Fall EEL 6022 Summer 2015 Test 2

| August 30, 2017

Question
z1 = a + if (center)

radius #1 = |b|

z2 = 6a ‐ i(8f) (center)

radius #2 = |c|

z = 6b + i(

Fall
EEL 6022 Summer 2015 Test 2

First Attempt counts 5%. Deadline: 11:59 pm June 29
Nov 3
Nov 5
Second Attempt counts 65%. Deadline: 11:59 pm June 30
Nov 7
Third Attempt counts 30%. Deadline: 11:59 pm July 1
If you miss a deadline, I credit your attempt with the score on your next
submission. If you don’t submit a third attempt, I credit the third attempt with
the previous submission.
Submit your answers as FILE UPLOADS, not TEXT ENTRY.
EEL6022_(703 or
Download IDCodesU15Test2.xls from FILES to get your abcdef data.
799)F15Test2IDs.xlxs

Using Word doc or notepad or some other software that can be mouse­copied,
prepare your solutions files in this manner. Type your answers into a column like
the format below.
Only one carriage return at the end of each line.
Space between the row number and the datum.
Enclose complex answers in parentheses.
Many formats are acceptable, but be careful if you’re using "e" and "i";
3 + 4e03i is acceptable, but 3 + 4ie03 is not.
For example
1. a 1. 6
2. b 2. ­8
3. c 3. 4
4. d 4. ­2
5. e 5. 11
6. f 6. ­3
7. Answer to #1 7. 0.566565
8. Answer to #2 8. 0.566565
9. Answer to #3 9. 0.566565
10. Answer to #4, α
10. 0.566565
11. Answer to #4, β
11. 0.566565
12. Answer to #4, γ
12. 0.566565
These answers are not correct. See last page for correct
sample answers.

Jun 19­11:23 AM

1

Problem 1

z0 = 0 (center of circle)

z1

Green line is 0V

z­1­ = b + ia
z

z2 = √(a2+b2)

z2

z0

z = z1/2

or
Circle (rim) is 1V
Green line is 0V

What is the voltage at z ?
Accurate to ±0.00001
z0

z2

z
z1

Circle (rim) is 1V

Jun 18­1:02 PM

2

Problem 2

z1 = a + if (center)
radius #1 = |b|
z2 = 6a ­ i(8f) (center)
radius #2 = |c|
z = 6b + i(6c)

Circle (rim) #1 at 1V
z1

z2

Circle (rim) #2 at 1000V

What is the voltage at z ? Accurate to ±0.001

Jun 18­1:20 PM

3

z1 = 0

z1

z2 = bi
z3 = ci (center)
z2

z = (b+c)i
z3

z

Outer circle (rim) at 10V
Inner circle (rim) at 0V

What is the voltage at z? (Accurate to ±0.001)

Jun 18­1:33 PM

4

Problem 4

x2

x1

x3

z plane

w2

w3

w1
w plane

or

w1 = c+id, w2 = b+ic, w3 = a+if

w1

w3
w2

Jun 18­1:43 PM

5

Write down the form of the Schwarz­Christoffel integral mapping the red
region to the green region.
f(z) = A ∫ζ=zζ=0 (ζ-x1)α(ζ-x2)β(ζ-x3)γ dζ

+

B

What are the numerical values (±0.001) of the exponents α, β, and γ ?

Here is a sample with correct answers.
[Entry # / correct answer / points off]
1.0000 7.0000
0
2.0000 -3.0000
0
3.0000 -6.0000
0
4.0000 2.0000
0
5.0000 4.0000
0
6.0000 7.0000
0
7.0000 0.3711
0
8.0000 519.6240
0
9.0000 8.8889
0
10.0000 0.3858
0
11.0000 -0.6771
0
12.0000 0.2913
0

Jun 21­8:19 AM

6

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