[amp_mcq option1=”1.2 x 10-8 $$\\Omega $$-m” option2=”1.4 x 10-8 $$\\Omega $$-m” option3=”1.6 x 10-8 $$\\Omega $$-m” option4=”1.8 x 10-8 $$\\Omega $$-m” correct=”option4″]<\/p>\n
The correct answer is $\\boxed{\\text{A}}$.<\/p>\n
The specific resistance of a material is the resistance of a wire of that material with a unit length and unit cross-sectional area. It is denoted by $\\rho$.<\/p>\n
The resistance of a wire is given by the equation $R = \\rho \\frac{l}{A}$, where $l$ is the length of the wire, $A$ is the cross-sectional area of the wire, and $\\rho$ is the specific resistance of the material.<\/p>\n
In this case, we are given that $l = 200 \\text{ m}$, $R = 21 \\Omega$, and $d = 0.44 \\text{ mm}$. The diameter of the wire is $d = 2r = 0.44 \\times 2 = 0.88 \\text{ mm}$. The cross-sectional area of the wire is $A = \\pi r^2 = \\pi \\left(0.44 \\times 10^{-3} \\text{ m}\\right)^2 = 1.3 \\times 10^{-6} \\text{ m}^2$.<\/p>\n
Substituting these values into the equation for resistance, we get $R = \\rho \\frac{l}{A} = 21 \\Omega = \\rho \\frac{200 \\text{ m}}{1.3 \\times 10^{-6} \\text{ m}^2}$. Solving for $\\rho$, we get $\\rho = \\frac{21 \\Omega \\times 1.3 \\times 10^{-6} \\text{ m}^2}{200 \\text{ m}} = 1.2 \\times 10^{-8} \\Omega \\text{ m}$.<\/p>\n
Therefore, the specific resistance of the copper wire is $\\boxed{1.2 \\times 10^{-8} \\Omega \\text{ m}}$.<\/p>\n
The other options are incorrect because they are not equal to the specific resistance of the copper wire.<\/p>\n","protected":false},"excerpt":{"rendered":"
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