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.

Question

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.

ash2326 · Answer

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 · Answer

so 12000 g?

ash2326 · Answer

Yeah, now find volume
Volume= mass/density

anonymous · Answer

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

anonymous · Answer

1,349.83 cm^2 ?

anonymous · Answer

@ash2326 @theyatin what do you think?

ash2326 · Answer

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

anonymous · Answer

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

anonymous · Answer

*then

ash2326 · Answer

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

anonymous · Answer

length=volume/ area of cross section?

ash2326 · Answer

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

anonymous · Answer

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

ash2326 · Answer

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

anonymous · Answer

.209 cm^2 ?

ash2326 · Answer

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

anonymous · Answer

so 0.0209 cm^2 ?

ash2326 · Answer

yeah now you find length

anonymous · Answer

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

anonymous · Answer

64,585.17 ?

anonymous · Answer

what would be the unit?

ash2326 · Answer

$$\frac{cm^3}{cm^2}$$???

anonymous · Answer

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

ash2326 · Answer

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

anonymous · Answer

resistance? R=v/i ?

ash2326 · Answer

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 · Answer

R=ρ(micro ohms-cm)×3090199.522 cm ?

anonymous · Answer

then multiply it to 1924 ?

ash2326 · Answer

Yeah:D

anonymous · Answer

5945643879 ?

ash2326 · Answer

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

anonymous · Answer

why divide it by 10^6 ?

ash2326 · Answer

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

anonymous · Answer

oh okay thanks so the answer will be 5945.54 ohms ?

ash2326 · Answer

Yeah:D

anonymous · Answer

then whats next? ;D

ash2326 · Answer

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 · Answer

so that must be 645.8517 ?

ash2326 · Answer

64585.17/100=>64.581517 meters

anonymous · Answer

no its 645.8517

ash2326 · Answer

yeah, you're right. Sorry :(

anonymous · Answer

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

ash2326 · Answer

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

anonymous · Answer

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

ash2326 · Answer

welcome:D