alfers101 2 years ago 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.

1. 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

2. alfers101

so 12000 g?

3. ash2326

Yeah, now find volume Volume= mass/density

4. theyatin

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

5. alfers101

1,349.83 cm^2 ?

6. alfers101

@ash2326 @theyatin what do you think?

7. ash2326

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

8. alfers101

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

9. alfers101

*then

10. ash2326

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

11. alfers101

length=volume/ area of cross section?

12. ash2326

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

13. alfers101

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

14. ash2326

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

15. alfers101

.209 cm^2 ?

16. ash2326

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

17. alfers101

so 0.0209 cm^2 ?

18. ash2326

yeah now you find length

19. alfers101

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

20. alfers101

64,585.17 ?

21. alfers101

what would be the unit?

22. ash2326

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

23. alfers101

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

24. ash2326

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

25. alfers101

resistance? R=v/i ?

26. 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

27. alfers101

R=ρ(micro ohms-cm)×3090199.522 cm ?

28. alfers101

then multiply it to 1924 ?

29. ash2326

Yeah:D

30. alfers101

5945643879 ?

31. ash2326

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

32. alfers101

why divide it by 10^6 ?

33. ash2326

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

34. alfers101

oh okay thanks so the answer will be 5945.54 ohms ?

35. ash2326

Yeah:D

36. alfers101

then whats next? ;D

37. 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

38. alfers101

so that must be 645.8517 ?

39. ash2326

64585.17/100=>64.581517 meters

40. alfers101

no its 645.8517

41. ash2326

yeah, you're right. Sorry :(

42. alfers101

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

43. ash2326

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

44. alfers101

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

45. ash2326

welcome:D