Question

A 3- phase, $\Delta$-connected, 4 pole, 50 Hz induction motor has a stator resistance of $0.5\Omega$ per phase at the operating temperature. For a line current of 12 A, the total stator input is 3600 W. Neglecting stator core loss, the value of torque developed will be_________ N-m. (Answer upto 2 decimal places)

• A. 22.46

Answer 1

The correct option is A 22.46
$\text{Given, f = 50 Hz,}$

$\text{P = 4}$

$\text{Power input,}{P}_{in}=3600W$

$\text{Phase current,}{i}_p=\frac{I_L}{\sqrt{3}}=\frac{12}{\sqrt{3}}A$

$\text{Total stator loss}=3i_p^2{r}_s$

$=3\times {\left(\frac{12}{\sqrt{3}}\right)}^2\times 0.5$

$=3\times \frac{12\times 12}{3}\times 0.5=72W$

$\text{Power across air gap,}$

$P_G=P_m-\text{stator loss}$

$=3600-72=3528W$

$\text{Synchronous speed,}$

$N_s=\frac{120f}{P}=\frac{120\times 50}{4}=1500rpm$

${\omega }_s=\frac{2\pi \times 1500}{60}rad/sec$

$\text{Torque developed,}$
$T_c=\frac{P_g}{{\omega }_s}=\frac{3528\times 60}{2\pi \times 1500}=22.46N-m$