A conductor has a diameter of 1.00m and length 2.00m . If the resistance of the material is 0.1 ohms , it's resistivity is
To find the resistivity (ρ) of a material, we can use the formula:
ρ = (R × A) / L
where:
ρ = resistivity of the material
R = resistance of the conductor
A = cross-sectional area of the conductor
L = length of the conductor
In this case, the resistance of the material is given as 0.1 ohms and the length of the conductor is 2.00 m. However, we still need to find the cross-sectional area (A) of the conductor in order to calculate the resistivity.
To find the cross-sectional area, we need to know the shape of the conductor. If the conductor is a cylinder, we can use the formula for the area of a circle:
A = π × r^2
where:
A = cross-sectional area of the conductor
π = pi (approximately 3.14159)
r = radius of the conductor
The diameter of the conductor is given as 1.00 m. We can use this to find the radius (r) using the formula:
r = d / 2
where:
d = diameter of the conductor
Plugging in the values, we can calculate the radius of the conductor:
r = 1.00 m / 2 = 0.50 m
Now that we have the radius, we can find the cross-sectional area:
A = π × (0.50 m)^2 = 0.7854 m^2
Finally, we can calculate the resistivity by substituting the values into the formula:
ρ = (0.1 ohms × 0.7854 m^2) / 2.00 m = 0.03927 ohm-meters (rounded to five decimal places)
Therefore, the resistivity of the material is approximately 0.03927 ohm-meters.