In case of a Squirrel-cage induction motor using three-phase bridge inverter, which one of the following statements is correct for speed control?  

Solution:-
In an induction motor, approximate torque eqⁿ considering stator impedance is negligible is given below:-

\(\rm T=\frac{3}{\omega_s}\cdot\frac{v^2}{\left(\frac{r_2}{s}\right)^2+X_2^2}\cdot\frac{r_2}{s}\)

At starting, s = 1

∴ \(\rm T_{st}=\frac{3}{\omega_s}\cdot\frac{v^2}{r_2^2+x_2^2}\cdot r_2\)

∴ \(\rm r_2^2<<x_2^2\)

∴ \(\rm T_{st}=\frac{3}{\omega_s}\cdot\frac{v^2}{x_2^2}\cdot r_2\)

\(\rm T_{st}=\frac{3}{2\pi f}\cdot\frac{v^2}{x_2^2}\cdot r_2\)

∴ x ∝ f

∴ \(\rm T_{st}=\frac{3}{2\pi}\cdot\frac{v^2}{x_2^2}\cdot r_2\)

given voltage is constant

∴ \(\rm T_{st}\propto\frac{1}{f^3}\)

Hence, if frequency increases, then starting torque decreases and if frequency decreases, then starting torque increases.

Hence, both option 1 and option 3 are correct.

The correct answer is option "4"