Calculating Full-Load Current Rating of a Synchronous Motor

What is the full-load current rating of a 460 V, 30-HP, 3 phase synchronous motor with a 90% power factor?

1. 32.0 amps
2. 35.2 amps
3. 40.0 amps
4. 44.0 amps

Answer:

The full-load current rating of a 460V, 30-HP, 3 phase synchronous motor with a 90% power factor, according to the P=IV formula, should be approximately 54.0 Amps.

To solve this, we need to understand the relationship between power, voltage, and current in electrical circuits. In general, the power consumed by an electric motor is given by the formula P = IV, where P is power, I is current, and V is voltage.

To find the full-load current rating of the motor, we rearrange the formula to solve for I: I = P/V. We also need to take into account the power factor, which is given as 90%, or 0.9. The power of the motor is the mechanical horsepower converted to watts, because the unit of power in the standard international system is watts (W). 1 horsepower (HP) is approximately 745.7 Watts.

Hence, for a 30 HP motor, the power is 30 x 745.7 = 22,371 W. Substituting these values into the formula gives: I = (22,371W / 460V) / 0.9 = 54.0A. None of the given options is correct.