EE 210 201213FA Final Exam Solution

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EE 210 FALL 2012

Final Exam Time: December 17, 2012 6:50 – 8:40 pm

Exam format: A Student Name: PSU ID #: Section #: 01 9:05A – 9:55A (Mitchell) - Lab T 11:15A – 2:15P (Agrawal)

02 9:05A – 9:55A (Mitchell) - Lab T 2:30P – 5:30P (Laftchiev)

03 9:05A – 9:55A (Mitchell) - Lab W 2:30P – 5:30P (Laftchiev)

04 12:20P – 1:10P (Salvia) - Lab W 6:30P – 9:30P (Price)

05 12:20P – 1:10P (Salvia) - Lab R 11:15A – 2:15P (Kotobi)

06 12:20P – 1:10P (Salvia) - Lab R 2:30P – 5:30P (Price)

07 12:20P – 1:10P (Salvia) - Lab R 8:00A – 11:00A (Agrawal)

08 9:05A – 9:55A (Mitchell) - Lab W 11:15A – 2:15P (Kotobi)

01H 1:25P – 2:15P (Mitchell) - Lab T 8:00A – 11:00A (Tyson) Grade: /100 NOTE: 1. The exam is composed of 5 matching questions (2 points each) and 30 multiple-choice

questions (3 points each). There is only ONE correct answer to each question. If you get stuck on a problem – move on!

2. You are NOT allowed any notes, books, calculators, or cell phones. 3. Show all work, circle the correct answer on the exam booklet, and code your answer on the

computer scan sheet. 4. Turn in the computer scan sheet and this exam booklet.

Best Wishes for a Happy Holiday!

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Table of trigonometric values:

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Matching questions: (10 pts) Match each circuit element on the left with a possible phasor representation on the right. 1. A.

2. B.

3. C.

4. D.

5. E.

0S SV V

SI

SV

SI

Re

Im

90S SV V

SI

SV

SI

Re

Im

SV

SI

SV

SI

Re

Im

SV

SI

SV

SI

Re

Im

SV

SISV

SI

Re

Im

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Multiple-choice questions; only one correct answer for each question: (90 pts) 6 – 7. Consider the following driven RLC circuit:

6. Determine cv (0 ) for the circuit.

A. Vcv ( 0 ) 15

B. Vcv ( 0 ) 10

C. Vcv ( 0 ) 9

D. Vcv ( 0 ) 6

E. Vcv (0 ) 0

7. Determine Li ( ) for the circuit.

A. L

9i ( ) A

R

B. L

15i ( ) A

R

C. L

3i ( ) A

R

D. L

5i ( ) A

R

E. Li ( ) 0 A

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8 – 9. Consider this circuit in answering the following two questions.

8. Which differential equation describes the transient response for iL(t) when t ≥ 0 s?

A. d2iL

dt2 +

1

RC

diL

dt +

1

LCiL 0

B. d2iL

dt2 +

R

L

diL

dt +

1

LCiL 0

C. d2iL

dt2 +

L

R

diL

dt +

1

LCiL 0

D. d2iL

dt2 +

1

LC

diL

dt +

1

RCiL 0

E. d2iL

dt2 +

1

LC

diL

dt +

R

LiL 0

9. If L = 8 mH and C = 2 mF, what value of R will make the transient response critically

damped?

A. 1 Ω

B. 4

C. 16 Ω

D. 4 k

E. 1 MΩ

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10. Consider a series RLC circuit that is source-free for t ≥ 0 and having the following characteristic equation:

2s 8s 20 0

Determine the solution form of the inductor’s current Li t for t ≥ 0.

A. A2t 6 t

L 1 2i t A e A e

B. A4t 2t

L 1 2i t A e A e

C. A4t

L 1 2i t e D cos( 2t ) D sin( 2t )

D. A2t 12t

L 1 2i t A e A e

E. A2t

L 1 2i t e ( D cos( 4t ) D sin( 4t ))

11. Consider a driven RLC circuit with a sudden change in the circuit at t=0. For t 0, the

inductor’s current is given by the expression

A2t tL f 1 2i ( t ) i A e A e

Determine 1A and 2A if the initial conditions are 5 A and 4 A/sL Li 0 i 0 and the

final steady-state value (as t ∞) is 4 ALi ( ) .

A. 1 2A 5, A 4

B. 1 2A 1, A 4

C. 1 2A 9, A 10

D. 1 2A 3, A 2

E. 1 2A 5, A 6

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12 – 13 . Consider this LC circuit in answering the following two questions.

12. Determine the natural frequency of oscillation.

A. ωo = 16 x 10-6 rad/s

B. ωo = 4 x 10-3 rad/s

C. ωo = 4 rad/s

D. ωo = 250 rad/s

E. ωo = 62500 rad/s

13. The initial conditions are 0 6 ALi and 0 4 VCv . What is the maximum value of the

voltage vC(t)?

A. 3 V

B. 4 V

C. 5 V

D. 6 V

E. 10 V

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14. For a parallel RLC circuit driven by a current source with an abrupt change in the supplied current at t0, which of the following conditions is not true?

A. - +L 0 L 0i (t ) i (t )

B. - +C 0 C 0i (t ) i (t )

C. - +R 0 R 0i (t ) i (t )

D. - +L 0 L 0v (t ) v (t )

E. - +C 0 C 0v (t ) v (t )

15. The voltage across one of the elements of a driven series RLC circuit is given in the

following graph. Determine the circuit element and the type of circuit response.

A. Capacitor, underdamped circuit

B. Capacitor, overdamped circuit

C. Inductor, critically damped circuit

D. Resistor, overdamped circuit

E. Resistor, underdamped circuit

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16. Convert the following impedance expression to its polar equivalent form:

Z = (−3 + j4) kΩ A. 5 36.9 kΩ

B. 5 53.1 kΩ

C. 5 143.1 kΩ

D. 5 53.1 kΩ

E. 5 126.9 kΩ

17. Express the following current phasor in its rectangular (Cartesian) form.

10 2 135 mAI

A. (10 + j10) mA

B. (10 – j10) mA

C. (–10 – j10) mA

D. (–10 + j10) mA

E. (–20 + j20) mA

18. Write the following voltage expression as a phasor quantity.

[10 2 cos(100 ) 10 2 sin(100 )] Vv t t A. 20 45 V

B. 20 45 V

C. 20 135 V

D. 10 45 V

E. 10 45 V

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19. Solve for the equivalent impedance of the following circuit at ω = 103 rad/s.

A. 2 4

5 5eqZ j

B. 2 4

5 5eqZ j

C. 2 4

5 5eqZ j

D. 4 4

5 5eqZ j

E. 4 2

5 5eqZ j

20. A series RC combination has an equivalent impedance 2 4 keqZ j at = 500 rad/s.

Determine the equivalent impedance at = 2000 rad/s. A. 0.5 4 keqZ j

B. 2 16 keqZ j

C. 8 4 keqZ j

D. 2 1 keqZ j

E. 8 16 keqZ j

0.25 mF2 Ω

5 mH

Zeq

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5.362)2.16.1( jZ

21. A passive circuit’s Thevenin impedance, ZTh = RTh + jXTh , has both positive resistance and reactance terms, i.e., RTh > 0 Ω and XTh > 0 Ω. Which of the following circuits can be used to realize ZTh?

A. circuit i only

B. circuits i and vi

C. circuits i and v

D. circuit iii only

E. circuits ii and vi

22. The two-terminal source-free RLC network shown below can be characterized by an

impedance at a frequency ω = 1 krad/s. Which of the five phasor diagrams is feasible, if the voltage and current scales within each diagram are the same?

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23. Determine the phasor voltage AV for the circuit below.

A. 1 3 VAV j

B. 1 VAV j

C. 1 3 VAV j

D. 2 2 VAV j

E. 2 VAV j 24. Determine an expression for the output voltage vout(t) for the circuit below under sinusoidal

steady-state conditions.

A. 5cos 500 10cos 1000 53.1 Voutv t t t

B. 25cos 500 53.1 2cos 1000 Voutv t t t

C. 5cos 500 2cos 1000 Voutv t t t

D. 15cos 1000 53.1 Voutv t t

E. 5cos 500 Voutv t t

2 VSV j 2 4 ASI j

AV

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25. In writing a set of mesh current equations for the sinusoidal steady-state circuit, which of the following is an incorrect expression?

A. 3 17 XI I I

B. 3 2I j

C. 2 1 2 2 43 5 0I I jI I I

D. 4 2 4 35 5 2 0I I j I I

E. 1 1 2 3 4 34 3 2 2 2 0j I I I j I I j j I

1I 2I

3I4I

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26 – 27. A sinusoidal voltage source vs(t) with an angular frequency 1000 rad/s has the phasor diagram shown below, corresponding to t = 0 s. The voltage scale (in volts) and current scale (in amperes) for the phasor diagram are the same.

26. The value L of the inductor is given by:

A. 0.333 mH

B. 0.667 mH

C. 1.0 mH

D. 3.0 mH

E. the inductance L cannot be determined from the information given.

27. The time domain expression for the voltage source is given by: A. 3cos 1000 90 Vsv t t

B. 4cos 1000 Vsv t t

C. 5cos 1000 Vsv t t

D. 5cos 1000 36.9 Vsv t t

E. 13 cos 1000 56.3 Vsv t t

-4

-3

-2

-1

0

1

2

3

4

-2 -1 0 1 2 3 4 5

CI

outV

LI

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28-29. Consider the following circuit:

28. Determine the frequency at which the transfer function /out inH V V is purely

imaginary.

A. 0

B. 1

LC

C. R

L

D. 1

RC

E.

29. Which of the following phrases best describes this circuit’s function? A. Oscillator circuit

B. Highpass filter

C. Lowpass filter

D. Bandpass filter

E. Bandstop filter

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30 – 31. Consider a circuit with an input voltage inv t and an output voltage outv t that is

characterized by the following voltage transfer function:

0.003

4 0.003out

in

V jH

V j

30. An input voltage 10cos 1000 20inv t t is applied to the circuit. The corresponding

output voltage outv t will be:

A. 3cos(1000 36.9 ) Voutv t t

B. 3cos(1000 16.9 ) Voutv t t

C. 6cos(1000 20 ) Voutv t t

D. 6cos(1000 53.1 ) Voutv t t

E. 6cos(1000 73.1 ) Voutv t t

31. Which frequency response sketched below best characterizes the Bode magnitude plot of this circuit?

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32. Determine the RMS voltage for the periodic signal below.

A. 1 V

B. 8

2V

C. 50 V D. 7 V

E. 10 V 33. The input voltage of a circuit is given by:

10cos 2 60 90inv t t V

If the input current of the circuit has an amplitude of 5 mA and lags behind the voltage by 36.9o, determine the average power absorbed by the circuit.

A. 15 mW

B. 20 mW

C. 30 mW

D. 40 mW

E. 50 mW

0

4

10

2

8 6

2 4 6 8 10

4 6 95 8732101

t [s]

vx ( t ) [V]

0

4

10

2

8 6

2 4 6 8 10

0

4

10

2

8 6

2 4 6 8 10

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34 – 35. Consider this circuit in solving the following two problems.

34. What best describes ZL if there is to be maximum average power transfer to the load? A. Series RC: RL = 50 Ω, CL = 1 pF

B. Series RL: RL = 50 Ω, LL = 1 H

C. Series RC: RL = 50 Ω, CL = 10 pF

D. Series RC: RL = 25 Ω, CL = 1 pF

E. Series RL: RL = 25 Ω, LL = 1 H

35. Determine the average power dissipated in the load assuming that the impedance is chosen to achieve the maximum transfer of average power. A. 0.01 W

B. 0.05 W

C. 0.1 W

D. 0.5 W

E. 1.0 W

EE 210 201213FA Final Exam Solution

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