# In a synchronous machine, as the machine size decreases:

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In a synchronous machine, as the machine size decreases:
1. p.u. armature resistance increases and p.u. synchronous reactance decreases
2. p.u. armature resistance decreases and p.u. synchronous reactance increases
3. p.u. armature resistance and p.u. synchronous reactance both decreases
4. p.u. armature resistance and p.u. synchronous reactance both increase

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Correct Answer - Option 1 : p.u. armature resistance increases and p.u. synchronous reactance decreases

Concept:

The synchronous machine has one armature and one rotor. Both are wire wound so both have their own inductive reactance and resistance.

We can define synchronous impedance as Zs = Xa + Xr + Ra

X= Armature reactance, Xr = Rotor reactance

We are not calculated Xr and Ra as its very low in value and effect is also less.

Therefore, we can say that the major component in the synchronous impedance of a synchronous machine is armature reaction reactance.

Explanation:

Flux density is defined as flux per unit area. i.e. B$\frac{\phi }{A}$

Where ϕ = flux per pole

A = area of core

Size of the machine is directly proportional to area

i.e. size of machine ∝ area of machine ∝ $\frac{1}{{{B_m}}}$

Hence with the increase in magnetic flux density, the size of the machine decreases.

As the machine size decreases, p.u. armature resistance increases and p.u. synchronous reactance decreases.