EGR 2201

1. EGR 2201 Circuit Analysis Professor Nick Reeder

2. Reminders • Please turn off cell phones. • No food or soft drinks in the classroom. • Stow water bottles at floor level.

3. EGR 2201 Unit 1Basic Concepts • Read Alexander & Sadiku, Chapter 1. • Homework #1 and Lab #1 due next week. • Quiz next week.

4. What This Course Is About • In this course you’ll learn mathematical techniques for studying electric circuits. • Our focus is not on practical circuits that do interesting things. • You’ll study those in later courses, using the techniques that you learn in this course.

5. The Math That We’ll Use

6. Calculator or Math Software • Some of the math we’ll do is time-consuming with a basic calculator. • Examples: TI-30 or Casio fx-115 • It’s faster with a powerful calculator that can solve systems of linear equations and manipulate complex numbers. • Examples: TI-86 or TI-89 • You can use any calculator on exams, but no cell phones. • Another option: Use MATLAB software, which we will learn how to use.

7. Calculator or Math Software (Cont’d.) • Be aware of the calculator policy for the Fundamentals of Engineering exam and the Principles and Practice of Engineering exam, administered by the National Council of Examiners for Engineering and Surveying (NCEES). • In a few years you may decide to take these exams for professional advancement.

8. What is a Circuit? • Our book’s definition (page 4):An electric circuit is an interconnection of electrical elements. • Five electrical elements that we’ll focus on: • Resistors • Capacitors • Inductors • Voltage Sources • Current Sources

9. Example Circuit: A Power Supply from a Flat-Screen Television Resistor Capacitors Inductor

10. Schematic Diagrams • To discuss circuits, we draw schematic diagrams that represent those circuits. • Schematic diagrams do not show the parts of the circuit as they actually look. Instead, they contain standard symbols that represent electrical elements.

11. Example Schematic Diagram: A Radio Transmitter (from book’s page 4) Inductor Symbol Resistor Symbol Capacitor Symbol

12. A Simpler Example Schematic Diagram: Flashlight Switch • When the switch is open (as drawn), no current flows, so the bulb is dark. • When the switch is closed, current flows, and the bulb lights. Light Bulb Battery (Voltage Source)

13. Another Simple Example: A Voltage Source And Two Resistors

14. Polarity of a Battery • Note that the symbol for a battery is asymmetric. The end with the longer line represents the battery’s positive terminal, and the other end represents its negative terminal. Positive terminal +  Negative terminal

15. Direction of Current Flow • For historical reasons, we say that in our simple circuit current flows out of the battery’s positive terminal and into its negative terminal. • Modern science tells us that electrons actually move in the opposite direction, but we’ll follow the standard convention shown above.

16. Element Ratings • The schematic diagrams so far have been incomplete. • They show what kinds of elements are in the circuit and how those elements are connected to each other. • But they do not show numerical ratings that let us quantify the circuit’s behavior. • Every voltage source has a numerical rating in volts (V). • Every resistor has a numerical rating in ohms ().

17. Examples of Voltage Sources • What is the rating of these sources? • Flashlight battery ____ V • Wall outlet ____ V • But the battery is a DC voltage source, while the outlet is an AC voltage source.

18. DC Versus AC • In a direct-current (DC) circuit, current flows in one direction only. • The textbook’s Chapters 1 through 8 cover DC circuits. • In an alternating-current (AC) circuit, current periodically reverses direction. • The book’s Chapters 9 through 11 cover AC circuits.

19. Schematic Symbols for Independent Voltage Sources • Several different symbols are commonly used for voltage sources:

20. V or v? • Some authors use uppercase letters for constant quantities, such as V for the voltage of a constant DC voltage source. • And they use lowercase letters for time-varying quantities, such as v for the voltage of an AC voltage source. • Our textbook mentions this convention on pages 7 and 10, but usually uses lowercase letters for both constant and time-varying quantities.

21. DC Voltage Sources on Our Trainer Fixed +5 V voltage source No matter which red socket you use, you must also use the GROUND socket. Fixed -5 V voltage source Variable positive voltage source, controlled by the left-hand knob. We’ll usually use this one. Variable negative voltage source, controlled by the right-hand knob.

22. Using a Digital Multimeter to Measure Voltage • We’ll use a digital multimeter, like the Fluke 45 shown, to measure voltage. • Note that the meter has a red lead and a black lead. See next slide ….

23. Meter’s Red and Black Leads • When you measure a voltage, the order of the red and black leads determines whether the value is displayed as positive or negative. Meter will display 5.00 V Meter will display 5.00 V

24. Resistance • Resistance is opposition to the flow of electrons. • Resistance’s unit of measure is the ohm(). • A perfect conductor would have zero resistance and a perfect insulator would have infinite resistance. • A resistor is a device manufactured to have a specific amount of resistance.

25. Resistor Ratings • The resistors in our labs range in value from 10  to 10,000,000 . • Instead of having the value printed in numbers on the case, our resistors are marked with a four-band color code to indicate the value.

26. Resistor Color Code • The first three color bands specify the resistance’s nominal value.

27. Resistor Color Code(Cont’d.) • The fourth band (“tolerance band”) gives the percent variation from the nominal value that the actual resistance may have. • Many websites have color-code charts and calculators, such as this one.

28. Tolerance Calculations • To find a resistor’s tolerance in ohms, multiply its nominal value by the percentage tolerance. • Example: For a 220  resistor with 5% tolerance, the tolerance in ohms is 220  0.05 = 11 . • Then…

29. Tolerance Calculations (Cont’d.) • To find the minimum value that a resistor can have, subtract its tolerance in ohms from its nominal value. • In example above, the nominal value was 220  and the tolerance was 11 . So the minimum value is 220   11  = 209 . • To find the maximum value that a resistor can have, add its tolerance in ohms to its nominal value. • In example above, the maximum value is 220  + 11  = 231 .

30. Using a Digital Multimeter to Measure Resistance • Digital multimeters can measure resistance as well as voltage. • When measuring a resistor’s resistance, the resistor must be out of circuit: definitely no power applied and disconnected from other elements.

31. Selecting the Measurement Type on the Digital Multimeter DC Voltage DC Current Resistance AC Voltage AC Current

32. Plugging the Meter’s Leads into the Jacks Red lead here to measure voltage or resistance. Red lead here to measure current. Black lead always in this jack.

33. Same Circuit Layout, but Different Element Ratings • These two circuits will perform differently. In particular, the different element ratings will result in: • Different current values • Different voltage values

34. Current • Current is the flow of electric charge through a circuit. • We use the symbol I or i to represent current. • Current’s unit of measure is the ampere,or amp(A). • For example, • To say that a current is 2.5 amperes, we write i= 2.5 A

35. Voltage • Voltage is a measure of how forcefully charge is being pushed through a circuit. • We use the symbol V or v to represent voltage. • Voltage’s unit of measure is the volt (V). • For example, • To say that a voltage is 5 volts, we write v= 5 V

36. Summary of Some Electrical Quantities, Units, and Symbols

37. Plumbing Analogy • It may help to think of a circuit as being like a plumbing system, with water flowing through pipes. • On this analogy, voltage is like the water pressure in a pipe. Its value will be different at different points in the circuit. • Current is like the volumetric flow rate through a pipe. • See Wikipedia article on Hydraulic analogy.

38. Plumbing Analogy in Our Simple Circuit A wire is like a water pipe. The amount of electricity per second flowing through a wire is the current, which is measured in amperes. The voltage (pressure) at this point is greater than the voltage at this point. A voltage source is like a water pump. Its voltage rating (in volts) tells you how strong it is. Resistors are like partial blockages in the pipe. They restrict the amount of current that flows through the circuit.

39. The Goal of Circuit Analysis • This course’s main goal: to learn how, given the schematic diagram of a circuit, to compute the voltages and currents in the circuit. • For some circuits, such as this one, the math is simple (basic algebra). • More complicated circuits require more powerful math (trig, complex numbers, calculus, differential equations…).

40. Large and Small Numbers • We must often deal with very large or very small numbers. • Example: a resistor might have a resistance of 680,000  and a current of 0.000145 A. • It’s not convenient to use so many zeroes when writing or discussing numbers. Instead we use SI prefixes (or engineering prefixes), which are abbreviations for certain powers of 10.

41. Table 1.2  1,000,000,000,000 1,000,000,000 1,000,000 1,000 1 / 1,000 1 / 1,000,000 1 / 1,000,000,000 1 / 1,000,000,000,000  We rarely use these.

42. Engineering Prefix Game • You must memorize these prefixes. • To practice, play my Metric Prefix matching gameat http://nreeder.com/flashgames.htm. • You must also be able to convert between numbers written with engineering prefixes and numbers written in everyday (floating-point) notation. • To practice, play my Engineering- Notation game.

43. Using Engineering Prefixes • Whenever you have a number that’s greater than 1000 or less than 1, you should use these prefixes. • Examples: • Instead of writing 680,000 , write 680 k(pronounced “680 kilohms”). • Instead of writing 0.000145 A, write 145 A (pronounced “145 microamps”).

44. Calculator’s Exponent Key • Scientific calculators have an exponent key (usually labeled EE, EXP, or E) that lets you easily enter numbers with engineering prefixes. • Examples: • To enter 680 k, press 680 EE 3. • To enter 145 , press 145 EE −6.

45. Calculator’s Engineering Mode • Most scientific calculators also have an engineering mode, which forces the answer always to be displayed with one of the engineering powers of 10. • Learn how to use this feature of your calculator. It will save you from making mistakes.

46. Measuring Voltage • A voltmeter is an instrument designed to measure voltage (also called potential difference). • Voltage measurements are always made across elements. • To measure avoltage in a circuit, you don’t need to disconnect any elements. Measuring the voltage across R1.

47. Positive or Negative Voltage? • When you measure a voltage, the displayed value may be positive or negative. • In the drawing, the meter’s + lead is connected to point a and its – lead to point b. To indicate this, wewould say that we’re measuring vab. • If we swapped the leads, we’d be measuring vba. • These two voltages, vab and vba, have the same magnitude but different signs. • Example: If vab= 1.60 V, then vba must be 1.60 V. a b

48. Voltage Drops and Rises • If vab = 1.60 V, wesay that there’s a voltage drop of1.60 V from point a to point b. • Equivalently, we say that there’s a voltage rise of 1.60 V from point bto point a. • Though it may seem confusing, we could also say that there’s a voltage rise of 1.60 V from point a to point b, or that there’s a voltage drop of 1.60 V from point b to point a. a b

49. Measuring Current • An ammeteris an instrument designed to measure current. • To measure the current at a point, you must break the circuit at that point and insert the ammeter in such a way that the current flowsthrough the ammeter. Measuring current.

50. Positive or Negative Current? • When you measure a current, the displayed value may be positive or negative. • Note that in thedrawing, the meter’s + lead is connected to the battery and its – lead to R1. • The displayedvalue is the current flowing into the + lead and out of the – lead.