Which of the following coil will have large resonant frequency?

Answer: Option D

Resonant Frequency: The resonant frequency of a coil in an AC circuit is determined by both its inductance and capacitance. It is given by the formula:

$$f_r=\frac{1}{2\pi \sqrt{LC}}$$

where $$f_r$$ is the resonant frequency, L is the inductance, and C is the capacitance.

Effect of Capacitance: From the formula, it is clear that the resonant frequency is inversely proportional to the square root of the capacitance. Therefore, a lower capacitance results in a higher resonant frequency.

Options Analysis:

Option A: A coil with large resistance - The resistance of the coil does not directly affect the resonant frequency.

Option B: A coil with low resistance - Similar to option A, resistance does not directly impact the resonant frequency.

Option C: A coil with large distributed capacitance - Larger capacitance results in a lower resonant frequency.

Option D: A coil with low distributed capacitance - Lower capacitance results in a higher resonant frequency.

Therefore, the coil with low distributed capacitance will have a large resonant frequency.