Final answer:
The length of a tungsten wire with a specific resistance can be found using the resistivity formula for cylindrical objects, taking into account the diameter and required resistance of the wire.
Step-by-step explanation:
To determine how long a tungsten wire should be to have a specific resistance, we must use the resistivity formula for a cylindrical object:
R = ρ × (L/A)
where R is resistance, ρ is resistivity, L is length, and A is the cross-sectional area of the wire which can be calculated using the formula A = π(d/2)^2, where d is the diameter.
For a 0.100-mm diameter tungsten filament with a desired resistance of 0.200Ω at 20.0°C, we use tungsten's resistivity at that temperature, rearrange the formula to solve for length (L), and use the given diameter to find the cross-sectional area.
Thus, the length of the tungsten filament can be calculated once the resistivity of tungsten is known.