what is the diameter of a 1.00 m length of tungsten wire whose resistance is 0.22 ohms?
To calculate the diameter of a tungsten wire, we need to use the formula for the resistance of a wire:
Resistance (R) = (ρ * L) / A
where:
R is the resistance,
ρ (rho) is the resistivity of the material (for tungsten, ρ = 5.6 x 10^-8 Ω·m),
L is the length of the wire, and
A is the cross-sectional area of the wire.
Rearranging the formula, we can solve for the cross-sectional area:
A = (ρ * L) / R
Now, let's substitute the given values into the formula:
ρ = 5.6 x 10^-8 Ω·m
L = 1.00 m
R = 0.22 Ω
A = (5.6 x 10^-8 Ω·m * 1.00 m) / 0.22 Ω
A = 2.55 x 10^-7 m^2
The cross-sectional area (A) represents the area of a circle, so we can use the formula for the area of a circle to calculate the diameter:
A = π * (d/2)^2
Rearranging the formula, we can solve for the diameter (d):
d = √((4 * A) / π)
Now, let's substitute the value of the cross-sectional area (A) into the formula:
d = √((4 * 2.55 x 10^-7 m^2) / π)
d ≈ 6.37 x 10^-4 m
Therefore, the diameter of the 1.00 m length of tungsten wire with a resistance of 0.22 ohms is approximately 6.37 x 10^-4 meters (or approximately 0.637 mm).