Resistance in a wire, sanity check about units.

[Cade]

Homework Statement

A x cm long wire has a diameter of y mm and a resistivity of 4.0x10-7 ohm-cm. Calculate its resistance.

Homework Equations

R = p*L/A

The Attempt at a Solution

First, I convert the given information into SI units:
Length = x*10^-2 m
Diameter = y*10^-3 m
Resistivity = 4*10^-5 ohm/m

Next, cross-sectional area of a wire/cylinder is pi*r^2 = pi*(d/2)^2 = (1/4)pi*d^2

R = p*L/A = p*L/((1/4)pi*d^2) = (4 L p)/(d^2 pi)

If x = 20 cm and y = 0.3mm,
R = (4*20*10^-2 *4*10^-5)/((0.3*10^-3)^2*Pi) = 113.177 ohms

Is this correct? My TA told me that I converted the units wrongly, and that the correct answer is 0.0113177 ohms.

 

[SammyS]

How did you convert 4.0*10^-7 ohm-cm to units of ohm-m ?

1 cm = 1*10^-2m .

 

[Cade]

4.0*10-7 ohm-cm * 10^-2 m/cm = 4.0*10^-9 ohm-m

Oh, that's the mistake, I did it in the opposite direction.

 

[SammyS]

4.0*10-7 ohm-cm * 10^-2 m/cm = 4.0*10^-9 ohm-m

Oh, that's the mistake, I did it in the opposite direction.

And now you should get the accepted answer.

 

[rwisz]

Your calculations and conversions seem to be correct. The resistance value you calculated is indeed 113.177 ohms. However, it is always important to do a sanity check on your units to ensure that your final answer is in the correct units.

In this case, the units for resistance are ohms, so your final answer should also be in ohms. It seems that your TA may have mistakenly converted the resistivity from ohm-cm to ohm/m, resulting in a different final answer.

It is always important to double check your units and make sure they are consistent throughout your calculations. In this case, it would be helpful to clarify with your TA about the correct units for resistivity and how it should be converted.

Overall, your approach and calculations seem correct, but it is always good to do a sanity check on your units to ensure accuracy.