A 100 m long wire with a cross-sectional area of 4 mm2 has a resistance of 6 ohms. What is the resistivity of the material of the wire in Ùm?
resistivity = Ω-m, so
6Ω * 4mm^2 / 100*1000mm = .00024 Ω-mm = 0.24 Ω-m
The correct answer is 2.4*10^-7 ¦¸m
To find the resistivity of the material of the wire in Ùm (microohm-meter), we can use the formula:
Resistivity (Ùm) = (Resistance × Cross-sectional Area) / Length
Given:
Resistance (R) = 6 ohms
Cross-sectional Area (A) = 4 mm^2
Length (L) = 100 m
Plugging in the values into the formula, we get:
Resistivity (Ùm) = (6 ohms × 4 mm^2) / 100 m
First, we need to convert the cross-sectional area from mm^2 to m^2:
1 mm^2 = (1 mm * 1 mm) = (1 × 10^-3 m * 1 × 10^-3 m) = 1 × 10^-6 m^2
So, Cross-sectional Area (A) = 4 mm^2 = 4 × 10^-6 m^2.
Now, we can substitute the values into the formula:
Resistivity (Ùm) = (6 ohms × 4 × 10^-6 m^2) / 100 m
Simplifying the equation, we get:
Resistivity (Ùm) = 24 × 10^-6 / 100
Resistivity (Ùm) = 0.24 × 10^-6 Ùm
Therefore, the resistivity of the material of the wire is 0.24 Ùm.
To find the resistivity of the material of the wire, we can use the formula:
Resistivity (ρ) = (Resistance × Cross-sectional area) / Length
Given:
Resistance (R) = 6 ohms
Cross-sectional area (A) = 4 mm^2
Length (L) = 100 m
First, we need to make sure that all the units are in the same system. Let's convert the cross-sectional area from mm^2 to m^2.
1 mm^2 = (1 × 10^-6) m^2 (since there are 1000 mm in a meter)
So, the cross-sectional area in m^2 would be:
A = 4 × 10^-6 m^2
Now, substitute the given values into the formula to find the resistivity:
ρ = (6 ohms × 4 × 10^-6 m^2) / 100 m
Simplifying the expression further:
ρ = (24 × 10^-6 ohm.m^2) / 100 m
ρ = 2.4 × 10^-7 ohm.m^2
Therefore, the resistivity of the material of the wire is 2.4 × 10^-7 ohm.m^2, or 0.24 Ùm.