Two-phase AC servomotor characteristic: The rotor has resistance R and standstill reactance X. State the condition under which the torque–speed curve is approximately linear over a useful range.

Introduction / Context:
Servomotors used in control systems should offer a reasonably linear torque–speed characteristic around the operating region to simplify design and ensure faithful tracking. Two-phase AC servomotors are designed with intentionally high rotor resistance to achieve this property.

Given Data / Assumptions:

• Two-phase AC servomotor with rotor resistance R and standstill reactance X.
• Objective: near-linear torque versus speed (or slip) characteristic across the intended operating slip range.

Concept / Approach:
The air-gap power and electromagnetic torque depend on rotor impedance R + jX_s (seen at slip frequency). A linear torque–speed region is favored when the reactive and resistive parts are comparable—avoiding excessive current phase angles and sensitivity to slip. The design rule-of-thumb is to make rotor reactance roughly equal to rotor resistance at the significant slip frequency, i.e., X ≈ R, which straightens the curve over a practical operating range.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Common Pitfalls:

Final Answer: