The parameter of an equivalent circuit of a three-phase induction motor affected by reducing the rms value of the supply voltage at the rated frequency is

Understanding Induction Motor Equivalent Circuit Parameters

An induction motor's behavior under various operating conditions can be represented using an equivalent circuit. This circuit consists of several parameters that model the physical aspects of the motor, such as winding resistances, leakage reactances, and the magnetic circuit's properties.

Analyzing Parameter Sensitivity to Voltage Reduction

The question asks which parameter in the equivalent circuit is most affected when the RMS supply voltage is reduced while maintaining the rated frequency.

**Stator Resistance ($R_s$)

The stator resistance represents the ohmic resistance of the stator winding copper. This is a physical property determined by the material and dimensions of the winding wires. It is generally considered constant and is not directly influenced by changes in the supply voltage magnitude.

Rotor Resistance ($R_r^{\prime }$)**

Similarly, the rotor resistance, referred to the stator ($R_r^{\prime }$), represents the resistance of the rotor bars and end rings. Like stator resistance, it's a physical property dependent on the rotor's construction and is typically assumed to be constant, irrespective of the supply voltage.

**Rotor Leakage Reactance ($X_r^{\prime }$)**

Leakage reactance, both for the stator ($X_s$) and the rotor ($X_r^{\prime }$), is related to the magnetic flux that does not link both stator and rotor windings. These reactances depend primarily on the motor's geometry and the frequency of the supply. While extreme voltage changes might slightly alter flux distribution, leakage reactance is not considered the parameter most directly affected by voltage reduction compared to others.

**Magnetizing Reactance ($X_m$)**

Magnetizing reactance ($X_m$) is associated with the magnetizing branch of the equivalent circuit, which represents the flow of flux in the motor's core. This flux is essential for the motor's operation. According to Faraday's Law, the induced voltage (and hence the main flux) is related to the frequency and applied voltage. Specifically, the main flux ($\Phi$) is approximately proportional to the ratio of voltage to frequency ($\frac{V}{f}$).

When the RMS supply voltage ($V$) is reduced while the frequency ($f$) remains constant, the main magnetic flux ($\Phi$) in the motor core decreases. The magnetizing reactance ($X_m$) is inversely related to the magnetizing inductance ($L_m$), i.e., $X_m=2\pi f{L}_m$. The inductance $L_m$ is dependent on the magnetic properties of the core material. Changes in flux level can alter the magnetic state of the core, particularly concerning saturation. As voltage decreases, the flux decreases, potentially altering the effective inductance and thus the magnetizing reactance ($X_m$). This makes $X_m$ sensitive to voltage variations.

Conclusion

Based on the analysis, the magnetizing reactance ($X_m$) is the parameter most significantly affected by a reduction in the RMS supply voltage because it directly relates to the main magnetic flux established in the motor core, which is dependent on the applied voltage.

Final Answer Selection

Therefore, the parameter most affected by reducing the RMS value of the supply voltage at the rated frequency is the magnetizing reactance.