what is the diameter if a 1.00m tungsten wire whose resistence is 0.22 ohms?
To find the diameter of the tungsten wire, we can use the formula for the resistance of a wire:
R = (ρL) / (A)
where:
R is the resistance of the wire (0.22 ohms),
ρ is the resistivity of the material (tungsten in this case),
L is the length of the wire (1.00 m), and
A is the cross-sectional area of the wire.
To find the diameter, we need to calculate the cross-sectional area of the wire, and then use it to find the diameter.
The resistivity of tungsten is ρ = 5.6 x 10^-8 ohm⋅m.
First, let's rearrange the formula:
A = (ρL) / R
Now, plug in the values:
A = (5.6 x 10^-8 ohm⋅m)(1.00 m) / 0.22 ohms
Simplifying the equation, we have:
A = 2.545 x 10^-7 m^2
Now, let's calculate the diameter. The diameter (d) is related to the area (A) by the formula:
A = π(d/2)^2
Rearranging the equation to solve for the diameter:
d = 2√(A/π)
Now, substitute the value of A:
d = 2√(2.545 x 10^-7 m^2 / π)
Calculating the diameter using a calculator, we find:
d ≈ 0.0160 m
Therefore, the diameter of the 1.00 m tungsten wire with a resistance of 0.22 ohms is approximately 0.0160 meters.