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alfers101

This is a problem that i want to solve but i can't really answer it. It's a sample problem from my book: The density of a copper is 8.89 is 8.89 g/cm^3 and the ρ=1924μΩ-cm. Determine the length(m) and resistance of 12kg of copper; the cross-section of which in 2.09mm^2.

  • one year ago
  • one year ago

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  1. ash2326
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    Copper wire can be considered as a cylinder. Here we have cross section given as 2.09 mm^2 To find length, we need to find the volume We have the density as 8.89 g/ cm^2 Mass= 12 kg Could you find the volume? Do remember to change mass in kg to grams, this will give you volume in cm^3

    • one year ago
  2. alfers101
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    so 12000 g?

    • one year ago
  3. ash2326
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    Yeah, now find volume Volume= mass/density

    • one year ago
  4. theyatin
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    density hai mass hai volume= length into cross section you can find length

    • one year ago
  5. alfers101
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    1,349.83 cm^2 ?

    • one year ago
  6. alfers101
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    @ash2326 @theyatin what do you think?

    • one year ago
  7. ash2326
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    Yeah you're right. Sorry My battery was out of juice

    • one year ago
  8. alfers101
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    than after i got the volume, whats next? getting the length?

    • one year ago
  9. alfers101
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    *then

    • one year ago
  10. ash2326
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    \[\text{Volume}= \text{Area of Cross section} \times \text{length}\]

    • one year ago
  11. alfers101
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    length=volume/ area of cross section?

    • one year ago
  12. ash2326
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    Yeah, remember to convert cross section into cm^2, it's given in mm^2 Then you'll get length in cm

    • one year ago
  13. alfers101
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    length= 1,349.83 cm^2/0.209cm^2 ??

    • one year ago
  14. ash2326
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    1 mm = 1/ 10 cm \[1 mm^2= \frac{1}{10\times 10} cm^2\]

    • one year ago
  15. alfers101
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    .209 cm^2 ?

    • one year ago
  16. ash2326
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    area of cross section=2.09 mm^2=2.09/100 cm^2

    • one year ago
  17. alfers101
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    so 0.0209 cm^2 ?

    • one year ago
  18. ash2326
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    yeah now you find length

    • one year ago
  19. alfers101
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    length= 1,349.83 cm^2/0.0209cm^2 ?

    • one year ago
  20. alfers101
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    64,585.17 ?

    • one year ago
  21. alfers101
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    what would be the unit?

    • one year ago
  22. ash2326
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    \[\frac{cm^3}{cm^2}\]???

    • one year ago
  23. alfers101
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    oh i get it. its cm. cause i saw both cm^2

    • one year ago
  24. ash2326
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    good, now you have the length. You need to find the resistance. Do you have any idea, how to find that?

    • one year ago
  25. alfers101
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    resistance? R=v/i ?

    • one year ago
  26. ash2326
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    that's right but there is one more relation relating resistance with the property of material and the dimensions of the wire. \[R=\rho(\text{micro ohms-cm}) \times \frac{\text{Length (in cm)}}{\text{Area of cross section(in cm^2)}}\] From this you'll get resistance in micro ohms

    • one year ago
  27. alfers101
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    R=ρ(micro ohms-cm)×3090199.522 cm ?

    • one year ago
  28. alfers101
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    then multiply it to 1924 ?

    • one year ago
  29. ash2326
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    Yeah:D

    • one year ago
  30. alfers101
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    5945643879 ?

    • one year ago
  31. ash2326
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    Yeah this is right but this in micro ohms. Divide by 10^6 to get resistance in ohms

    • one year ago
  32. alfers101
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    why divide it by 10^6 ?

    • one year ago
  33. ash2326
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    Because resistance we found is in micro ohms \[1 micro ohm=\frac{1}{10^6} \text{ohms}\]

    • one year ago
  34. alfers101
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    oh okay thanks so the answer will be 5945.54 ohms ?

    • one year ago
  35. ash2326
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    Yeah:D

    • one year ago
  36. alfers101
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    then whats next? ;D

    • one year ago
  37. ash2326
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    Yeah that's all we found length and resistance Wait a min, we need to find length in meters. For that divide length in cm by 100 as 1 meter= 100 cms

    • one year ago
  38. alfers101
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    so that must be 645.8517 ?

    • one year ago
  39. ash2326
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    64585.17/100=>64.581517 meters

    • one year ago
  40. alfers101
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    no its 645.8517

    • one year ago
  41. ash2326
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    yeah, you're right. Sorry :(

    • one year ago
  42. alfers101
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    its alright :) then whats next? we will repeat it again? because we got the wrong length?

    • one year ago
  43. ash2326
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    nope, we found the resistance correctly. question asked length in meters that's why we changed it

    • one year ago
  44. alfers101
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    oh thanks a lot. :D a massive thank you! God bless :D

    • one year ago
  45. ash2326
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    welcome:D

    • one year ago
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