ENGG 1203 Tutorial

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ENGG 1203 Tutorial

Electrical Circuit (II) and Project 1 Mar Learning Objectives

Analyze circuits with resistors Illustrate stages and components used in the project

News Mid Term (TBD) Revision tutorial (TBD) Project Brief plan (8 Mar)

Ack.: HKU ELEC1008 and MIT OCW 6.01

Quick Checking

Assuming the voltage at node N0 = 0, compute the voltage at node N1 in each of these circuits.

2

IR

V/2

Quick Checking

Assuming the voltage at node N0 = 0, compute the voltage at node N1 in each of these circuits.

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3 IR

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Analyzing Circuits Assign node voltage variables to every node except ground

(whose voltage is arbitrarily taken as zero) Assign component current variables to every component in

the circuit Write one constructive relation for each component in terms

of the component current variable and the component voltage Express KCL at each node except ground in terms of the

component currents Solve the resulting equations

Power = IV = I2R = V2/R

Question: Finding Resistances via Circuit Analysis Determine the indicated parameters for

each of the following circuits. Because the resistors are in series, the

resistance between successive nodes will be proportional to the voltage between the nodes.

R1 V∝ 1 = 1R;R2 V∝ 2 − V1 = 1R; R3 V∝ 3 −V2 = 2R;R4 V∝ 4 −V3 = 4R;R5 V∝ 5 −V4 = 2R.

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Question:Another Example Determine the indicated

parameters for each ofthe following circuits.

KCL at the left-center node determines that a 1Acurrent flows rightward through R2.To make V1 −V2 = 2V, it follows that R2 = 2Ω.

KCL at the right-center node then determines that a 3A current flows downward through R1.To make 10V-V2 = 6V, it follows that R1 = 2Ω.

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Question: Another Example

If VAB = 4V, determine R1, R2, R3 and R4.

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Solution

VAB = 4V If VB = -1.5V VA = 2.5V

By potential divider,R1:R2 = 1:1, R3:R4 = 1:1

You can pick any value for resistances.

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3 4

3 1.5BRV V

R R

2

1 2

5 2.5ARV V

R R

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Solution

If VB = -1V VA = 3VBy potential divider,R1:R2 = 2:3,R3:R4 = 2:1

If VB = -2V VA = 2VBy potential divider,R1:R2 = 3:2, R3:R4 = 1:2

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1 2

5 3ARV V

R R

4

3 4

3 1BRV V

R R

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Question: Resistance Calculation using Parallel/Series CombinationsFind Req and io in the circuit of the figure.

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Solution

12 // 6 4 20 // 80 16

4 16 20

40V

5Ω

15Ω6Ω

12Ω

60Ω

20Ω 80Ω

i0

Req

40V

5Ω

15Ω

4Ω

60Ω

16Ω

i0

Req

(i)

(ii)

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Solution

0 0

15 // 20 // 60 7.5

40 7.5 5 3.2eqR

V IR i i A

40V

5Ω

15Ω 60Ω20Ω

i0

Req

(iii)

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Question: Circuit Analysis with multiple sources Find vo in the circuit of the figure.

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Solution

Step 1: Define the node voltage (v1,v2,v3) Step 2: Define the current direction

1Ω

40V

2Ω

4Ω

8Ω

20V

v1v2 v3

5A

+v0

--

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Solution

Apply: 1) V = IR 2) KCL Step 3: Consider node 1

1 2 11 2

405 3 70 12 1

v v v v v

v1

5A

(40-v1)/1(v1-v2)/2

1Ω

40V

2Ω

4Ω

8Ω

20V

v1v2 v3

5A

+v0

--

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Solution

Step 3: Consider node 2

Step 4, 5: From (1) and (2),v1 = 30V, v2 = 20V, v0 = v2 = 20V

2 31 2 21 25 4 7 20 2

2 4 8v vv v v v v

v2

5A

(v1-0)/4

(v2-v0)/8

(v1-v2)/2

1Ω

40V

2Ω

4Ω

8Ω

20V

v1v2 v3

5A

+v0

--(v2-v3)/8

Rube Goldberg Machine

(Tentative) At least five distinct stages with different triggering mechanisms

The machine is started with pushing a button/switch, and is ended by popping a balloon.

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START button

Out

put

Out

put

Inpu

t

Out

put

Inpu

t

Out

put

Inpu

t

Act

uato

r to

pop

the

ballo

on

Inpu

t

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Probing Questions for the Project Big questions

How to design an (complicated) electrical system? How do you (as a team) build a multi-stage Rube Goldberg

Machine that is functional and creative? Small questions

How do you describe the stages that are involved in the machine?

How do you describe the electrical components in the machine? How do you demonstrate your skills of technical design and

implementation? How do you demonstrate your ability to work effectively with

diverse teams? How do you demonstrate your originality and inventiveness?

Brief Plan for the Project

A brief plan for the project construction No technical requirement A way to start thinking about the project A block diagram with illustrations

Showing how the machine works after pressing the START button

No fire/chemicals/heat/explosion/knife No water Use green beans Lego bricks are fine…

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Design a reliable and robust machine because of the “Professor’s Negation Field”

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Systems that You Have Built in Lab Sessions Ball counting

Lab 1 – Lab 4 The tunnel increments its internal counter every

time a ball rolls through the tunnel. When three balls have

rolled through thetunnel, it raises adigital DONE signal.

Not necessarily to usestraight tube

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Systems that You Will Build in Lab Sessions Light tracking

Lab 5 – Lab 7 The head can follow the direction of a light source Decide your own light source triggering mechanism

Light

Sensors and Actuators in the Project

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Circuit isolation

Generation of air flow

Generation of rotation

Circuit isolation Contact switch Contact switch

Generation of sound

Generation of push force

Sensors and Actuators in the Project

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Sensing of rotation

Non-contact switch

Time counter START button

Non-contact switch LED

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Mechanical Parts in the Project Metal ball

Stages triggering Metal pulley, sloted wheel

eye hook, Wheeled castor Pulley, conveyor belt, sling …

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Mechanical Parts in the Project Aluminum cage (New Requirement) Plastic board Bracket Hinge Cable tie and cable mount

Weak fix joint betweencomponents

A Stage in the Rube Goldberg Machine In a stage, an electrical sensor is triggered by an

external mechanical input, the sensor then switches on the actuator(s) through buffers.

Electrical actuator then moves mechanical parts, which finally trigger the electrical sensor in the next stage.

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Act

uato

r

Sen

sor

Buf

fer

Electrical signal

Mechanical signal for next stage

Mechanical signal from previous stage M

echa

nica

l pa

rt

A Partial Stage in the Rube Goldberg Machine

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Sensor (Push)

Actuator (Push)

Sensor (Rotation)

Actuator (Push)

Buffer

A Partial Stage in the Rube Goldberg Machine

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Sensor(Non contact)

Actuator (Fan)

Buffer Actuator (Light)

A Partial Stage in the Rube Goldberg Machine Ball counting circuit:

A sensor only Light tracking circuit:

Sensor + Buffer +Actuator (Not yet acomplete stage)

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Act

uato

r

Sen

sor

Buf

fer

Mec

hani

cal

part

Stages in the Rube Goldberg Machine

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Sensor(Button) Actuator

(Fan)

Buffer

Actuator (Rotation)

Mechanical parts

Sensor(Rotation)

Buffer

(Mechanical parts in the second stage are missed.)

(Appendix) Discussions about the thermistor in Lecture 5 pp. 52 – 55

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that page

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R1 = 80Ω, R2 = 10Ω, R3 = 20Ω,R4 = 90Ω, R5 = 100Ω

Battery: V1 = 12V, V2 = 24V, V3 = 36V Resistor: I1, I2, …, I5 = ?

(Appendix) Question: Circuit Analysis

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Solution a

VN = 0 I1: M R5 V1 R1 B I2: M V3 R3 R2 B I4: M V2 R4 B

Step 1, Step 2

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Solution b

VM = 0 I1: B R1 V1 R5 M I2: B R2 R3 V3 M I4: B R4 V2 M

Let’s try another reference ground

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Solution b

I1: B R1 V1 R5 M I2: B R2 R3 V3 M I4: B R4 V2 M Different direction, different result?

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Solution b

KCL of Node B: I1 + I2 + I4 = 0 VB – VM = R1I1 – V1 + R5I1

I1 = (VB – VM + V1)/(R1 + R5) = (VB + 12)/180

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Solution b

VB – VM = R2I2 + R3I2 – V3

I2 = (VB – VM + V3)/(R2 + R3) = (VB + 36)/30

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Solution b

VB – VM = R4I4 – V2

I4 = (VB – VM + V2)/R4 = (VB + 24)/90

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Solution b

KCL of Node B: I1 + I2 + I4 = 0 (VB + 12)/180 + (VB + 36)/30 + (VB + 24)/90 = 0 VB = – 92/3 V

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Solution b

I1 = (VB + 12)/180 = –14/135 A = – 0.104A I2 = (VB + 36)/30 = 8/45 A = 0.178A I4 = (VB + 24)/90 = –2/27 A = – 0.074A

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(Appendix) Notes about Multimeters

Our multimeters allow you to measure current, voltage, and resistance. You connect the multimeter to a circuit using two leads. You can use The black lead should be plugged into the ground (common) jack. The red lead should be plugged into a jack labeled “V-Ω-mA,”.

Because the meter probes are large, they can bridge, and thereby make unwanted electrical connections (“short circuits”) between adjacent pins of small components. Such short circuits can damage your circuit. To avoid this, you can measure the resistance or voltage across points in your breadboard by using short wires that are connected to the meter probes.

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The breadboards have holes into which wires and components can be inserted. Holes in the long top row (labeled +) are connected internally (as are those in the second row, bottom row and next-to-bottom row), as indicated by the horizontal (green) boxes (above). These rows are convenient for distributing power (+10 V) and ground. Each column of 5 holes in the center areas is connected internally, as indicated by two representative vertical (blue) boxes (above). Note that the columns of 5 are NOT connected across the central divide.

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(Appendix) Notes about Breadboard

(Appendix) Notes about Wire and Resistors Wire

We have a lot of wire kits that contained wires of different lengths that are pre-cut and pre-stripped. Use these if you can. Try to select wires that are just the right length, so they can lie flat on the board. Messes of loopy wires are harder to debug and more likely to fall apart. If you need a longer wire, cut what you need from a spool. Use one of the pre-stripped wires for guidance on how much to strip: too little and it won’t go deep enough into the breadboard; too much, and you’ll have a lot of bare wire showing, risking shorts against other wires and components.

Resistors We use quarter-watt resistors, which means that they can

dissipate as much as 250mWunder normal circumstances. Dissipating more than 250mW will cause the resistor to overheat and destroy itself.

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(Appendix) Notes about Potentiometer (or Pot) It is a three terminal device whose electrical properties depend on

the angle of its mechanical shaft. The following figure shows a picture of the pot that we will use in lab (left), the electrical symbol used for a pot (center), and an equivalent circuit (right).

The resistance between the bottom and middle terminals increases in proportion to the angle of the input shaft (θ) and the resistance between the middle and top terminal decreases, so that the sum of the top and bottom resistors is constant. We define a proportionality constant α, which varies between 0 and 1 as the angle of the potentiometer shaft turns from 0 to its maximum angle Θ, which is approximately 270 for the potentiometers that we use in lab.

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By connecting a pot as a variable resistor (using top and middle terminals), the resistance across those terminals is proportional to the angle of the shaft. By connecting a pot as a voltage divider (top terminal to a voltage source and bottom terminal to ground), the voltage at the middle terminal is made proportional to the angle of the shaft.

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(Appendix) Notes about Photoresistor A photoresistor is a two terminal device whose electrical

resistance depends on the intensity of light incident on its surface. A photoresistor is made from a high resistance material. Incident photons excite the electrons – liberating them from the atoms to which they are normally held tightly – so that the electrons can move freely through the material and thereby conduct current. The net effect can be characterized by plotting electrical resistance as a function of incident light intensity, as in the following plot (notice that the axes are logarithmically scaled).

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Normal room lighting is between 10 and 100 lux. Illuminance near a 60 watt light bulb (as we will use in lab) can be greater than 10,000 lux.

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