Final answer:
To find the diameter of the tungsten filament, we can use the formula for resistance (R = (ρL)/A). Given the resistance, resistivity, and length, we can solve for the cross-sectional area (A). Then, using the formula for the cross-sectional area of a circle (A = πr^2), we can determine the radius (r) of the filament. Finally, we multiply the radius by 2 to find the diameter.
Step-by-step explanation:
To find the diameter of the tungsten filament, we can use the formula for resistance:
R = (ρL)/A
Where R is the resistance, ρ is the resistivity, L is the length of the filament, and A is the cross-sectional area.
Given that the resistance is 0.2002 ohms, the resistivity is 9.0 x 10^-7 ohm*m, and the length is 7.0 cm, we can rearrange the formula to solve for the cross-sectional area:
A = (ρL)/R
Substituting the given values, we have:
A = (9.0 x 10^-7 ohm*m) * (7.0 x 10^-2 m) / 0.2002 ohms
Simplifying the expression, we find:
A ≈ 2.48 x 10^-5 m^2
To find the diameter of the filament, we can use the formula for the cross-sectional area of a circle:
A = πr^2
Where A is the cross-sectional area and r is the radius (half the diameter) of the filament.
Substituting the known value of the area, we can rearrange the formula to solve for the radius:
r = sqrt(A / π)
Substituting the given value of the area, we have:
r = sqrt(2.48 x 10^-5 m^2 / π)
Simplifying the expression, we find:
r ≈ 0.00355 m
Finally, to find the diameter, we multiply the radius by 2:
Diameter ≈ 2 * r ≈ 2 * 0.00355 m ≈ 0.0071 m ≈ 7.1 cm