What is the resistivity of a cylindrical material wire whose length is 2.0mm a resistance of 4.0 ohms diameter of wire is 0.8mm
The resistivity of the cylindrical wire can be calculated using the formula:
resistance = (resistivity x length) / cross-sectional area
Rearranging this formula, we get:
resistivity = (resistance x cross-sectional area) / length
The cross-sectional area of the wire can be calculated using the formula:
cross-sectional area = π x (diameter/2)^2
Substituting the given values, we get:
cross-sectional area = π x (0.8/2)^2 = 0.5027 mm^2
Now, substituting the values of resistance, length, and cross-sectional area, we get:
resistivity = (4.0 x 0.5027) / 2.0 = 1.01 ohm-mm^2/m
Therefore, the resistivity of the cylindrical wire is 1.01 ohm-mm^2/m.
To find the resistivity of the cylindrical wire, we can use the formula:
resistance = resistivity x (length / cross-sectional area)
Given:
resistance = 4.0 ohms
length = 2.0 mm
diameter = 0.8 mm
First, we need to convert the length and diameter to meters (since resistivity is usually given in ohm-meters):
length = 2.0 mm = 2.0 x 10^(-3) meters
diameter = 0.8 mm = 0.8 x 10^(-3) meters
Next, we need to calculate the cross-sectional area of the wire. The cross-sectional area of a cylinder is given by the formula:
area = π x (radius)^2
radius = (diameter / 2) = (0.8 x 10^(-3) meters) / 2
radius = 0.4 x 10^(-3) meters
Now we can calculate the cross-sectional area:
area = π x (0.4 x 10^(-3))^2
area = π x (0.16 x 10^(-6)) = 0.16π x 10^(-6) m^2
Finally, we can rearrange the formula to solve for resistivity:
resistivity = (resistance x area) / length
resistivity = (4.0 ohms x 0.16π x 10^(-6) m^2) / (2.0 x 10^(-3) meters)
resistivity ≈ 3.2π x 10^(-2) ohm-meters
Therefore, the resistivity of the cylindrical wire is approximately 3.2π x 10^(-2) ohm-meters.