# GATE Papers >> EEE >> 2019 >> Question No 20

Question No. 20

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

##### Answer : (C) magnetizing reactance

Solution of Question No 20 of GATE 2019 EEE Paper

(The faculty has only thought that by changing voltage the current drawn will change and since magnetizing curve is non linear the ratio of flux linkage and current will also change and hence magnetizing reactance will changes . But if we talk about practical motor with ELECTRICAL ENGINEERING ?EE-2019? © All rights reserved by Thinkcell Learning Solutions Pvt. Ltd. No part of this booklet may be reproduced or utilized in any form without the written permission. change in voltage the current drawn changes.this will change leakage reactance ,temperature and operating point on magnetization curve .Due to all these changes all options are correct as every parameter should change.)

Variations in XI due to supply voltage variation

Rotor leakage reactance, (top curves), and rotor resistance, (bottom curves), variations with supply voltage and low slips at a motor temperature of 40°C – single –cage machine.

$\downarrow\mathrm I=\frac{\mathrm V\;\downarrow}{\mathrm z}$

When voltage alone reduces, the current drawn by Induction Motor reduces, Torque reduces

$\downarrow\boxed{{\mathrm T}_{\mathrm{cm}}\propto\mathrm V^2}\downarrow$

As the torque reduces, slip increases to get steady state operation.

$\uparrow{\mathrm T}_{\mathrm{cm}}\propto\frac{\uparrow\mathrm{sV}^2}{{\mathrm R}_2}$

The change in slip causes change in reactance of rotor

$\therefore{\mathrm X}_{2\mathrm r}={\mathrm{sX}}_2$