Why Does Recalculating Resistance of Resistors Yield Different Results?

[Philip Wong]

hi guys,
I know this sound strange but it did happen. I was working on a question asking about calculating the resistance of a resistors, using different material one is copper and another is aluminium. I got the right answer, and wrote down the formula and steps that I used. But then I only didn't put in the values that I actually used. Just formula, steps and answer. Now when I come back to look at it again, I couldn't get the same answer that I originally correct. Either could I back track how I did it, so I hope someone can point it out to me, how I did it in the first place, and did I do it right then.

Homework Statement

a 20mm long piece of copper wire (sigma = 5.8*10^7 (ohm.m)^-1) with a diameter of 0.01mm is used as a resistor. you want to design a resistor with the same resistance but the only wire avaiable to you is an aluminium wire (sigma = 3.4*10^7)ohm.m)^-1) with diameter 0.02 mm. calculate the length for the piece of aluminium wire for which the two resistances are the same

Homework Equations

R = pL/A

The Attempt at a Solution

the steps that I wrote down original listed below, and I haven't put in the fitted values then, but as I tries to put in all the values in again, I didn't get a consistence result.

Rcu = pL/A
= L/ (sigma* A)
= (L/sigma) (4/ pi d^2)
=4.39ohm

Values I used to reattempt to get answer:
L = 20mm = 0.02m
sigma = 5.8*10^7
d = (0.01*10-3) ^2

Rcu = (0.02/(5.8*10^7)) * (4/ (pi*(.01*10^-3)^2



Why...?

 

[rl.bhat]

hi guys,

Rcu = pL/A
= L/ (sigma* A)
= (L/sigma) (4/ pi d^2)
=4.39ohm

Values I used to reattempt to get answer:
L = 20mm = 0.02m
sigma = 5.8*10^7
d = (0.01*10-3) ^2

Rcu = (0.02/(5.8*10^7)) * (4/ (pi*(.01*10^-3)^2
Why...?

R = ρL/A

R_Cu = ρ_(Cu)L₁/A₁ = ρ_(Al)L₂/A₂ = R_(Al)

Substitute the values and find L2

 

[vela]

I think you must be plugging it into your calculator incorrectly. I just got the same answer you got originally.

 

[Philip Wong]

I think you must be plugging it into your calculator incorrectly. I just got the same answer you got originally.

ohh! indeed i have made a mistake at input my values. because I recalculated it everything, this time I've got a consistent answer.

ahaha! thanks

 

[paranormal]

Hello,

It seems like there may have been a mistake in your calculations. When using the formula R = pL/A, it's important to make sure that all the units are consistent. In your original attempt, you used a length of 20mm and a diameter of 0.01mm, but in your second attempt, you used a length of 0.02m and a diameter of 0.01mm. This inconsistency in units could have led to an incorrect answer.

Additionally, when using the formula, it's important to remember that the units for resistivity (p) are ohm-meters, not ohm-millimeters. So in your second attempt, you would need to convert the diameter from millimeters to meters before using it in the formula. This could also have contributed to the difference in your results.

I would suggest double checking your units and using the correct values for resistivity and diameter in your calculations. Also, it's always a good idea to write out the units in your calculations to help catch any mistakes. I hope this helps clarify things for you. Good luck with your calculations!