Question

The resistivity of the material of a wire, 1.0 m long and 0.4 mm in diameter, with a resistance of 2.0 ohms, is:

a) 4.0×10⁻⁷Ω⋅m
b) 1.0×10⁻⁶Ω⋅m
c) 2.0×10⁻⁷Ω⋅m
d) 5.0×10⁻⁷Ω⋅m

Answer 1

To find the resistivity of the material of a wire with a known resistance, length, and diameter, one must calculate the cross-sectional area of the wire and then use the formula for resistivity. The calculation shows that the correct resistivity of the wire, given its dimensions and resistance, is 2.0×10⁻·Ω⋅m. C is the correct answer.

Step-by-step explanation:

The question is asking for the resistivity of the material of a wire having certain dimensions and resistance.

The resistivity, ρ, can be found using the formula ρ = R(A/L), where R is the resistance, A is the cross-sectional area of the wire, and L is its length. To calculate the area, we use A = π(r²), with r being the radius of the wire.

First, we convert the diameter of the wire to meters and calculate the radius (r = diameter/2):

0.4 mm = 0.4 × 10⁻³ m, so r = 0.2 × 10⁻³ m.

Next, we calculate the cross-sectional area (A):

A = π(r²) = π((0.2 × 10⁻³) m)² ≈ 1.2566 × 10⁻· m².

Finally, we can find the resistivity (ρ):

ρ = R(A/L) = 2.0 Ω ((1.2566 × 10⁻· m²)/(1.0 m)) ≈ 2.0 × 10⁻· Ω⋅m, which matches option c).