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.

- anonymous

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- 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

so 12000 g?

- ash2326

Yeah, now find volume
Volume= mass/density

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## More answers

- anonymous

density hai mass hai volume= length into cross section you can find length

- anonymous

1,349.83 cm^2 ?

- anonymous

@ash2326 @theyatin what do you think?

- ash2326

Yeah you're right. Sorry My battery was out of juice

- anonymous

than after i got the volume, whats next? getting the length?

- anonymous

*then

- ash2326

\[\text{Volume}= \text{Area of Cross section} \times \text{length}\]

- anonymous

length=volume/ area of cross section?

- ash2326

Yeah, remember to convert cross section into cm^2, it's given in mm^2
Then you'll get length in cm

- anonymous

length= 1,349.83 cm^2/0.209cm^2 ??

- ash2326

1 mm = 1/ 10 cm
\[1 mm^2= \frac{1}{10\times 10} cm^2\]

- anonymous

.209 cm^2 ?

- ash2326

area of cross section=2.09 mm^2=2.09/100 cm^2

- anonymous

so 0.0209 cm^2 ?

- ash2326

yeah now you find length

- anonymous

length= 1,349.83 cm^2/0.0209cm^2 ?

- anonymous

64,585.17 ?

- anonymous

what would be the unit?

- ash2326

\[\frac{cm^3}{cm^2}\]???

- anonymous

oh i get it. its cm. cause i saw both cm^2

- ash2326

good, now you have the length. You need to find the resistance. Do you have any idea, how to find that?

- anonymous

resistance? R=v/i ?

- 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

R=ρ(micro ohms-cm)×3090199.522 cm ?

- anonymous

then multiply it to 1924 ?

- ash2326

Yeah:D

- anonymous

5945643879 ?

- ash2326

Yeah this is right but this in micro ohms. Divide by 10^6 to get resistance in ohms

- anonymous

why divide it by 10^6 ?

- ash2326

Because resistance we found is in micro ohms
\[1 micro ohm=\frac{1}{10^6} \text{ohms}\]

- anonymous

oh okay thanks so the answer will be 5945.54 ohms ?

- ash2326

Yeah:D

- anonymous

then whats next? ;D

- 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

so that must be 645.8517 ?

- ash2326

64585.17/100=>64.581517 meters

- anonymous

no its 645.8517

- ash2326

yeah, you're right. Sorry :(

- anonymous

its alright :) then whats next? we will repeat it again? because we got the wrong length?

- ash2326

nope, we found the resistance correctly.
question asked length in meters that's why we changed it

- anonymous

oh thanks a lot. :D a massive thank you! God bless :D

- ash2326

welcome:D

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