Let the Short Run Aggregate Production Function be given by:X = F(K:N) = AK°N'-°, where A = 10$, a = ½, and K = constant = 7$5. Arrive at the total output when K is constant at 7$; do so for N, = 1N, N, = 2N, ..., Ng = 9N.a. Put in a table that includes total product and the marginal product of labor.b. Draw the total product of labor in a graph and identify at least two marginal products. What do you seehappen to output when labor input increases?

3.8. Three identical 9-MVA, 7.2-kV/4.16-kV, single-phase transformers are connected in wye on the high-voltage side and delta on the low voltage side. The equivalent series impedance of each transformer referred to the high-voltage side is 0.12+ j0.82 O per phase. The transformer supplies a balanced three-phase load of 18 MVA, 0.8 power factor lagging at 4.16 kV. Determine the line-to-line voltage at the high-voltage terminals of the transformer.

3.15. The three-phase power and line-line ratings of the electric power system shown in Figure 3.34 are given below. (a) Draw an impedance diagram showing all impedances in per-unit on a 100-MVA base. Choose 20 kV as the voltage base for generator. (b) The motor is drawing 45 MVA, 0.80 power factor lagging at a line-to-line terminal voltage of 18 kV. Determine the terminal voltage and the internal emf of the generator in per-unit and in kV.

A 230-V shunt motor, having an armature resistance of 0.05 2 and a field resistance of 75 , draws Aline current of 7 A while running light at 1120 rpm. The line current at a given load is 46 A. Determine(a) the motor speed at the given load, (b) motor efficiency, and (c) total core and mechanical losses.Ans. (a) 1110.5 rpm; (b) 83.9%; (c) 903.9 W

1. A star connected 15 hp, 400 V, six pole, 50 Hz wound rotor induction motor has a stator to rotor turns ratio of 5 : 3. The rotor winding is also star connected. If the motor is connected to the rated voltage source at 50 Hz and the motor runs at 960 rpm.Determine: a) The operating slip of the motor. b) The induced voltage in the rotor winding per phase and its frequency. c) Speed (rpm) of the rotor field BR w.r.t the (i) rotor, (ii) stator. If the stator winding is short-circuited and the power supply is connected to the rotor winding while the motor runs at 970 rpm, determine: d) The direction of rotation of the motor w.r.t to the rotating magnetic field. e) Induced voltage in the stator winding per phase and its frequency.

1 Mark x 5 = 5 Marks] A 50-kW, 460-V, 50-Hz, two-pole, three phase induction motor has a slip of 5 % when operating a full-load conditions. At full-load conditions, the friction and windage losses are 700 W, and the core losses are 600 W. Find the following values for full-load conditions: a) The shaft speed (nm). b) The output power (Pout). c) The load torque (tload). d) The induced torque (Tind). e) The rotor frequency (f;).

3.17. The one-line diagram of a three-phase power system is as shown in Figure3.36. The transformer reactance is 20 percent on a base of 100 MVA, 23/115kV and the line impedance is Z = j66.125N. The load at bus 2 is Sz = 184.8MW +j6.6 Mvar, and at bus 3 is S3 = 0 MW +j20 Mvar. It is required tohold the voltage at bus 3 at 115/0° kV. Working in per-unit, determine thevoltage at buses 2 and 1.

2. (10pt) A conductor made of nickel ( p. = 6.8×10 N-m) has a rectangular cross section 5 x 2mm and is 5 m long. Determine the total resistance of this conductor. Calculate the diameter of a5m long copper wire that has a circular cross section that yields the same total resistance. For theсopper,the resistivity Pe is 1.7 × 10-8 N-m.

A 2400V/400V single phase transformer takes a no-load current of 0.5A and the core loss is 400W. The flux is 1Wb. i Determine the value of the magnetising and core loss components of the no-load current. ii Sketch the no load phasor diagram for the transformer and include the following phasors:

Sketch the process (cross section and top view of every photolithography mask) for making a bulk micromachined Si02cantilever on a (100) Si substrate. (Hint – use KOH in your process) Be sure to indicate how you would protect the backside of the wafer from being etched in EDP. (30 points)

5. Consider the railgun system below. The bar has width xo, mass mo, and current lo provided by the DC current source, and starts at rest at y = 0. There is an external magnetic field Bo, and the rails are of length yo measured from the bar's initial position. Assume no gravity (z-dir anyway) or air resistance effects. Think of the xy-plane as a flat tabletop. (a) Draw the position and velocity of the bar over time, including what you expect happens just outside the rail gun. Assume no other forces, such as gravity and air resistance. Provide the expression for y. (One plot, one expression) (b) Suppose someone messes up and attaches an AC current source instead of a DC current source.What happens to the bar? (Short answer)