A conductor has a diameter of
1.00mm and length 2.00m the
resistance of the material is 0.1Ω,
its resistivity is___
A. 3.93 x 10-6 Ωm
B. 2.55 x 102 Ωm
C. 3.93 x 10-8 Ωm
D. 2.55 x 102 Ωm
To find the resistivity (ρ) of the material, we can use the formula:
ρ = (R * A) / L
where R is the resistance, A is the cross-sectional area of the conductor, and L is the length of the conductor.
First, we need to find the cross-sectional area (A) of the conductor. The formula for the area of a circle is:
A = π * r^2
where r is the radius of the circle. The radius can be found by dividing the diameter by 2:
r = 1.00mm / 2 = 0.5mm = 0.0005m
Now we can find the cross-sectional area:
A = π * (0.0005m)^2 = 0.0000007854 m^2
Next, we can substitute the values into the formula for resistivity:
ρ = (0.1Ω * 0.0000007854 m^2) / 2.00m
Simplifying this expression gives:
ρ = 0.00000007854 Ωm
Therefore, the resistivity of the material is 7.854 x 10^-8 Ωm.
The closest answer choice is C. 3.93 x 10^-8 Ωm.
To find the resistivity of the material, we can use the formula:
Resistivity (ρ) = (Resistance x Cross-sectional Area) / Length
First, we need to find the cross-sectional area of the conductor. The formula for that is:
Area (A) = πr^2
Given that the diameter of the conductor is 1.00mm, the radius (r) would be half of that, which is 0.50mm or 0.00050m.
Therefore, the area of the conductor would be:
A = π(0.00050m)^2 = π(2.5 x 10^-7 m^2) = 7.85 x 10^-7 m^2
Now, we can substitute the values into the resistivity formula:
ρ = (0.1Ω x 7.85 x 10^-7 m^2) / 2.00m
= 7.85 x 10^-8 Ωm
So, the correct answer is C. 3.93 x 10^-8 Ωm.