Final answer:
A tungsten wire if it has a diameter of 0.183 × 10⁻³ m and a resistance of 2.29 kQ, the length of the tungsten wire is approximately 314.69 m.
Step-by-step explanation:
To determine the length of a tungsten wire with a given diameter and resistance, we can use the formula:
R = (ρ × L) / A
where
R is the resistance
ρ is the resistivity of tungsten
L is the length of the wire
A is the cross-sectional area of the wire.
We know the diameter of the wire, but we need to calculate the cross-sectional area first.
The cross-sectional area can be calculated using the formula:
A = π × r²,
where r is the radius of the wire.
Once we have the cross-sectional area, we can rearrange the first formula to solve for L:
L = (R × A) / ρ.
Substituting the given values, we find:
L = (2.29 × 10³ Ω × (π × (0.183 × 10⁻³ m / 2)²)) / ((5.6 × 10⁻⁸ Ω·m)) ≈ 314.69 m.
So therefore the length of the tungsten wire is approximately 314.69 m.