Question

In a Y- Y connected 3-phase induction motor, rotor current is zero while motor is at standstill. The winding factor of stator winding is 5 and the ratio of turns on stator and rotor is 4. If the ratio of effective turns of stator per phase and rotor per phase is 2, the winding factor of rotor winding will be ____

• A. 10

Answer 1

The correct option is A 10
$\text{Given ,motor is at standstill,}$
$\text{The respective induced emf in stator and rotor will be}$

$E_1=\sqrt{2}\pi f_1{K}_{{\omega }_1}{N}_1\varphi$

$E_2=\sqrt{2}\pi f_2{K}_{{\omega }_2}{N}_2\varphi$

$\text{After taking ratio,}$
$\frac{E_1}{E_2}=\frac{K_{{\omega }_1{N}_1}}{K_{{\omega }_2{N}_2}}=\frac{N_1^{\prime }}{N_2^{\prime }}(as{f}_1=f_2\text{at stand still}$

$\text{where,}$
$N_1^{\prime }=\text{Effective stator turns per phase}$
$N_2^{\prime }=\text{Effective rotor turns per phase}$
$N_1=\text{Stator turns per phase}$
$N_2=\text{Rotor turns per phase}$

$\text{Thus,}$ $\frac{5\times 4}{K_{{\omega }_2}}=2$

$\therefore K_{{\omega }_2}=\frac{5\times 4}{2}=10$