Physics, 20.11.2020 14:00, erin2077

A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9.11 V, and the current is found to be 36.0 A. Find the resistivity of the material.

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Answers

answered: anaisejackson19

ρ = 1.6*10⁻⁸ Ω/m.

Explanation:

Applying Ohm's Law to the wire, assuming that it can be treated as a pure resistance, the resistance of the wire can be obtained as follows:

$R = \frac{V}{I} = \frac{9.11V}{36.0A} = 0.253 \Omega (1)$

At the same time, we know that there exists a relationship between the resistance, the resistivity ρ, the length L and the area A of the wire, that is given for the following expression:

$R = \rho* \frac{L}{A} (2)$

The area of the circular section of the wire, can be expressed as a function of the diameter d, as follows:

$A = \frac{\pi*d^{2} }{4} = \frac{\pi*(0.002m)^{2}}{4} = \pi*10e-6 (3)$

Replacing the left side of (2) by (1), and (3) on the right side, we can solve for the resistivity ρ as follows:

$\rho = \frac{R*A}{L} = \frac{0.253\Omega*\pi*10e-6}{50.0m} = 1.6e-8 \Omega/m$

ρ = 1.6*10⁻⁸ Ω/m

answered: Guest

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explanation:

answered: Guest

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A wire 50.0 m long and 2.00 mm in diameter is connected to a source with a potential difference of 9...