anonymous
  • anonymous
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.
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ash2326
  • ash2326
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
anonymous
  • anonymous
so 12000 g?
ash2326
  • ash2326
Yeah, now find volume Volume= mass/density

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More answers

anonymous
  • anonymous
density hai mass hai volume= length into cross section you can find length
anonymous
  • anonymous
1,349.83 cm^2 ?
anonymous
  • anonymous
@ash2326 @theyatin what do you think?
ash2326
  • ash2326
Yeah you're right. Sorry My battery was out of juice
anonymous
  • anonymous
than after i got the volume, whats next? getting the length?
anonymous
  • anonymous
*then
ash2326
  • ash2326
\[\text{Volume}= \text{Area of Cross section} \times \text{length}\]
anonymous
  • anonymous
length=volume/ area of cross section?
ash2326
  • ash2326
Yeah, remember to convert cross section into cm^2, it's given in mm^2 Then you'll get length in cm
anonymous
  • anonymous
length= 1,349.83 cm^2/0.209cm^2 ??
ash2326
  • ash2326
1 mm = 1/ 10 cm \[1 mm^2= \frac{1}{10\times 10} cm^2\]
anonymous
  • anonymous
.209 cm^2 ?
ash2326
  • ash2326
area of cross section=2.09 mm^2=2.09/100 cm^2
anonymous
  • anonymous
so 0.0209 cm^2 ?
ash2326
  • ash2326
yeah now you find length
anonymous
  • anonymous
length= 1,349.83 cm^2/0.0209cm^2 ?
anonymous
  • anonymous
64,585.17 ?
anonymous
  • anonymous
what would be the unit?
ash2326
  • ash2326
\[\frac{cm^3}{cm^2}\]???
anonymous
  • anonymous
oh i get it. its cm. cause i saw both cm^2
ash2326
  • ash2326
good, now you have the length. You need to find the resistance. Do you have any idea, how to find that?
anonymous
  • anonymous
resistance? R=v/i ?
ash2326
  • ash2326
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
anonymous
  • anonymous
R=ρ(micro ohms-cm)×3090199.522 cm ?
anonymous
  • anonymous
then multiply it to 1924 ?
ash2326
  • ash2326
Yeah:D
anonymous
  • anonymous
5945643879 ?
ash2326
  • ash2326
Yeah this is right but this in micro ohms. Divide by 10^6 to get resistance in ohms
anonymous
  • anonymous
why divide it by 10^6 ?
ash2326
  • ash2326
Because resistance we found is in micro ohms \[1 micro ohm=\frac{1}{10^6} \text{ohms}\]
anonymous
  • anonymous
oh okay thanks so the answer will be 5945.54 ohms ?
ash2326
  • ash2326
Yeah:D
anonymous
  • anonymous
then whats next? ;D
ash2326
  • ash2326
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
anonymous
  • anonymous
so that must be 645.8517 ?
ash2326
  • ash2326
64585.17/100=>64.581517 meters
anonymous
  • anonymous
no its 645.8517
ash2326
  • ash2326
yeah, you're right. Sorry :(
anonymous
  • anonymous
its alright :) then whats next? we will repeat it again? because we got the wrong length?
ash2326
  • ash2326
nope, we found the resistance correctly. question asked length in meters that's why we changed it
anonymous
  • anonymous
oh thanks a lot. :D a massive thank you! God bless :D
ash2326
  • ash2326
welcome:D

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