What is the diameter of a 1.00 meter length of tungsten wire whose resistance is 0.32 ohm (electrical resistance)?
4.7*10^-4
To determine the diameter of a tungsten wire based on its length and resistance, we can make use of the "resistivity" of tungsten. Tungsten has a known resistivity value, which is a measure of a material's inherent resistance to electric current flow.
The formula to calculate the resistance of a wire is as follows:
Resistance (R) = (resistivity * length) / cross-sectional area
To rearrange the formula and solve for the cross-sectional area, we get:
Cross-sectional area = (resistivity * length) / Resistance
First, we need to determine the resistivity of tungsten. The resistivity of tungsten is approximately 5.6 x 10^-8 ohm-meter.
Now, let's substitute the given values into the formula:
Cross-sectional area = (5.6 x 10^-8 ohm-meter * 1.00 meter) / 0.32 ohm
Cross-sectional area = 1.75 x 10^-7 square meters
The cross-sectional area represents the area of the wire's circular cross-section.
To find the diameter of the wire, we can use the formula for the area of a circle:
Area = π * (diameter/2)^2
Rearranging the formula to solve for the diameter:
diameter = √((4 * cross-sectional area) / π)
Substituting the calculated cross-sectional area:
diameter = √((4 * 1.75 x 10^-7 square meters) / π)
diameter ≈ 2.65 x 10^-4 meters or 0.265 millimeters
Therefore, the diameter of the 1.00 meter length of tungsten wire with a resistance of 0.32 ohms is approximately 0.265 millimeters.
0.2
The formula for resistance is:
total resistance = (resistivity) * (length)/(area)
filling in from the problem statement:
0.32 ohms = (resistivity) * 1m/(area)
looking up the resistivity for tungsten:
at 20 C
restivity = 5.28 * 10^-8 ohms*m
leaving just the area unknown:
0.32 ohm = (5.28 * 10^-8)(ohm-m) * (1 m)/(area)
Solve for the area. Then, assuming a round wire, find the diameter that gives that area.