω)=pL/A

    so p for copper is 16.6 ohm-meters at 0.C and that number comes from the resistance (or Ω) of a cube 1mx1mx1m. so that is the Ω per m^3

    so p= Ω/m^3. so if i took the area (m^2 and multiplied it by the length in m it would give me volume or m^3. so length times area times ohm gives me resitive value? well no but Ω/m^3* tm^3 = tΩ (the tm^3 coming from Am^2*Lm)

    Ω=(Ω/m^3)*Lm/Am^2 = l*A*Ω? is confusing to me
    Ω=(Ω/m^3)*Lm/Am^2 simplified is A^4 = L which obviously is not true

    I=V/R where voltage and current are directly proportional R=V/I so for each material shouldn't there be ratio or coefficient that you could multiply times area giving you Ω per m^3 as your resistivity value, which you could assign a value create an si unit? (temperature coefficients to be factored later)
    I don't know if this makes sense but if someone could see where im going wrong or explain the resistivity formula at greater depth or how it is derived would be appreciated thanks
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,790
    No there is no ohms per cubic meter here. There is:

    1. rho with units of ohm-meters
    2. L with units of meters
    3. A with units of meter^2
    Combining them with the formula leaves resistance in ohms, like this
    Code ( (Unknown Language)):
    1.  
    2. ohms = (ohms-meter)(meter) / meter^2
    3.      = ohms (meter^2) / (meter^2)
    4.      = ohms
    5.  
     
  3. mac_mula

    Thread Starter New Member

    Jan 25, 2012
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    0
    what is an ohm-meter? it was defined in my module as the resistance of a cube of material that measures 1m by 1m by 1m deep.
     
  4. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    If you were to draw a cubic meter of copper into a rather long continuous wire of 1mm diameter it would have a very different resistance end-to-end than the resistance between two faces of a cubic meter [1mx1mx1m] copper block.
     
  5. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,790
    An ohm-meter is a unit that you get when you multiply a value in ohms times a length in meters. If the units of rho were ohms per cubic meter then the formula you referenced would make no sense because the units don't come out right.

    See the second and third expressions on the wiki page and you can see how the unit of Ohm-meter comes about. It comes about because you have an area divided by a length.

    http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
     
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