Final answer:
The length of the tungsten wire with a diameter of 0.119×10⁻³ m and a resistance of 2530 Ω, using a resistivity of 5.62×10⁻⁸ Ω⋅m, is calculated to be 5.03×10⁴ m.
Step-by-step explanation:
To calculate the length of a tungsten wire with a given diameter and resistance, we can use the formula for resistance of a uniform cylindrical conductor:
R = ρ L/ A
where:
R is the resistance,
ρ (rho) is the resistivity of the material,
L is the length of the conductor, and
A is the cross-sectional area of the conductor.
We are given:
R = 2530 Ω (ohms),
ρ (resistivity of tungsten) = 5.62×10⁻⁸ Ω⋅m,
Diameter (d) = 0.119×10⁻³ m.
The cross-sectional area A can be calculated using the area formula for a circle, A = π d²/4.
By plugging in the values and solving for L, we get:
A = π(0.119×10⁻³ m / 2)² = π(0.119×10⁻³ m / 2)² = 1.11×10⁻⁸ m²
R = 2530 Ω
ρ = 5.62×10⁻⁸ Ω⋅m
Solving the formula for L, we get:
L = {R ⋅ A}/{ρ} = {2530 Ω ⋅ 1.11×10⁻⁸ m²}/{5.62×10⁻⁸ Ω⋅m} = 5.03×10⁴ m
So, the length of the tungsten wire is 5.03×10⁴ m.