Question

The two cages of a 3-phase, 50 Hz, 4-pole delta-connected induction motor have respective standstill leakage impedances of $(2+j8)$ and $(9+j2)\Omega /\text{phase}$. The gross torque developed at 1450 rpm when the effective rotor voltage is 400 V/phase is_________ N-m.

• A. 61.4

Answer 1

The correct option is A 61.4
$\text{Synchronous speed,}$ ${\omega }_s=\frac{1500\times 2\pi }{60}=157rad/s$

$\text{Slip,}$ $s=\frac{1500-1450}{1500}=\frac{1}{30}$

$\text{Torque,}$
$T_1=\frac{3}{157}\frac{(400{)}^2\times (2\times 30)}{\left[\right(2\times 30{)}^2+\left(8{)}^2\right]}$
$=50.1N-m$

$\text{Torque,}$
$T_2=\frac{3}{157}\frac{({400}^2\times 9\times 30)}{(9\times 30{)}^2+(2{)}^2}$

$T_{\text{(}total)}=T_1+T_2=50.1+11.3=61.4N-m$