November, 2019

NEW TRIER & BOCA RATON TRYOUT

Circuit Lab C Kevin Hao1'* and Asher Noel2'!

1 University of Florida, B.S. Biology '21 M.D '24 2Harvard University, B.A. Computer Science & Statistics '23

Directions:

1. This test is separable. Only marks within the designated boxes will be scored. 2. Work is not required; however, incorrect solutions are eligible for partial credit. 3. Full credit necessitates correct significant figures and units. 4. Each team will have 10 minutes to complete the practical section. Proctors will invite

competitors at designated times. Replacement parts will not be given.

Team Number: Team Name: Team Members:

b:XC»N\

VNoo . MWir k!q€\

Good Luck!

*email: kevin@floridascienceolympiad.org fcmail: ashernoel@college.harvard.edu

Scioly.org Circuit Lab C

Note: This page is for administrative use. No competitor action is required.

Page Number Possible Score Test Score 2 24 3 32 4 28 5 36 6 32 7 22 8 24 9 26

Lab 60 Total 274

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Author Statement: This exam was written for the benefit of the Science Olympiad community.

To ensure that neither of the test writers' alma maters gain an unfair advantage, they will release the exam immediately after its administration

on the scioly.org test exchange.

1

Scioly.org Circuit Lab C

Fill in the blank: Identify the last name of the individual associated with the following epithets:2 (1 point each)

R;c>nc*vyyw\

Mattel

\W Vg-

UAAcv

1. Killed an elephant.

2. Flew a kite in a thunderstorm

3. FSolved equations; exclaimed: "and then there was light!"

4. Thought his work had "no practical applications!"

5. Showed that Q ccV for capacitors.

6. Experimentally supported Maxwell years before Hertz.

7. Born in 1816 and died in 1892.

8. Invented the Bunsen Burner.

9. Published "On the Attractive force of Electric Fire."

10. Only major 18th century female contributor to the field.

Multiple Choice: Select the best answer for the following questions:2 (2 points each)

11. What is the best technique to reduce radiation above 200 Ghz?

A. Twisted Pairs B. Coaxial Cables C. Waveguides

12. What is the standard RMS voltage and frequency in Vanuatu?

C. 200V, 50Hz 0

D. Fiber Optics

D. 220V, 50Hz A. 120V, 60Hz B. 180V, 50I4z

13. How many deaths were due to Electrocution in 1993 in the US.?

~S] A. 150 B. 550 C. 850 D. 1050

14. Which multiway switching system was prohibited in the US in 1923?

C. Carter A. Traveler B. Alternative

15. How are Foucault currents minimized?

B. Resistance A. Autoclaving B. Resistance C. Lamination

16. Which side of a PN Junction has a negative charge?

C. Neither

D. Hao

D. Powerwashing

A A. Anode B. Cathode C. Neither D. Big Foot

17. What increases with temperature to increase the conductivity of semiconductors?

B. e~ energy C. # of mobile e~ D. e~ degeneracy C- A. e mobility

2 /28

Scioly.org Circuit Lab C

18. The skin effect (Increases/Decreases) power loss in (AC/DC) circuits.

fry I A. Increases, AC B. Decreases, AC C. Increases, DC D. Decreases, DC

19. What is the term for the dependence of the state of a system on its history

D. Coercivity <1- A. Remembrance B. Markovity C. Hysteresis

20. What is the approximate value of the relative permeability for iron cores?

Dj A. 1 B. 14 C. 153 D. 209

21. What is the degree of the time term in the SI units of the henry?

C- a n R _i C. -2 A. 0 B.-1

22. What are the SI units for the proton magnetic moment?

B. J/T e> A. T C. C T

D. -3

D. C/T

23. In a different universe, the vacuum permeability and permittivity are both eight times their value in our universe. If Maxwell's theories hold, what is the speed of light?

D A. c/8 B. c/64 C. c/512 D. c/4096

24. Determine the voltage(V/?3 jmd current IR3 across R3. Provide your answer to 3 significant figures. 1 (8 pts; 4, OttC^

^7 4. \ ~

\J* -C,

cO \.c y/

= i .ov R2

R1 1.0C1

^0= O.S A

= COO V

3 WV

d>"' 2. on

Ir3= O.S53 A

25. Determine VR3 and IV1. Then, draw the equivalent circuit with Vu Req, labels, and values.1

(12 pts; 4, 4, 4)

R2 -VvV 12C1

R1 Kit- S

V1 '.10 V

p - i C i * *

PmV1 * (&*• feTr XLSL.

+ ^ „ </« J _

VR3 = 4.C7 V Ivy = Q.11Z A

R4 ion S4on

Equivalent Circuit

\ZSL

3

Scioly.org Circuit Lab C

26. Determine VR3 and the power PR\+R2. Provide your answer to 3 significant figures.2 (12 pts; 6, 6)

So Or~£) \/ov = &a v/

VR3 = 2/5.0 V Pm+R2 = MoV Scote6

s.oa^-V1 I.R3 ==-240 V >20Q

7.0Q 1 11

27. Determine the current ( I x ) through the resistor R1 and the voltage ( V o ) across the resistor R2. Provide your answers to 3 significant figures. 1 (8 pts; 4, 4)

70fJ0O ^- ->-0.00s. a- v°-:

H,0 OQ -l.i-U -Q \JQ^ So V is*

4 lOOO

Ix = (~> -XS AA A

CISmA

Vn= &Q.Q ^

i * {2.2/*; - J — ^

_=_25 V \5mA Vo>20W:

28. Draw the Thevenin equivalent circuit with respect to the terminals A and B in the circuit below. Provide your answers to 3 significant figures. 1 (8 pts)

(2^t^ ; VJ0\\<*^e Offn efiaV

M (* '•*•&)' = H.%12-(1^) = &•»*«»•*'»•«•

rt«.= cio^foY'= >.s.«-5.1 -CI LhZ\ISL.

O 10 A R1

-Wv-

Xvi 80 _=_500 V

30Q R2 VMM R3

AAA f'T'-TAMr 5.20

-io —STT- "°

I

lJAft

•A

4a

-SOO b£±_ J. V/*<4~1/A6 - * i-2- —5^r~ -- o

V/^r

\W

—^— Thevenin

.B

I <

4

Scioly.org Circuit Lab C

29. Determine the voltage Vb across resistor R1 and the current /1 through the dependent source in the circuit below. Provide your answer to 3 significant figures.1 (12 pts; 6, 6)

"Z- (00<? n ,000

TyOOO * U U '

VB = "SA •*% V h =

30. The switch in the circuit shown has been in the OFF position for a long time. At t = 0, the switch moves instantaneously to the ON position. Determine the voltage across the capacitor after the switch has moved to the ON position l/o(0+)), the time constant of the capacitor r for t > 0, and the voltage across the capacitor Va(t) for t > 0. 1 (18 pts; 4, 4, 10)

\EE°

|ri Y :3mA X<*a

HOKA. •WAT—

V 2 R2 OFF t=0 ON y\ AAA \ - jU <i+>

I* R4

5.0kCl ~\y + v V ={ 2000lx UR3

5,0kQ

40/cD

T:-. | [TT5g

V1 =—75 V

^ o^e*> Mo i<n_

\*f»0 HO.000 V.^VC,V

r&srpr^tp,

SSSSSS^ s

H S , 0 V T = 2.&9H1Q-*1 s V0(t) = ~V

15 -Wqvtoxio1;^ \)0CoJ)-H sv

vo(0+) =

31. Find the value of the unknown resistance that will result in the maximum power dissipation for the elements connected between nodes a and b.1 (6 pts)

rAaSl <XV<i<. occo<s u-V\« ir^

<2.,

Rs^i.o-a

R1 I Wv • J V1 >R2 — in v >6Q > >6Q >

T ?

Rz = •yo.o rz_

R3 ?

5

Scioly.org Circuit Lab C

32. Determine and VQ. Provide your answer to 3 significant figures2 (8 pts; 4, 4)

0

R1 Vi Wv-

4kCi

V1 :=_3 V

= - I V

R4 -VWJ

K- = l . o o v

1 I _ K, = ~1.00 V

R2 lR3 5*fl 8 kO >2kO

33. Determine V0i and Vo2. Provide your answer to 3 significant figures.2 (12 pts; 6, 6)

1 . r-V As

\ ^ ^ KA A

I ^

-^V1 j-~f5 V

.Vol ,R1 >5000

<|m«| lR2 •2kO

~ 1.

-±rV2 l

'lWo2 k5kD + / R3

4000

Yz R4 1kO

Vol = v v;2 = 3 . £ v /

34. Determine the current through R3 (Ix) and the necessary value of the left voltage source (Vi) for which Ix = 0. Provide your answer to 3 significant figures. 2 (12 pts; 6, 6)

V/

\Jo 2. ^0 V/

UO - -H/*

R2 R4 47MJ

— S/9- AA A 1000

j,Fov \x -0, Vox\.o\/ I 1

220kQ

1 I

/ x = S - ^ o Vi = ~~2. ,\3 r^v/

6

Scioly.org Circuit Lab C

35. Consider a point charge 2q located at the origin and a point charge - q located at x = a with a >0. Refer to the diagram below to answer the following questions.2 (12 pts; 3, 3, 3, 3)

(a) Where would we need to put a point charge Q in order for the total force on Q to be zero?

(b) What is the work done on Q in order to place the charge at this location? (c) What is the assembling energy, U, for this configuration of charges? (d) What value of Q is needed to make the force on each charge equal to 0? Use only your

expression for U.

oq C2-+

b} UJ= (3-1L

c) 0 = ^[(3-2-l£)Q-W]

ci) Q. = 2_(s + 7

36. A thin wire with uniform linear charge density Ai lies along the z axis. An infinite conducting cylinder with uniform linear charge density A2 has its axis of symmetry aligned with the z axis. The inner and outer radii of the cylinder are a and b respectively. A second infinite conducting cylinder with uniform linear charge density A3 also has its axis of symmetry along the z axis . I ts inner and outer radii are c and d with c >b. Find the electr ic f ield E ( r )

everywhere in terms of AI,A2,A3, r, and any relevant physical constants.2 (10 pts)

V ~

< C e K : ̂ (yb- —^ v-

<r^b; EC

b ̂r- ̂ <1 ; EcO - W

C C r i j : £ ( y \ ^ o

r z - t r f a Y ~

/ 22

Scioly.org Circuit Lab C

37. Part 1: Show the direction of current travel at each terminal by drawing arrows pointing towards or away from each of the terminals in the PNP and NPN transistor diagrams provided below. There should be a total of 8 arrows drawn, 4 on each schematic. Answer the questions. Part 2: Show the direction of current travel in each of the 2 loops. This can be accomplished with a minimum of 2 arrows, but you will not be penalized for using more. 1 (12 pts; 8, 4)

Part 1 t 1

lE

f Use this arrow forir

1

EaUl —AAA-c switch

j Ns

•0-c at for bpth parts

» small, controlling c u r r e n t — - l a r g e , controlled current

38. Identify the name of the first two circuits; find Vout given Vin = 5.0V.1 (8 pts; 2, 2, 4)

•rX" 0-Dl

A &iC Supply

Diode

I Load

+

0.7 V

Ri. .n

+

0.7 V

Ri™ loud* E3

Name = Pu4\- UlaU^ ^»d4^<Name= 3-lb V

39. What are two properties of the combinatorial gate abstraction?2 (4 pts; 2, 2)

- Q e x A ° > c e ^ o \ o v i e _

<S\oA\c_ W»SGf>Y\Y>e TS

8

Scioly.org Circuit Lab C

40. Simplify the following Boolean expressions.2 (6 pts; 2, 2, 2)

Uns impl i f i ed A = (x + z)(x 4- y)(z + y)

Uns impl i f i ed B = w(wxyz)

Uns impl i f i ed C = (ad)(bc)(cd)

A= xy H- X % B = © C =

41. Given acd 4- abed,

(a) Create a truth table (b) Create a Karnaugh map with correct loops (c) Find the equivalent minimum product of sums expression

Credit: MIT 6.111 2 (20 pts; 6,10,4)

a b c d Q X O

X 0 X 0

X \ X X o X X o X X o

X X o X X \

X X o X X X \ X X X o X X X 0

X X X e> X X X X O

AB

CD

00

01

11

10

00 01 11 10 O o o O

\ \ O o o o o o o o 1 o

r . , t u . . D , , f C Equivalent Minimum Product ol bums=

9

Scioly.org Circuit Lab C

Hands-On Task Practice: For the following questions, your circuit diagrams and calcu­lations MUST be composed of components that are provided (e.g., use the resistor values provided). You will have 10 minutes to complete the questions in this section.

42. Draw a simple circuit diagram such that its input is about 9 V (Vi) and output is about 3 V (within +/- 10%). Calculate its theoretical output voltage (VQ). Provide your answer to 3 significant figures. HINT: Your answer should NOT be 3.00 V.1 (10 pts)

"TAovvj £«*.«*»,.vis - HWS c~u\ • 4 *5 -Me

\>r-w w*

t./nca. Theoretical V0 = Wtvc'tis , \Ja - "Z -%\ V

43. Construct the circuit from Q42. Record V{ and Va to 3 signihcant figures. 1 (10 pts; 5,5)

Vi = Uac\eS> V0 = Cav>eS

44. Determine the resistance and tolerance of the following theoretical resistors. You should be able to do each of these in seconds.2 (20 pts; 1 pt. each)

A Red-Orange-Yellow-Brown-Red F Violet-Blue-Pink-Violet

B Orange-Grev-White-Green G White-Black-White-Silver

C Blue-Yellow-Gold-Blue H Red-Green-Blue-Gold

D Purnle-Blue-White I Red-Oranee-Yellow-Brown

E Brown-Brown-Brown-Brown-Brown 1 Blue-Violet-Grev-Brown

Resistance Tolerance Resistance Tolerance

A *234 el _T2_ Z F O A R G

C 61 £ -1 C.-2S>c1o H VOlo

n I

E l \ U \ \ °J0 J

45. Sketch a possible schematic diagram for the following breadboard configuration with correct resistor values and a 10 uF capacitor.2 (20 pts)

/ 60