Which of the following coil will have large resonant frequency?

A coil with large resistance
A coil with low resistance
A coil with large distributed capacitance
A coil with low distributed capacitance

The correct answer is: A coil with low distributed capacitance.

A coil’s resonant frequency is the frequency at which the inductive and capacitive reactances cancel each other out, resulting in a purely resistive load. The resonant frequency of a coil is given by the formula:

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

where $L$ is the inductance of the coil and $C$ is the distributed capacitance of the coil.

As you can see from the formula, the resonant frequency of a coil is inversely proportional to the square root of the distributed capacitance. This means that a coil with a low distributed capacitance will have a higher resonant frequency than a coil with a high distributed capacitance.

The distributed capacitance of a coil is caused by the physical construction of the coil. The windings of the coil act as capacitors, and the insulation between the windings also acts as a capacitor. The distributed capacitance of a coil can be reduced by using a smaller coil, using a higher-grade insulation, or using a different winding technique.

The resonant frequency of a coil is an important factor in many applications. For example, in radio receivers, the resonant frequency of the coil is used to select the desired station. In power supplies, the resonant frequency of the coil is used to filter out noise.