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How long is a tungsten wire if it has a diameter of _____?

User MoneyBall
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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.

User Joao Cunha
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