EECS 100Spring Semester 1998Practice Final Examination3 Hours, Closed Book. Two: 812"ý 11" Sheets of Notes Allowed.May 2, 20031. (30 minutes) Refer to the circuit shown as Figure 1.(a) Write expressions for Kirchoô's Current Law at nodes X and Y.(b) Make Thevenin Equivalents for the elements inside the dashedboxes A and B.(c) Solve for voltages Vxand Vy.(d) Find the power dissipated in the network as drawn in Fig. 1.12. (30 Minutes) The circuit shown in Figure 2 is a parallel resonant LRCcircuit with a resonant frequency f0of 1.0 MHz.(a) Find the values of the components L and C,inéH and éF.(b) Find the voltage appearing across the components at resonance.(c) Find the quality factor Q.(d) Find the frequencies at which the voltage across the componentswould be -3.0 dB from the voltage at resonance.3. (30 minutes) In the circuit shown as Fig. 3, all four devices are n-channel MOSFETs with a value of k which is very large. Logical \1" is4 ! 12 volts, and the threshold voltage of the MOSFET transistors is2.0 V. Points A and B are considered inputs, and X and Y are outputs.(a) Find the relation between X and Y when A and B are at logic\0".(b) Find the logic values of X and Y when A =0,B =1.(c) Suppose that B = 0 continuously, but A brieòy goes to logic \1", and then returns to zero. what would X and Y be then ?(d) Name the specióc type of logic block that this circuit represents.24. (30 minutes) A load manager for PG& E determines that his sector,which includes Tracy and Manteca, is drawing a total of 580 mega-voltamperes (MVA), with an overall phase angle of óve degrees, lagging.However, a commercial break is coming up on \The Simpsons", whichcauses customers to turn up their air conditioners a notch, meaning anadditional load of 70 MVA at thirty-óve degrees, lagging.(a) Find the total load after the TV commercial: active, reactive, andapparent power.(b) Find the total current in each phase, if the line voltage (volt-age between the phases) is 380 kilovolt RMS, and there are threephases.(c) If the load manager were to switch in a synchronous capacitor toprovide a minimum load for his sector, what would the equivalentcapacitance from each phase to ground be?(d) What would the adjusted power be after this correction?5. (30 Minutes) An induction motor delivers 25 hp and runs with a realeñciency (mechanical power out / active power in) of ninety-four per-cent. Speed is 1746 rpm. Line voltage is 480 VRMS 3á and the phaseangle is ten degrees lagging. The three windings in the motor are delta-connected.(a) What is the slip s ?(b) Find the phasor current Imin each phase of the ac line. Expressin form I6í.(c) Find the current in each of the delta-connected phases(d) Find the total reactance X0.(e) Find Rstator.(f) Find the reòected rotor resistance at 100 % slip, R00.36. (30 Minutes) A synchronous machine is used to generate 60 Hz electricalenergy into a resistive load. The machine operates at 3600rpm. Theoverall electrical demand is 800 megawatts at zero phase. The òuxproduct in each phase provided by the rotor Ná0is 10:0 Weber andthe phases are wye-connected. The power angle ñ is 30 degrees.(a) Find the rms line voltage ( the voltage between the phases).(b) How many poles does this machine have?(c) What is the value of the reactance Xsin each phase ?(d) Find the excitation voltage e. Draw a phasor diagram labelingthe stator current, the stator reaction, and the excitation e, andthe output voltage (all referenced to ground) for one
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