Final answer:
To calculate various parameters of a synchronous motor, we use the given information about line voltage, frequency, pole pairs, synchronous impedance, full load current, and rotational loss. We then calculate the line current, power factor, maximum power developed, maximum power output, maximum shaft torque, and efficiency of the motor.
Step-by-step explanation:
To calculate the values, we will use the given information:
- Line voltage (V): 208 V
- Frequency (f): 50 Hz
- Pole pairs (p): 12
- Synchronous impedance (Zs): 0.75 + j7.5 Ω/phase
- Full load current (I): 25 A
- Rotational loss: 1.2 kW
a) To calculate the line current (IL), we can use Ohm's Law for a Y-connected system: IL = √3 × I = √3 × 25 = 43.3 A
b) To calculate the power factor (PF), we can use the formula: PF = cos(θ) = Re(Zs) / |Zs| = 0.75 / 7.6 = 0.0987
c) To calculate the maximum power developed, we can use the formula: Pmax = 3 × V × IL × PF = 3 × 208 × 43.3 × 0.0987 = 2730.4 W
d) To calculate the maximum power output, we subtract the rotational loss: Poutput = Pmax - Rotational loss = 2730.4 - 1200 = 1530.4 W
e) To calculate the maximum shaft torque, we can use the formula: Tmax = Poutput / (2π × f) = 1530.4 / (2π × 50) = 4.89 Nm
f) To calculate the efficiency, we can use the formula: Efficiency = Poutput / (Pinput + Rotational loss) = 1530.4 / (2730.4 + 1200) = 0.2977 or 29.77%