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EE 10, Fall 2014, Final ExamDecember 19, 2014

Instructions: This exam booklet consists of four problems, blank sheets for the solutions,

reference sheets with mathematical identities, and additional blank sheets. Please follow

these instructions while answering your exam:

1. Write your name and student identification number below.

2. Write the names of students to your left and right as well.

3. You have 3 hours to finish your exam.

4. Write your solutions in the provided blank sheets after each problem.

5. The sheets marked Scratch will NOT be graded. These sheets are provided for

your rough calculations only.

6. Write your solutions clearly. You may box in your final answer. Illegible solutions will

NOT be graded.

7. Be brief.

8. Open Book & open notes only. NO homework solution!

NAME:______________________________________

STUDENT ID:_________________________________

NAMES OF ADJACENT STUDENTS:

LEFT:__________________________________

RIGHT:_________________________________

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Problem Score

#1

#2

#3

#4

Total 100

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Problem 1:

a. Determine the value of Vc(t) and()

just after time t = 0.

b. Determine the complete solution of Vc(t) for the case when Vs(t) = where = 109.Use C1 = 20pF, C2 = 10 pF, L= 1nH, R = 10 Ohms for this part.

(15 + 15 = 30 points)

Figure 1.

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Problem 2: Refer to Figure 2 for this problem. The inductor has an initial current i L(0-) = Io. VB

is a DC source.

a. Derive an expression for the current iL(t) for t 0.

( 10 points)

Figure 2.

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Problem 3: Refer to the figure for this problem.

a. Derive a phasor domain Thevenin equivalent of the network shown in Fig. 3a.

b. Derive an expression for the angle by which v1(t) leads is(t), in the circuit shown in Fig.3b.

c. For what value of o(possibly in terms of L,C, and p), is the voltage v1(t) in phase withis(t)?

(5 + 5 +10 = 20 points)

Figure 3.

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Problem 4: Refer to Figure 4 for this problem. Assume is(t) = Acost. With A > 0.

a. Draw the phasor domain equivalent circuit of the circuit shown.

b. Write equations that describe sinusoidal steady state circuit behavior. Use the mesh cur-

rent method with the shown loop currents.

Assume M = L1 =L2 for the following parts:

c. Solve for i1(t), i2(t), and i3(t) in the phasor domain.

d. What is the sinusoidal steady state voltage across the resistor? Why?

e. Draw a phasor diagram showing the phasors of i1(t), i2(t), i3(t), and v1(t), v2(t), and vc(t).Use the voltage across the resistor as your reference (i.e. assume it has zero phase).

(5 + 5 + 10 + 10 + 10 = 40 points)

Figure 4.

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Reference Sheet #1

Trigonometric Identities:

0

0

sin cos 90 cos 2

cos sin 90 sin 2

cos cos cos sin sin

sin cos cos sin sin

cos cos 2 cos 2 cos 2

cos cos 2 sin 2 sin 2

sin sin 2 sin 2 sin 2

sin sin 2 cos 2 sin 2

cos 2 2 co

A A A

A A A

A B A B A B

A B A B A B

A B A B A B

A B A B A B

A B A B A B

A B A B A B

A

2 2 2 2

3

3

2 2 1

s 1 cos sin 1 2 sin

sin 2 2 sin cos

cos 3 4 cos 3cos

sin 3 3sin 4 sin

cos sin cos tan

A A A A

A A A

A A A

A A A

a A b A a b A b a

Complex Arithmetic:

1 1 1 2

1 1 1 2

1 2 1 2 1 2

1 2 1 2 1 2

2 2 1

1 2 1 2 1 2 1 2

Re Re ReIm Im Im

Re Re Re Im Im

Im Re Im Im Re

cos sin

where , tan

where cos , sin

,

1 1

j

j

j

z z z zz z z z

z z z z z z

z z z z z z

e j

x jy re r x y y x

re x jy x r y r

z z z z angle z z angle z angle z

z z

* *

, 1

,

angle z angle z

x jy x jy angle z angle z

Quadratic Equations:2

2 4The roots of 0 are

2

b b acax bx c x

a

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= 109

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