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What is the diameter of a 1.00 m length of tungsten wire whose resistance is 0.26 Ω ? Express your answer using two significant figures.

User Todotresde
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To solve this problem, we first need to understand the properties of the materials involved and the formulas related to them. The resistivity of tungsten is 5.60 x 10^-8 ohm meters. The resistance of this particular length of tungsten is given as 0.26 ohms and its length is 1.00 meter.

The resistance (R) of a wire can be calculated using the formula R = rho * (L/A) where rho is the resistivity, L is the length, and A is the cross-sectional area. In order to find the cross-sectional area first, we will rearrange the formula to A = rho * (L/R). Substituting the known values, we get:

A = 5.60 x 10^-8 * (1.00 / 0.26), which equals roughly 2.15 x 10^-7 square meters.

Given the area, we can now calculate the diameter of the wire. The cross-sectional area of a wire is also equal to pi*(d/2)^2, where d is the diameter of the wire. By rearranging this formula, we get d = 2*sqrt(A/pi). Therefore, substituting the calculated area into this formula gives:

d = 2 * sqrt(2.15 x 10^-7 / pi), which equals about 0.00052 meters or, equivalently, 0.52 millimeters, with the result rounded to two significant figures.

So, the diameter of the tungsten wire is approximately 0.52 mm.

User Adam Milward
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