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.