Calculating the Resistivity of a Metal Wire

Given data:
- Length of the wire (L) = 1 m
- Resistance of the wire (R) = 0.84 Ω
- Diameter of the wire (d) = 0.2 m

To calculate the resistivity (ρ) of the wire, we can use the formula:

ρ = (R * A) / L

where:
- ρ is the resistivity of the wire
- R is the resistance of the wire
- A is the cross-sectional area of the wire
- L is the length of the wire

Calculating the Cross-sectional Area (A)

The cross-sectional area of a wire can be calculated using the formula:

A = π * (d/2)^2

where:
- A is the cross-sectional area
- d is the diameter of the wire

Substituting the given value of diameter (0.2 m) into the formula:

A = π * (0.2/2)^2
A = π * 0.1^2
A = π * 0.01
A = 0.0314 m²

Calculating the Resistivity (ρ)

Now, substituting the values of resistance (0.84 Ω), cross-sectional area (0.0314 m²), and length (1 m) into the formula:

ρ = (0.84 Ω * 0.0314 m²) / 1 m
ρ = 0.0264 Ω·m

Therefore, the resistivity of the metal wire is 0.0264 Ω·m.

Explanation:

Resistivity is a measure of how strongly a material opposes the flow of electric current. It depends on the physical properties of the material, such as its length, cross-sectional area, and resistance.

In this case, we are given the length of the wire (1 m), the resistance of the wire (0.84 Ω), and the diameter of the wire (0.2 m). By using the formulas for cross-sectional area and resistivity, we can calculate the resistivity of the wire.

First, we calculate the cross-sectional area of the wire using the given diameter. Then, we substitute the values of resistance, cross-sectional area, and length into the formula to find the resistivity.

The resistivity of the wire is an important property as it helps determine the wire's conductivity and its suitability for specific applications. Different materials have different resistivities, and by knowing the resistivity, we can compare and select materials based on their electrical properties.

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