Temperature variation of resistance

[jsantor1]

So the problem I am working on is.. A 100 cm long copper wire of radius 0.45 cm has a potential difference across it sufficient to produce a current of 5.0 A at 20°C. Find a) What is the potential difference. b) If the temperature of the wire is increased to 200°C, what potential difference is now required to produce a current of 5.0 A

I solved part a easily by finding the resistance of the wire and plugging that into V=IR with the solution being 1.34mV.

Now for part b i used the equation R=R0[1+alpha(T-T00)] and plugged back into V=IR but my solution keeps coming out wrong... please help me out here I am totally confused...

 

[LowlyPion]

So the problem I am working on is.. A 100 cm long copper wire of radius 0.45 cm has a potential difference across it sufficient to produce a current of 5.0 A at 20°C. Find a) What is the potential difference. b) If the temperature of the wire is increased to 200°C, what potential difference is now required to produce a current of 5.0 A

I solved part a easily by finding the resistance of the wire and plugging that into V=IR with the solution being 1.34mV.

Now for part b i used the equation R=R0[1+alpha(T-T00)] and plugged back into V=IR but my solution keeps coming out wrong... please help me out here I am totally confused...

Where did you get your first answer? What is the driving potential?

 

[jsantor1]

The first part you use R= resistivity* L/A. This gives you the resistance and with the currecnt use V=IR to solve for potential difference...

 

[jsantor1]

anyone?...

 

[LowlyPion]

The first part you use R= resistivity* L/A. This gives you the resistance and with the currecnt use V=IR to solve for potential difference...

I get a different answer for the initial resistance then. I used 16.8 nΩm and I get 3.73 x 10^-4Ω.

What value of α are you using?

 

[jsantor1]

well my answer is correct according to the book...the value for the resistivity of copper I am using is 1.7E-8

 

[LowlyPion]

well my answer is correct according to the book...the value for the resistivity of copper I am using is 1.7E-8

Yes. You're right. I made an error calculating the area. Sorry.

Now what are you using for your temperature α ?

I have 3.9 x 10^-3 per degree C for copper.

 

[jsantor1]

That's what I'm using as well, getting a new resistance of .04824 and then getting a potential difference of 241.24mV which is coming out wrong for some reason

 

[LowlyPion]

That's what I'm using as well, getting a new resistance of .04824 and then getting a potential difference of 241.24mV which is coming out wrong for some reason

Using the calculator at
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html

I get 4.56 x 10^-4Ω (using the 2.68 x 10^-4 Ω for 20 C)

That yields 2.28 mV.

 

[jsantor1]

hmm that worked..do u know why my calculator is not computing these correctly?

 

[LowlyPion]

hmm that worked..do u know why my calculator is not computing these correctly?

You have to be careful with the powers of 10. Looks like you might have dropped a 0 somewhere in entering the numbers. Sometimes these problems unfortunately become more about arithmetic than physics. Just be careful is the only advice I can give, but then I guess you already know that.

 

[jsantor1]

thank you...