A wire of 1.0 m long, 0.2 mm diameter and has a resistance of 10 ohm. Calculate the resistivity of its material.?

Question

Answer

L = 1.0 m, D = 0.2 mm

, r = 0.2 /2 mm

= 0.2/2× 1000m = 1 × 10power -4 m

R = 10 ohm.
P=?

Here, We know that

P = RA /l
= R × πr2/l

So that,

10× 3.14×(1×10power- 4 )square
/1.0

The answer is :.

{ 3.14 × 10 power -7 ohm m.}

Answer

Calculating the Resistivity of a Wire

Understanding Resistivity: Resistivity is a measure of a material's ability to resist the flow of electric current. It is denoted by the Greek letter rho (ρ) and is measured in ohm-meters (Ω.m).

Formula for Resistivity: The formula for resistivity is ρ = RA/L, where ρ is resistivity, R is resistance, A is cross-sectional area, and L is length.

Calculating Cross-Sectional Area: The cross-sectional area of a wire is given by the formula A = πr^2, where r is the radius of the wire.

Converting Diameter to Radius: The diameter of the wire is given as 0.2 mm, so the radius can be calculated as r = d/2 = 0.1 mm = 0.0001 m.

Calculating Cross-Sectional Area: Using the formula A = πr^2, the cross-sectional area of the wire is A = π(0.0001)^2 = 3.14 x 10^-8 m^2.

Calculating Resistivity: Using the formula ρ = RA/L and the given values of R = 10 Ω, A = 3.14 x 10^-8 m^2, and L = 1.0 m, we can calculate the resistivity as ρ = (10 Ω)(3.14 x 10^-8 m^2)/1.0 m = 3.14 x 10^-7 Ω.m.

Explanation: The resistivity of a material is an intrinsic property that is determined by the material's composition and structure. In this problem, we are given the length, diameter, and resistance of a wire and asked to calculate the resistivity of its material. To do this, we use the formula for resistivity, which relates the resistance of a wire to its dimensions and the resistivity of its material. We start by calculating the cross-sectional area of the wire using the formula A = πr^2, where r is the radius of the wire. The radius can be calculated from the given diameter of the wire. We then use the formula ρ = RA/L to calculate the resistivity, using the given values of R, A, and L. The final result is the resistivity of the material in ohm-meters.

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