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Current through two different types of wire of different diameter

  • #1

Homework Statement



For what electric field strength would the current in a 2.0 mm diameter nichrome wire be the same as the current in a 1.0 mm diameter aluminum wire in which the electric field strength is 0.0080 V/m?

aluminum diameter = 1.0 mm
Same current(I) flowing through both wires

Homework Equations



J = sigma*E........ I/A = sigma*E
so.....I = sigma*E*A
sigma = 1/rho
sigma = conductivity; rho = resistivity

The Attempt at a Solution



Equating the two currents, I solved for the unknown E-field:

E(nichrome) = (E*A*sigma(aluminum))/(A*sigma(nichrome))
rho(nichrome) = 1.1*10^-6 Ωm
rho(aluminum) = 2.82*10^-8 Ωm

I calculated the E-field to be approximately 0.078 V/m, but this was apparently wrong. Help would be appreciated..!
 

Answers and Replies

  • #2
SammyS
Staff Emeritus
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Show us the steps you took, so we can help you.
 
  • #3
Really? All I did was "Equate the two current equations"......
So here it is:

σEA = σEA

The left side representing Nichrome, and then the right side representing aluminum. Then I solved for the E-field of the unknown wire getting:

E = (σEA)/(σA)

The top part of the fraction being aluminum properties, and the bottom being the properties of Nichrome. Is there anything that I have done wrong????
 
  • #4
ehild
Homework Helper
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Your derivation was correct, I got the same result. What is the problem with it?

ehild
 
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,253
972
Really? All I did was "Equate the two current equations"......
So here it is:

σEA = σEA

The left side representing Nichrome, and then the right side representing aluminum. Then I solved for the E-field of the unknown wire getting:

E = (σEA)/(σA)

The top part of the fraction being aluminum properties, and the bottom being the properties of Nichrome. Is there anything that I have done wrong????
How are the two areas related?
 
  • #6
The homework website says my answer of 0.078 V/m is wrong. I'm utterly confused. I'll have to address my professor about this problem, as well as the other problem. I've double checked every single possible error for units, etc. as well.
 

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