Correct Answer - Option 2 : inversely proportional to air gap length

**Air gap length in a synchronous machine:**

- The length of the air gap is a very important parameter because it greatly affects the performance of the machine.
- The air gap in a synchronous machine affects the value of short circuit ratio (SCR) which can affect many other parameters.

**Magnetizing reactance:**

The magnitude of magnetizing reactance is influenced by air-gap length as under:

**Magnetizing reactance (X**_{ar}) = ω L_{ar}

Where,

ω = angular frequency

L_{ar} = magnetizing inductance

And**, L**_{ar} ∝ (N_{ph}^{2}) / (air-gap reluctance)

- So, a synchronous machine with a large air-gap has a low value of L
_{ar} and X_{ar}.
- In other words,
**the magnitude of magnetizing reactance (X**_{ar}) is inversely proportional to air-gap length.
- The armature leakage reactance X
_{al} is usually treated as constant.
- As X
_{ar} plays a dominant role on synchronous reactance (X_{s}). So it can be stated that X_{s} is inversely proportional to air-gap length.

__Advantages of larger air-gap:__

- As reactance is decreasing with the larger air-gap the
**stability limit will be increased.**
- The smaller value of inherent regulation.
**Better cooling and noise reduction.**
- The value of
** synchronizing power will be higher.**
- Less value of unbalanced magnetic pull.

__Disadvantages of larger air-gap:__

- Larger diameter and hence larger size.
- More amount of field mmf is required.
- Increase in overall cost.