Question

A three-phase, four-pole, 30hp,220 V (line-line), 60 Hz, wye-connected induction motor draws a current of 77 A from the line source at a PF of 0.88 lagging. The slip is s=0.05. At this operating point, we have

Pₛₗ = 1033 W and P = 485 W

Find the power across air gap Pₐ

Answer 1

The power across the air gap (Pa) of the induction motor is found by adding the rotor slip loss (Psl) and the mechanical power output (P), which gives Pa = 1033 W + 485 W = 1518 W.

Step-by-step explanation:

To find the power across the air gap (Pa) of an induction motor, you need to consider the power that is provided to the rotor across the air gap. This includes the power that is converted into mechanical power and the power that is lost due to the rotor slip (Psl). The air gap power can be calculated using the following relationship:

Pa = Psl + Pm

where Pm is the mechanical power output and Psl is the rotor stator power loss due to slip. Given that Psl = 1033 W and the mechanical power loss P is 485 W, we can calculate the air gap power:

Pa = 1033 W + 485 W = 1518 W

Therefore, the power across the air gap of the induction motor is 1518 W.