what is the resistance of air gap in plug key in a circuit.

You will have to tell us what a "plug key" is.

Air gaps are essentially open circuits. Current can only flow if there is alternating current or the voltage is high enough to cause ionization of the air.

The resistance of the air gap in a plug key, also known as a switch, is generally considered to be infinity (∞) for practical purposes. This is because air is a poor conductor of electricity, and therefore offers a very high resistance to the flow of electric current.

To understand why air has such a high resistance, we need to look at the atomic structure of air. Air is made up of various gases, primarily nitrogen (N2) and oxygen (O2). These gases consist of molecules made up of atoms bonded together. In the case of nitrogen and oxygen, these molecules are diatomic, meaning they consist of two atoms bonded together.

When an electric current tries to pass through air, it needs to overcome the resistance offered by the air molecules. In air, the atoms and molecules are not freely moving and conducting electricity like in a metal conductor. Instead, they rely on the movement of electric charges, such as electrons, to carry the current.

However, air molecules are much larger and denser than electrons. As a result, the movement of electrons through the air encounters numerous collisions with the air molecules, effectively impeding the flow of current. These collisions cause the electrons to lose energy and momentum, increasing the resistance.

Since air has such a high resistance, it is commonly used as an insulator to prevent the flow of current. When a plug key or switch is opened, the circuit is broken, creating an air gap where the resistance is essentially infinite. This ensures that current cannot flow through the gap, effectively interrupting the circuit.

It is important to note that in very high voltage scenarios, such as in power transmission lines, air can break down and ionize due to the intense electric field. This results in the formation of a conductive path through the air, known as a spark or arc, which significantly reduces the resistance. However, in normal household circuits and low voltage applications, the resistance of the air gap remains extremely high.