Lecture 1: Intro & Circuit Variables Nilsson 1.1-1.6, 2.1-2.4 ENG17 : Circuits I Spring 2015 1 March 31, 2015

1

Lecture 1:Intro & Circuit VariablesNilsson 1.1-1.6, 2.1-2.4

ENG17 : Circuits I

Spring 2015

March 31, 2015

2

Overview

• Personal Introduction• Course Introduction• Units• Circuit Analysis• Voltage / Current• Basic Circuit Element• Power / Energy• Voltage & Current Sources• Electrical Resistance• Circuit Model• Kirchhoff’s Laws

3

Dr. Kyle Montgomery

• B.S. 2004 University of Houston• 3 years @ Schlumberger• M.S. 2008 Purdue University• Ph.D. 2012 Purdue University

– Thesis: Novel Approaches for Wide Bandgap Solar Cells

4

What I do now…besides teach…

• Advise students• Research

– Novel solar cells w/compound semiconductors

– New materials for lighting, solar cells, and beyond

– High speed, high power transistors– Alternative energy storage solutions

5

Philosophy…on teaching…and life

• Teaching is not confined to classroom time• Conceptual understanding is key• Life really sucks sometimes…how can I

help?

6

Overview


7

ENG17: Circuits 1

• Electrical quantities and elements• Resistive Circuits• Transient and steady-state responses of

RLC circuits• Sinusoidal excitation and phasors• Complex frequency and network functions• Power Calculations

8

Course Structure

• TAs– Matt Clements– Songjie Bi– Chi Van Pham– Burcu Ercan– Yuhao Liu– Xin Zhao (Tuesday discussions)– Nathan Ellis (Thursday discussions)

• Course Website is:– http://www.kmontgomery.net/teaching/eng17/– Smartsite used primarily for grades

• Also using Piazza

http://www.kmontgomery.net/teaching/eng17/

http://www.kmontgomery.net/teaching/eng17/

9

Overview


10

SI Units

11

Derived Units

12

Prefixes

13

Examples

14

Overview


15

Big Picture

• Need justifies design

• Design specs filter to concept, circuit model, prototype

• Circuit analysis necessary for foundation

16

Overview


17

Voltage

18

Current

19

Ohm’s Law

20

Water Analogy

• Water pressure = voltage• Water flow = current

21

Overview


22

Ideal Element

• Passive sign convention

23

Fundamental Quantities

1.Voltage (v)2.Current (i)3.Charge (q)4.Flux (Φ)

24

Overview


25

Power ≠ Energy

• Power = Time Derivative of Energy• UNITS!

– Power in Watts– Energy in Watt-hrs or Joules

• Positive Power = Power Delivered to Circuit

• Negative Power = Power Extracted from Circuit

𝑝=𝑑𝑤𝑑𝑡

𝑝=𝑖𝑣

26

27

Overview


28

5 Ideal Basic Circuit Elements

• Voltage Sources• Current Sources• Resistors• Inductors• Capacitors

“Active Elements”Generate Electric Energy

“Passive Elements”Do NOT Generate Electric Energy

29

Ideal SourcesVoltage Source(const. voltage)

Current Source(const. current)

Circle means “Independent Source”

30

Dependent Sources

Voltage Sources Current Sources

Diamond means “Dependent Source”

31

Schematics

WireAssume No Resistance

NodeAny defined point (usually a point of intersection)

Valid configuration

32

Schematics (w/dependents)

Valid configurationInvalid configuration

Invalid configurationValid configuration

33

Schematics - GND

• Ground (GND) is a common connection• Typically connect to Earth GND• Always a zero [V] reference potential

GND Connect

34

Overview


35

Ohm’s Law

Note change in sign

Assume ideal resistance(no change w/time)

36

Conductance

• Conductance, G– Units: siemens [S]

37

Power & Ohm’s Law

𝑉=𝐼𝑅

𝑃= 𝐼𝑉

Therefore…

Ohm’s Law

Power Relationship

𝑃= 𝐼2𝑅

𝑃=𝑉 2

𝑅 𝑃= 𝐼 2

𝐺

𝑃=𝑉 2𝐺or

or

38

Examples

𝑣𝑎=1𝐴∗8Ω=8𝑉

𝑣𝑎=−1 𝐴∗20Ω=−20𝑉 𝑖𝑑=−50𝑉25Ω

=−2𝐴

𝑖𝑏=0.2𝑆∗50𝑉=10 𝐴

39

Overview


40

Designing a Circuit Model

41

Additional Elements

Short Circuit

Open Circuit

Switch

42

Schematic

1.5V 9V

Batteries Lamp

Case

SwitchSpring

43

Overview


44

The Setup

Use common subscripts

Establish Reference Polarities

Establish Nodes that Connect Elements

7 unknowns…need 7 equations

From Ohm’s Law: 𝑣1=𝑖1𝑅1

𝑣𝑐=𝑖𝑐𝑅𝑐

𝑣 𝑙=𝑖𝑙𝑅 𝑙

45

Kirchhoff’s Current Law (KCL)

The algebraic sum of all the currents at any node in a circuit equals zero.

Therefore:• Assign signs to currents at each node• Positive (+) for current leaving a node• Negative (-) for current entering a node• Or vice versa

𝑁𝑜𝑑𝑒𝑎 : 𝑖𝑠−𝑖1=0𝑁𝑜𝑑𝑒𝑏 : 𝑖1+𝑖𝑐=0𝑁𝑜𝑑𝑒𝑐 :−𝑖𝑐−𝑖𝑙=0𝑁𝑜𝑑𝑒𝑑 : 𝑖𝑙− 𝑖𝑠=0

46

Kirchhoff’s Voltage Law (KVL)

The algebraic sum of all the voltages around any closed path in a circuit equals zero.

Therefore:• Assign signs to voltages in a loop• Positive (+) for voltage rise• Negative (-) for voltage drop• Or vice versa

𝑣 𝑙−𝑣𝑐+𝑣1−𝑣𝑠=0

47

Observations

• 7 equations 4 equations– Because I and V are related

through R, we only need one

• With only 2 branches at a node (in series), we only need to know 1 current

𝑣1=𝑖1𝑅1

𝑣𝑐=𝑖𝑐𝑅𝑐

𝑣 𝑙=𝑖𝑙𝑅 𝑙

𝑖𝑠− 𝑖1=0𝑖1+𝑖𝑐=0−𝑖𝑐−𝑖𝑙=0𝑖𝑙−𝑖𝑠=0

𝑣 𝑙−𝑣𝑐+𝑣1−𝑣𝑠=0𝑖𝑠=𝑖1=−𝑖𝑐=𝑖𝑙

48

KCL Example

49

KVL Example

Documents

Lecture 1: Intro & Circuit Variables Nilsson 1.1-1.6, 2.1-2.4 ENG17 : Circuits I Spring 2015 1 March 31, 2015