EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following timedomain circuit to the RMS Phasor Domain.


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1 Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts] Convert the following timedomain circuit to the RMS Phasor Domain. v( = 10sin(500 Volts i( = 2cos(500t + 45 ) Amps i ( v ( 2) [6 pts] For a frequency of 1000 rad/sec, answer the following questions a) The impedance of a resistor is = j0ω. What is the resistance value of the resistor? Z R b) The impedance of an inductor is Z L = 0 + j250ω. What is the inductance value ( in mh) of the inductor? c) The impedance of a capacitor is Z L = 0 j50ω. What is the capacitance value ( in uf) of the capacitor? Page 1 of 8
2 3) [2 pts] If i ( = 2sin(1000t + 60 ) Amps, determine the RMS phasor( eff ) representations of i(. I 4) [4 pts] if ω = 500 rad/sec and V eff = VRMS and Ieff = 2 60 ARMS, use the concept of the inverse phasor transform to determine the timedomain values v ( and i(. 5) [6 pts] Consider the circuit below with an unknown circuit element. i ( + v ( _ Unknown Element v( = 10 2 cos(100t 15 ) Volts i( = 2cos(100t + 30 ) Amps a) What is the real power P associated with the unknown element? b) What is the reactive power Q associated with the unknown element? c) What is the power factor angle and the power factor associated with the unknown element? Page 2 of 8
3 6) [8 pts] A load absorbs P = KW of real power with an apparent power ( S ) of 100 KVA. a) What are the two possible values for the power factor angle? b) Determine a value for the magnitude of the reactive power Q Z ab 7) [8 pts] Consider the circuit shown below : Z R1 Z C1 Z L1 Z C2 Z R2 ω = 250 rad / sec Z R1 = 20Ω Z R2 = 80Ω Z L1 = j83.333ω ZC1 = j10ω Z = j60ω a) Determine Z ab  the impedance observed looking into terminals a and b. C2 b) What value for C 1(in uf) will result in Z ab being entirely resistive ( Z ab = R + j0 ). (Hint: Use the Cartesian form of Z ab in part a and write it as Z ab = ZC1 + Z rest ) Page 3 of 8
4 8) [20 pts] For the circuit shown below: V I Z Load V = VRMS = j25 VRMS I = ARMS = j A ω = 1000 rad / sec RMS a) Determine the value of the load impedance Z Load. b) What is the power factor of the load? c) Is the load impedance inductive or capacitive? How do you know? d) if Z Load consists of two elements in series (a resistor in series with an inductor or a resistor in series with a capacitor), a. What is the value of the resistor? b. What is the value of the inductor (in mh) or the capacitor (in µ F )?. Page 4 of 8
5 9) [20 pts] Consider the following RMS phasor circuit: j 5Ω j 10Ω I X V 1 V g 5 I X I 1 I 2 V = 50 0 V g RMS a) Determine values for I1, I2, I X and V1. (Hint: mesh analysis is better than nodal) b) Determine the complex power associated with each source ( SVg and S5I X ). Indicate if the power calculated is being absorbed or delivered. (Note the direction of I 1  i.e what is the P.S.C) Page 5 of 8
6 10) [20 pts] Consider the following RMS phasor domain circuit:: I T I 2 I Vs = VRMS = 0 j20vrms 1 30 Ω V s R 1 40 Ω R 2 C j 30Ω L j 40Ω a) Determine I 1, I 2 and I T. b) Determine the complex power associated with all impedances and the source ( SR1, SR2, SL, SC, and SV ). Indicate the power as being absorbed or delivered. S c) Verify that the complex power supplied by the sources equals the sum of the complex powers absorbed by the impedances. More Space on Next Page Page 6 of 8
7 10 continued) Page 7 of 8
8 Extra Credit #1) [2 pts] An impedance is absorbing 900 Watts of real power and delivering 1200 VARs of reactive power. a) What is the power factor angle (θ) for the impedance? b) If V = 200 θ Volts V = V = 200 what is the magnitude of the current ( = I )? V M I M Extra Credit #2) [4 pts] Consider the circuit below. If Z eq = 6 + j8 Ohms when and Z eq = 6 j8 Ohms when ω = 50 rad / sec. Determine values for R, L and C ω = 100 rad / sec Z eq Page 8 of 8
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