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

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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 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 time-domain 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 time-domain 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

8) [20 pts] For the circuit shown below: V I Z Load V = 50 30 VRMS = 43.301+ j25 VRMS I = 1.414 38.13 ARMS = 1.1123 + j0.

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

10) [20 pts] Consider the following RMS phasor domain circuit:: I T I 2 I Vs = 20 90 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.

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

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?

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

11. AC Circuit Power Analysis

11. AC Circuit Power Analysis . AC Circuit Power Analysis Often an integral part of circuit analysis is the determination of either power delivered or power absorbed (or both). In this chapter First, we begin by considering instantaneous