Final answer:
The length of a tungsten wire cannot be determined solely by its diameter; additional information such as the desired resistance and the resistivity of tungsten is required for the calculation. Therefore, the correct answer is D. Insufficient information.
Step-by-step explanation:
To determine the length of tungsten wire with a given diameter necessary to achieve a specific resistance, we need to use the resistivity formula, R=ρL/A (where R is resistance, ρ is resistivity, L is the length of the wire, and A is the cross-sectional area of the wire).
The cross-sectional area A can be calculated from the diameter using the formula A=π(d/2)². Unfortunately, the given question does not contain enough information to complete the calculation, such as the resistivity of tungsten or the desired resistance. Therefore, the correct answer would be (D) Insufficient information.
If the question provided specific values for resistance and the resistivity of tungsten, you could use these along with the provided diameter to calculate the required length.
For example, if a 0.100-mm diameter tungsten filament needs to have a resistance of 0.200Ω at 20.0°C, then the length can be calculated using the appropriate formula. However, without this additional information, the question cannot be answered.