Question

A 2-pole, 60-Hz, Y-connected synchronous generator is connected to a 3-phase, Y-connected load. The mechanical torque applied to the generator shaft is 1,000 N·m. The internal losses are 50 kW, and the load operates at 480 V (line-to-line). The excitation (i.e., field current) is adjusted such that the output power factor is 0.8 lagging. The magnitude of the generator's line current (amperes) is most nearly

a. 320
b. 490
c. 640
d. 850

Answer 1

The magnitude of the generator's line current is approximately 67 A.

Step-by-step explanation:

To find the line current of the generator, we first need to calculate the apparent power of the generator using the formula:

Apparent power = (Output power) / (Power factor)

Given that the mechanical torque is 1,000 N·m, the output power can be calculated as:

Output power = (Torque x Speed) / (2π)

Substituting the values, we get: Output power = (1000 N·m x 60 Hz) / (2π) = 9,548.73 W.

Since the power factor is 0.8 lagging, the apparent power can be calculated as:

Apparent power = 9,548.73 W / 0.8 = 11,935.91 VA.

The line current can be calculated using the formula:

Line current = Apparent power / (√3 x Line-to-line voltage)

Substituting the values, we get:

Line current = 11,935.91 VA / (√3 x 480 V) ≈ 66.98 A.

Therefore, the magnitude of the generator's line current is most nearly 67 A (rounded to the nearest whole number).