Physics, 22.07.2020 21:01 slauravillalta

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be ? The resistivity of this metal is 1.68 × 10-8 Ω • m.

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Answer from: olorteguimikie

The diameter is $d = 6.5 *10^{-4} \ m$

Explanation:

From the question we are told that

The length of the cylinder is $l = 120 \ m$

The resistance is $\ 6.0\ \Omega$

The resistivity of the metal is $\rho = 1.68 *10^{-8} \ \Omega \cdot m$

Generally the resistance of the cylindrical wire is mathematically represented as

$R = \rho \frac{l}{A }$

The cross-sectional area of the cylindrical wire is

$A = \frac{\pi d^2}{4}$

Where d is the diameter, so

$R = \rho \frac{l}{\frac{\pi d^2}{4 } }$

=> $d = \sqrt{ \rho* \frac{4 * l }{\pi * R } }$

$d = \sqrt{ 1.68 *10 ^{-8}* \frac{4 * 120 }{3.142 * 6 } }$

$d = 6.5 *10^{-4} \ m$

Answer from: Quest

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hope this !

Answer from: Quest

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