What is the resistivity or cylindrical material wire whose 1.0m length has a resistance of 2.0 ohms? the diameter of the wire is 0.5mm
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To find the resistivity of the cylindrical material wire, we can use the formula:
Resistance (R) = (Resistivity (ρ) * Length (L)) / (Area (A))
Given:
Length (L) = 1.0 m
Resistance (R) = 2.0 ohms
Diameter (d) = 0.5 mm
First, we need to find the radius (r) using the formula:
Radius (r) = Diameter (d) / 2
Radius (r) = 0.5 mm / 2 = 0.25 mm = 0.25 x 10^-3 m
Next, we can calculate the area (A) using the formula:
Area (A) = π * (Radius (r))^2
Area (A) = π * (0.25 x 10^-3 m)^2
Area (A) = π * (6.25 x 10^-8) m^2
Now, we can rearrange the formula for resistance and solve for resistivity (ρ):
Resistivity (ρ) = (Resistance (R) * Area (A)) / Length (L)
Resistivity (ρ) = (2.0 ohms * π * 6.25 x 10^-8 m^2) / 1.0 m
Resistivity (ρ) = 3.14 x 10^-7 ohm-meter
Therefore, the resistivity of the cylindrical material wire is 3.14 x 10^-7 ohm-meter.
To find the resistivity of a cylindrical wire, you can use the formula:
Resistance = (Resistivity * Length) / Cross-sectional area
We are given the length of the wire (1.0 m) and the resistance (2.0 ohms).
First, we need to find the cross-sectional area of the wire using its diameter. The formula for the cross-sectional area of a wire is:
Area = π * (radius)²
Given that the diameter of the wire is 0.5 mm, we can calculate the radius by dividing the diameter by 2:
Radius = 0.5 mm / 2 = 0.25 mm = 0.25 × 10^(-3) m
Now we can calculate the cross-sectional area using the formula:
Area = π × (0.25 × 10^(-3))²
Next, rearrange the formula for resistivity:
Resistivity = (Resistance × Cross-sectional area) / Length
Plug in the known values:
Resistivity = (2.0 ohms × π × (0.25 × 10^(-3))²) / 1.0 m
Now we can calculate the resistivity of the wire by multiplying and dividing:
Resistivity ≈ 2.52 × 10^(-7) ohm-m
Therefore, the resistivity of the cylindrical wire is approximately 2.52 × 10^(-7) ohm-m.