Question

A 10-m-long wire with a diameter of 0.80 mm has a resistance of 1.1ω. of what material is the wire made?

Answer 1

The radius of the wire is 
$r= \frac{d}{2}= \frac{0.80 mm}{2}=0.40 mm=0.4 \cdot 10^{-3}m$
and so the cross-sectional area of the wire is
$A=\pi r^2=\pi ( 0.4 \cdot 10^{-3}m)^2 =5\cdot 10^{-7} m^2$

The relationship between the resistance of the wire R, its length L, its cross-sectional area A and the resistivity of the material $\rho$ is
$\rho = \frac{RA}{L}$
So by using the data of the problem we find the resistivity of the material:
$\rho= \frac{(1.1 \Omega)(5 \cdot 10^{-7}m^2)}{10.0 m}=5.5 \cdot 10^{-8} \Omega \cdot m$

And by looking at the table of the resistivities for different materials, we find that this value corresponds to tungsten, so the wire is made of tungsten.

Answer 2

Because of its resistivity of 5.5 x 10 ⁻⁸ Ωm, the wire is made of tungsten material.

Further explanation

Given:

• A 10-m-long wire ⇒ $\boxed{ \ L = 10 \ m \ }$
• A diameter of 0.80 mm ⇒ $\boxed{ \ D = 0.80 \ mm = 8.0 \cdot 10^{-4} \ m \ }$ or the radius of the wire is $\boxed{ \ r = \frac{1}{2} D \ }$ ⇒ $\boxed{ \ r = 0.40 \ mm = 4.0 \cdot 10^{-4} \ m \ }$
• A resistance of 1.1 Ω ⇒ $\boxed{ \ R = 0.80 \ \Omega \ }$

Question:

Of what material is the wire made?

The Process:

Step-1

Let us find out the cross-sectional area of the wire.  The shape of the wire cross-section is a circle, and the wire itself is a tube.

Area of circle is

$\boxed{ \ A = \pi r^2 \ } \ or \ \boxed{ \ A = \frac{1}{4} \pi D^2 \ }$

Whichever formula we use, the results remain the same.

$\boxed{ \ A = \pi (4.0 \cdot 10^{-4})^2 \ } \ or \ \boxed{ \ A = \frac{1}{4} \pi (8.0 \cdot 10^{-4})^2 \ }$

We get  the cross-sectional area of the wire of $\boxed{ \ A \approx 5.0 \cdot 10^{-7} \ m^2 \ }$

Step-2

In the next step, we have to calculate the resistivity of the material. After that, we compare it to the table of the resistivity of various materials.

We use the electric resistivity formula shown by

$\boxed{ \ \rho = R \ \frac{A}{L} \ }$.

where,

• ρ = resistivity  (in Ωm)
• R = resistance (in Ω)
• A = the cross-sectional area (in m²)
• L = length (in m)

Let us find out the resistivity of the material by substituting all the data above and calculating it.

$\boxed{ \ \rho = \frac{(1.1 \ \Omega )(5.0 \cdot 10^{-7} \ m^2)}{10 \ m} \ }$

We get a resistivity value of $\boxed{ \ \rho = 5.5 \cdot 10^{-8} \ \Omega m \ }$.

Based on the source table that contains the resistivity of various materials, the wire is made of tungsten.

_ _ _ _ _ _ _ _ _ _

Notes

Let us consider the relationship between resistance, resistivity, wire length, and cross-sectional area.

$\boxed{ \ R = \rho \ \frac{L}{A} \ }$

The conclusions that can be drawn from the formula are as follows.

• Resistance is directly proportional to resistivity and length, i.e., $\boxed{ \ R \sim \rho \ } \ or \ \boxed{ \ R \sim L \ }$
• Resistance is inversely proportional to the cross-sectional area. i.e., $\boxed{ \ R \sim \frac{1}{A} \ }$
• Resistance is inversely proportional to the square of the radius or diameter of the cross-sectional area, if the cross-section of the wire is a circle, i.e.,  $\boxed{ \ R \sim \frac{1}{r^2} \ } \ or \ \boxed{ \ R \sim \frac{1}{D^2} \ }$

Learn more

1. How long is the wire? A problem of density  brainly.com/question/4178726#
2. About the mass and density of substances  brainly.com/question/4053884
3. The theoretical density of platinum which has the FCC crystal structure. brainly.com/question/5048216