Calculate the total input to the rotor and the rotor copper loss for an induction motor given its parameters.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for the induction motor.

Given:

Calculate the synchronous speed ( $N_s$ ).
$N_s = \frac{120f}{P}$ $N_s = \frac{120 \times 50 \text{ Hz}}{4 \text{ poles}}$ $N_s = 1500 \text{ rev/min}$
Convert the synchronous speed to angular synchronous speed ( $\omega_s$ ).
$\omega_s = \frac{2\pi N_s}{60}$ $\omega_s = \frac{2\pi \times 1500 \text{ rev/min}}{60 \text{ s/min}}$ $\omega_s = 50\pi \text{ rad/s} \approx 157.08 \text{ rad/s}$

5.4.1 The total input (in kilowatts) to the rotor.
The total input to the rotor is also known as the air gap power ( $P_{ag}$ ).
$P_{ag} = T \omega_s$ $P_{ag} = 80 \text{ Nm} \times 50\pi \text{ rad/s}$ $P_{ag} = 4000\pi \text{ W}$ $P_{ag} \approx 12566.37 \text{ W}$
Convert to kilowatts:
$P_{ag} = \frac{12566.37}{1000} \text{ kW}$ $P_{ag} = \boxed{\text{12.57 kW}}$

5.4.2 The rotor copper loss in watts.
Calculate the slip ( $s$ ).
$s = \frac{N_s - N_r}{N_s}$ $s = \frac{1500 \text{ rev/min} - 1440 \text{ rev/min}}{1500 \text{ rev/min}}$ $s = \frac{60}{1500}$ $s = 0.04$
Calculate the rotor copper loss ( $P_{cu\_rotor}$ ).
$P_{cu\_rotor} = s \times P_{ag}$ $P_{cu\_rotor} = 0.04 \times 12566.37 \text{ W}$ $P_{cu\_rotor} = \boxed{\text{502.65 W}}$

Answer