Aluminum wire has 0.25mm radius and length of 75 m . If resistance of wire is 10 ohm. Calculate the resistivity of aluminum ?

Question

Answer

Resistivity = (R x A)/length
Radius = 0.25mm = 0.00025 m
length = 75m
Resistance = 10 ohms
Area of cross section = πr^2
= 22/7 x 0.00025 x 0.00025
Resistivity =
(10 x 22/7 x 0.00025 x 0.00025 ) ÷ 75
= (220/7 x 0.00025 x 0.00025)/75
= 2.63 x 10 to the power (-8) ohmmeter

Answer

Calculation of resistivity of aluminum wire

Given Data:

Radius of aluminum wire (r) = 0.25mm

Length of aluminum wire (l) = 75m

Resistance of aluminum wire (R) = 10 ohm

Formula:

The resistance of a wire is given by the formula:

R = (ρ * l) / A

where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.

The cross-sectional area of a wire is given by the formula:

A = π * r^2

where r is the radius of the wire.

Solution:

First, we need to calculate the cross-sectional area of the aluminum wire:

A = π * r^2 = 3.14 * (0.25mm)^2 = 0.19635 mm^2

Now, we can use the resistance formula to calculate the resistivity of aluminum:

R = (ρ * l) / A

ρ = (R * A) / l = (10 ohm * 0.19635 mm^2) / 75m = 26.28 x 10^-9 ohm m

Answer:

The resistivity of aluminum wire is 26.28 x 10^-9 ohm m.

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