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Resistance of a metal wire of length 1 m is 26 Ω at 200 C. If the diameter of the wire is 0.33 mm, what will be the resistivity of the metal at that temperature?

User Rpilkey
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Final answer:

To find the resistivity of a metal wire, you can use the formula ρ = (RA) / L, where R is the resistance, A is the cross-sectional area, and L is the length of the wire. By calculating the cross-sectional area and substituting the values into the formula, you can determine the resistivity of the wire.

Step-by-step explanation:

The resistivity (ρ) of a metal can be calculated using the formula ρ = (RA) / L, where R is the resistance of the wire, A is the cross-sectional area of the wire, and L is the length of the wire.

First, we need to calculate the cross-sectional area of the wire using the formula A = πr^2, where r is the radius of the wire. Given that the diameter of the wire is 0.33 mm, we can calculate the radius by dividing the diameter by 2, giving us a radius of 0.165 mm or 0.165 x 10^-3 m.

Next, we substitute the values in the formula for resistivity, giving us ρ = (26 Ω x π x (0.165 x 10^-3 m)^2) / 1 m. Simplifying this equation gives us the resistivity of the metal wire at 200°C.

User Anhiqkao
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