Question

something's not right here....i'm doing an online lab to see the resistance of a pencil. i got a K (based of slope of V/I) at 301.9 volts per amp. then the lab says to find the length using R=rho (L/A) and it says A is the cross section and the diameter of the pencil is supposed to be 6mm. i plug in 301.9= 3.5*10^-4 (provided by the lab manual) *(L/0.0006). i get a length of 517.5 meters, which seems a bit long for a pencil. did i do something wrong with my units somewhere?

Answer 1

0.006m

Answer 2

We're solving for L right?

Answer 3

\[R = \rho (\frac{ L }{ A }) \implies L = \frac{ R }{ \rho } A\] so what ever that is

Answer 4

i thought .6 mm was .0006 m, not.006.

Answer 5

i double checked. it is .6 mm. i misstyped earlier.

Answer 6

Yeah, that's right, but the formula I wrote above, L signifies length right, so that's what you'll have to do, try it out and see what you get. If you have a small number in the denominator you'll always get a large number as a final answer, it's like taking the limit as it approaches 0, you'll get infinity.

Answer 7

that's the exact formula i used. 301.9=3.5*10^-4(L/0.0006) = 517.5

Answer 8

Mhm, are you sure all your numbers are right?

Answer 9

yeah. slope was 0.003312 according to logger pro and R=1/slope. R=301.9. they gave a rho value of 3.5*10^-4.

Answer 10

Check the units for everything

Answer 11

i don't know what units the ohms are in. i used volts/amp there so i don't know if they're meters or what

Answer 12

What are the units of rho in this case?

Answer 13

If you assume that the virtual pencil lead was made out of material of resistivity ρ = 3.5×10-4 Ωm (a composition of graphite) and the diameter of the lead was 0.6 mm, how long was the pencil? On average the real pencil rod has a diameter of 2.4 ± 0.1 mm and the length of 18.0 ± 0.1 cm. If it was made of the same material as the virtual pencil what resistance would it have? Propagate the errors in the dimension measurements into the final uncertainty of the calculated resistance.

Answer 14

Ok thats to calculate resistance, and that's the only formula you're given?

Answer 15

equation 3 in the lab manual is R=rho (L/A). equation 2 is R =V/I. those are the two i'm given

Answer 16

It gives you the length though?

Answer 17

Your resistance must be wrong

Answer 18

length we have to find. it says A is uniform cross section. so i assumed it was the diameter which says 0.6mm

Answer 19

resistance is just 1/slope. and slope was calculated by logger pro

Answer 20

The cross section is the area

Answer 21

not the diamater

Answer 22

So if you had a cylinder the cross section would be a circle A = pi *r^2

Answer 23

Notice the units

Answer 24

so pir^2

Answer 25

Bingo

Answer 26

ok. knew it had to have been something small like that.

Answer 27

And you were using the diameter of the lead, not the pencil length of the rod

Answer 28

well i don't have the info on anything but the graphite. i think because it's all virtual, the wood around the pencil is negligible here

Answer 29

so now i'm getting 48.8 cm. which sounds a bit better.

Answer 30

Ah I see it was just showing the real pencils, yeah so just find the right cross section, but it should work out now ;)

Answer 31

ok. thanks.

Answer 32

Yeah, just go over all your work again, and see if everything is right, lab work can sometimes get tedious and we miss out the little things, and if you can't figure out what's wrong, you might have a large error, but that's ok.