R = 0.407Ω.
The resistance R of a particular conductor is related to the resistivity ρ of the material by the equation R = ρL/A, where ρ is the material resistivity, L is the length of the material and A is the cross-sectional area of the material.
To calculate the resistance R of a wire made of a material with resistivity of 3.2x10⁻⁸Ω.m, the length of the wire is 2.5m and its diameter is 0.50mm.
We have to use the equation R = ρL/A but first we have to calculate the cross-sectional area of the wire which is a circle. So, the area of a circle is given by A = πr², with r = d/2. The cross-sectional area of the wire is A = πd²/4. Then:
R =[(3.2x10⁻⁸Ω.m)(2.5m)]/[π(0.5x10⁻³m)²/4]
R = 8x10⁻⁸Ω.m²/1.96x10⁻⁷m²
R = 0.407Ω
To determine the resistance of this wire is equal to 0.4082 Ohms.
Given the following data:
To determine the resistance of this wire:
First of all, we would determine the area of the wire by using this formula:
[tex]A =\frac{\pi d^2}{4} \\\\A =\frac{3.142 \times (5\times 10^{-4})^2}{4}\\\\A = 1.96 \times 10^{-7}\;m^2[/tex]
Now, we can determine the resistance of this wire:
[tex]R=\frac{\rho L}{A} \\\\R=\frac{3.2 \times 10^{-8} \times 2.5}{1.96 \times 10^{-7}}[/tex]
Resistance = 0.4082 Ohms.
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