Applied Functions: find the resistance of 100' of this wire

[Jeliramp]

The resistance of a wire varies directly as its length and inversely as the square root of it's diameter. If 50ft. of wire with a diameter of 0.01inces has a resistance of 5 ohms, what is the resistance of 100ft. of the same kind of wire with a diameter of 0.02 inches?

I converted feet into inches 50ft=600inches
then set my problem up like this,

5=k(600)/Square root of 0.01 I got 8.3 x 10 to the negative 4

for the second one I converted the feet to inches as well 100ft = 1200in
then I set my second problem up like this,

r=1200(8.3 x 10 to the negative 4)/ square root of 0.02

= .996/.14 = 7.11

I got 7.11 as an answer but our teacher gave us the answer and its not matching up. Can I get a walk through of how to do this problem or what I did wrong?
Thanks!

 

[tkhunny]

I think you are experiencing unit problems.

\(\displaystyle \L\,6\,\Omega\,=\,k*\frac{50\,ft}{\sqrt{0.01\,in}}\)

\(\displaystyle \L\,k\,=\,0.001\frac{\Omega}{\sqrt{in}}\)

\(\displaystyle \L\,k*\frac{100\,ft}{\sqrt{0.02\,in}}\,=\,8.485\,\Omega\)

 

[Jeliramp]

Applied Functions

The teacher gave the answer as 2.5 ohms. I appreciate your help.

 

[tkhunny]

Sorry, but 2.5 ohms makes no sense.

50 --> 100 is a factor of 2 in the numerator

\(\displaystyle \sqrt{0.01}\) --> \(\displaystyle \sqrt{0.02}\) is a factor less than 2 in the denominator

It must be greater than 6 ohms.

 

[skeeter]

The resistance of a wire varies directly as its length and inversely as the square root of it's diameter.

The solution provided by your teacher is correct, but the statement you provided above is incorrect ... resistivity of a wire varies directly as length and inversely as the square of its diameter.

R = kL/d²

5 = k*600/(.01)²

k = 5(.01)²/600 = 1/1200000

R = k*1200/(.02)²

R = 2.5 ohms

 

[tkhunny]

That's what I get for just reading the problem statement.

Excellent point!! ALWAYS think about every aspect of the problem. I did think it looked funny, but obviously I didn't think hard enough.

Good call, skeeter.

 

[Jeliramp]

Applied functions

I don't know another way to contact you to say thank you. So I'll say it here, Thank You!