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.
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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
alfers101
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so 12000 g?
ash2326
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Yeah, now find volume
Volume= mass/density
theyatin
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density hai mass hai volume= length into cross section you can find length
alfers101
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1,349.83 cm^2 ?
alfers101
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@ash2326 @theyatin what do you think?
ash2326
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Yeah you're right. Sorry My battery was out of juice
alfers101
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than after i got the volume, whats next? getting the length?
alfers101
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*then
ash2326
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\[\text{Volume}= \text{Area of Cross section} \times \text{length}\]
alfers101
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length=volume/ area of cross section?
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
alfers101
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length= 1,349.83 cm^2/0.209cm^2 ??
ash2326
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1 mm = 1/ 10 cm
\[1 mm^2= \frac{1}{10\times 10} cm^2\]
alfers101
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.209 cm^2 ?
ash2326
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area of cross section=2.09 mm^2=2.09/100 cm^2
alfers101
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so 0.0209 cm^2 ?
ash2326
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yeah now you find length
alfers101
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length= 1,349.83 cm^2/0.0209cm^2 ?
alfers101
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64,585.17 ?
alfers101
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what would be the unit?
ash2326
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\[\frac{cm^3}{cm^2}\]???
alfers101
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oh i get it. its cm. cause i saw both cm^2
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?
alfers101
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resistance? R=v/i ?
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
alfers101
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R=ρ(micro ohms-cm)×3090199.522 cm ?
alfers101
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then multiply it to 1924 ?
ash2326
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Yeah:D
alfers101
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5945643879 ?
ash2326
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Yeah this is right but this in micro ohms. Divide by 10^6 to get resistance in ohms
alfers101
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why divide it by 10^6 ?
ash2326
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Because resistance we found is in micro ohms
\[1 micro ohm=\frac{1}{10^6} \text{ohms}\]
alfers101
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oh okay thanks so the answer will be 5945.54 ohms ?
ash2326
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Yeah:D
alfers101
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then whats next? ;D
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
alfers101
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so that must be 645.8517 ?
ash2326
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64585.17/100=>64.581517 meters
alfers101
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no its 645.8517
ash2326
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yeah, you're right. Sorry :(
alfers101
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its alright :) then whats next? we will repeat it again? because we got the wrong length?
ash2326
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nope, we found the resistance correctly.
question asked length in meters that's why we changed it
alfers101
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oh thanks a lot. :D a massive thank you! God bless :D
ash2326
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welcome:D