PROBLEM 1: Op-Amps Figure 1 shows a simplified model of an operational amplifier (enclosed in a dashed box), shortened in EEE parlance as op-amp

PROBLEM 1: Op-Amps

Figure 1 shows a simplified model of an operational amplifier (enclosed in a dashed box), shortened in EEE parlance as op-amp. It is so-called because with the proper connections, it can be used to produce an output based on the application of various operations to the input (e.g. Figure 1: Amp Circuit differential, integral, arithmetic, and so on).

For the connection shown in the figure:

1. Find the Thevenin equivalent seen by the load resistance. Note that its voltage will be in terms of V_IN.

2. Find the maximum allowed for V_IN to limit the dissipation of a resistance R_L = 1kW to 3 Watts.

V_x⁺_-             0.5MW           1.3 V_x    .10⁴                 75W

V_IN                  3 kW          2kW               R_L⁺_-

    Figure 1: Op-Amp Circuit

PART 2: Power Flows

Within AC power systems, electricity is typically supplied by three-phase synchronous generators driven by turbines - steam, hydro, or otherwise. Due to mechanical limitations, it is extremely important that no generator experiences backflow of real power; if this happens, the generator will act as a motor and cause costly mechanical damage. In addition, wires have finite limits on the current they can carry without suffering considerable degradation; this is called ampacity.

For the system whose single-phase schematic is shown in Figure 2, determine which generators/sources, if any, are actually consuming real power, or whose power factor is less than 0.01, lead or lag. [20 pts]

NOTES/HINTS:

1. The thick rectangles (termed “bus bars”) may be considered as simple junctions.

2. It is suggested to use nodal analysis for this circuit.

PART 3: Long-distance Audio

A500-Hz sine-wave audio signal is to be broadcast from a SOW 8N speaker located 500 meters away from the amplifier. The audio cable used has a DC resistance of 0.05W/m and an inductance of 1mH/m. Find the apparent power required of the amplifier for (1} direct connection [5 pts]; and (2} connection with 1:4 ideal transformers placed at each end of the run. [5 pts].

PART 4: Line-drop Compensation

A Y-connected three-phase load located 15km away from the mainline consumes 500kVA at 0.8 lagging when supplied with 13.8kV. The wires from the mainline to the load have DC resistance 1.50W/km and inductance 60mH/km. If the mainline voltage is regulated at 14kV, find the voltage at the load prior to [10 pts], and subsequent to [10 pts], the addition of a D-connected bank of 10mF capacitors placed at the load end.