What is the thickness of the copper layer on a constantan wire?

In summary, the problem involves finding the thickness of a layer of copper that has been deposited on a piece of constantan wire. The resistivity of constantan and copper are given and the two layers are in parallel. The equation R = pl/A is relevant, where p is the resistivity, l is the length of wire, and A is the cross-sectional area. The cross-sectional area of the copper layer can be found by subtracting the cross-sectional area of the wire from the total area. Thanks to the hint given, the solution involves treating the layers as being in parallel.
  • #1
mysqlpress
83
1

Homework Statement



Here's the problem.
The resistance of a piece of constantan wire of radius 0.6mm is reduced to 1/3 its original resistance when a unifrom layer of copper is deposited on it. Find the thickness of the layer of copper
(Resistivity of constantan = 49*10^-8 ohm m
resistivity of copper =1.7*10^-8 ohm m

Homework Equations



I do think that it is related to
R =pl/A where p is the resistivity , l = length of wire
A = cross-section area

The Attempt at a Solution


I've tried ... but don't know how to work out
...
Thanks
 
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  • #2
Hint: The two layers are in parallel.
 
  • #3
Doc Al said:
Hint: The two layers are in parallel.

Yup.. and
Should I treated the cross-section area of copper as ( cross-section area of a big wire - cs a of a small wire) ? Since it is deposited .. I think on the surface of the constantan..covered it out...
 
  • #4
mysqlpress said:
Should I treated the cross-section area of copper as ( cross-section area of a big wire - cs a of a small wire) ?
Sure.
 
  • #5
Doc Al said:
Sure.

Okay, Thanks for your guide~~ :)
 

FAQ: What is the thickness of the copper layer on a constantan wire?

1. What is resistivity?

Resistivity is a measure of how strongly a material opposes the flow of electric current. It is represented by the Greek letter rho (ρ) and is measured in ohm-meters (Ωm).

2. How is resistivity related to conductivity?

Resistivity and conductivity are inversely related - as resistivity increases, conductivity decreases. Conductivity is the measure of how easily a material allows electric current to pass through it and is the inverse of resistivity.

3. What factors affect resistivity?

The main factors that affect resistivity are temperature, the type of material, and its physical dimensions. Generally, resistivity increases with temperature and is lower for materials with more free electrons and higher for materials with fewer free electrons. The length and cross-sectional area of a material also affect its resistivity.

4. What is the difference between resistivity and resistance?

Resistivity is an intrinsic property of a material, while resistance is a measure of how much a specific object or material resists the flow of electric current. Resistivity is dependent on the type of material and its physical dimensions, while resistance also takes into account other factors such as the shape and size of an object.

5. How is resistivity measured?

Resistivity is typically measured using a four-point probe technique, where four evenly spaced probes are placed on the surface of a material and a known current is passed through the outer probes while the voltage is measured between the inner probes. From this measurement, the resistivity of the material can be calculated using a specific formula.

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