A 400 V, 3 phase mesh connected synchronous motor runs at rated voltage and with excitationemf of 510 V. Its synchronous impedance per phase is 0.5+j0.4 Ω and friction, windage andiron losses are 900 W. Calculate the shaft power (or net) output, line current, pf and efficiencyfor (a) maximum power output and (b) maximum power input

This problem involves a bit of complex number manipulation and understanding of electrical power systems. Here's how you can solve it:

(a) Maximum Power Output

1. First, calculate the synchronous reactance (Zs) which is given as 0.5 + j0.4 ohm. The magnitude of Zs can be calculated using Pythagoras theorem, which gives √[(0.5)^2 + (0.4)^2] = 0.64 ohm.

2. The power angle (δ) at maximum power output is 90 degrees.

3. The power output (P) can be calculated using the formula P = V^2/Zs * sin(δ). Substituting the given values, we get P = (400)^2 / 0.64 * sin(90) = 250,000 W or 250 kW.

4. The line current (I) can be calculated using the formula I = V/Zs. Substituting the given values, we get I = 400 / 0.64 = 625 A.

5. The power factor (pf) at maximum power output is zero because the power angle is 90 degrees.

6. The efficiency (η) can be calculated using the formula η = Pout / (Pout + losses). Substituting the given values, we get η = 250,000 / (250,000 + 900) = 99.64%.

(b) Maximum Power Input

1. The power angle (δ) at maximum power input is 0 degrees.

2. The power input (P) can be calculated using the formula P = V^2/Zs * sin(δ). Substituting the given values, we get P = (400)^2 / 0.64 * sin(0) = 0 W.

3. The line current (I) can be calculated using the formula I = V/Zs. Substituting the given values, we get I = 400 / 0.64 = 625 A.

4. The power factor (pf) at maximum power input is one because the power angle is 0 degrees.

5. The efficiency (η) can be calculated using the formula η = Pout / (Pout + losses). Since the power output is zero, the efficiency is also zero.

Please note that the above calculations assume that the motor is operating in the linear region of its performance curve. If the motor is operating in the saturation region, the calculations would be more complex.