Amateur Extra License Class

1. Amateur Extra License Class Chapter 4 Electrical Principles

2. Electrical Principles • Energy • Unit of measurement is the Joule (J). • Work • Transferring energy. • Raising a 1 lb object 10 feet does 10 foot-pounds of work & adds potential energy to the object. • Moving the same object sideways does not do any work & does not add any potential energy to the object.

3. Electrical Principles • Electric and Magnetic Fields • Field • Region of space where energy is stored and through which a force acts. • Energy stored in a field is called potential energy. • Fields are undetectable by any of the 5 human senses. • You can only observe the effects of a field. • Example: Gravity

4. Electrical Principles • Electric and Magnetic Fields • Electric Field • Detected by a voltage difference between 2 points. • Every electrical charge has an electric field. • Electrical energy is stored by moving electrical charges apart so that there is a voltage difference (or potential) between them. • Voltage potential = potential energy. • An electrostatic field is an electric field that does not change over time.

5. Electrical Principles • Electric and Magnetic Fields • Magnetic Field • Detected by effect on moving electrical charges (current). • An electrical current has an associated magnetic field. • Magnetic energy is stored by moving electrical charges to create an electrical current. • A magnetostatic field is a magnetic field that does not change over time. • Stationary permanent magnet. • Earth’s magnetic field.

6. E5D04 -- What unit measures electrical energy stored in an electrostatic field? Coulomb Joule Watt Volt

7. E5D05 -- Which of the following creates a magnetic field? Potential differences between two points in space Electric current A charged capacitor A battery

8. E5D08 -- What type of energy is stored in an electromagnetic or electrostatic field? Electromechanical energy Potential energy Thermodynamic energy Kinetic energy

9. Electrical Principles • RC and RL Time Constants • Electrical energy storage. • Capacitors store electrical energy in an electric field. • Energy is stored by applying a voltage across the capacitor’s terminals. • Strength of field (amount of energy stored) is determined by the voltage across the capacitor. • Higher voltage  more energy stored. • Capacitors oppose changes in voltage.

10. Electrical Principles • RC and RL Time Constants

11. Electrical Principles • RC and RL Time Constants • Magnetic energy storage. • Inductors store electrical energy in a magnetic field. • Energy is stored by passing a current through the inductor. • Strength of field (amount of energy stored) is determined by the amount of current through the inductor. • More current  more energy stored. • Inductors oppose changes in current. • Generates a voltage (induced voltage) to oppose the voltage causing the change in current.

12. Electrical Principles • RC and RL Time Constants

13. Electrical Principles • Magnetic Field Direction • Left-Hand Rule Direction of Magnetic Field Magnetic Field surrounding wire Wire or Conductor with current through it Left-Hand Rule

14. Electrical Principles • RL and RC Time Constants • Time Constant. • When a DC voltage is first applied to a capacitor, the current through the capacitor will initially be high but will fall to zero. • When a DC current is first applied to an inductor, the voltage across the inductor will initially be high but will fall to zero. • “Time constant” is a measure of how fast this transition occurs.

15. Electrical Principles • RL and RC Time Constants • Time Constant. • In an R-C circuit, one time constant is defined as the length of time it takes the voltage across an uncharged capacitor to reach 63.2% of its final value. • In an R-C circuit, the time constant (TC) is calculated by multiplying the resistance (R) in Ohms by the capacitance (C) in Farads. • TC = R x C

16. Electrical Principles • RL and RC Time Constants • Time Constant. • In an R-L circuit, one time constant is defined as the length of time it takes the current through an inductor to reach 63.2% of its final value. • In an R-L circuit, the time constant (TC) is calculated by multiplying the resistance (R) in Ohms by the inductance (L) in Henrys. • TC = R x L

17. Electrical Principles • RL and RC Time Constants

18. Electrical Principles • RL and RC Time Constants

19. Electrical Principles • RL and RC Time Constants • Time Constant. • After a period of 5 time constants, the voltage or current can be assumed to have reached its final value. • “Close enough for all practical purposes.”

20. E5B01 -- What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage? An exponential rate of one One time constant One exponential period A time factor of one

21. E5B02 -- What is the term for the time it takes for a charged capacitor in an RC circuit to discharge to 36.8% of its initial voltage? One discharge period An exponential discharge rate of one A discharge factor of one One time constant

22. E5B03 -- The capacitor in an RC circuit is discharged to what percentage of the starting voltage after two time constants? 86.5% 63.2% 36.8% 13.5%

23. E5B04 -- What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel? 55 seconds 110 seconds 440 seconds 220 seconds

24. E5B05 -- How long does it take for an initial charge of 20 V DC to decrease to 7.36 V DC in a 0.01-microfarad capacitor when a 2-megohm resistor is connected across it? 0.02 seconds 0.04 seconds 20 seconds 40 seconds

25. E5B06 -- How long does it take for an initial charge of 800 V DC to decrease to 294 V DC in a 450-microfarad capacitor when a 1-megohm resistor is connected across it? 4.50 seconds 9 seconds 450 seconds 900 seconds

26. E5D03 -- What device is used to store electrical energy in an electrostatic field? A battery A transformer A capacitor An inductor

27. E5D06 -- In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow? In the same direction as the current In a direction opposite to the current In all directions; omnidirectional In a direction determined by the left-hand rule

28. E5D07 -- What determines the strength of a magnetic field around a conductor? The resistance divided by the current The ratio of the current to the resistance The diameter of the conductor The amount of current

29. Electrical Principles • Phase Angle • Difference in time between 2 signals at the same frequency. • Measured in degrees. θ= 45º

30. Electrical Principles • Phase Angle • Leading signal is ahead of 2nd signal. • Lagging signal is behind 2nd signal. Blue signal leads red signal. Blue signal lags red signal.

31. Electrical Principles • Phase Angle • AC Voltage-Current Relationship in Capacitors • In a capacitor, the current leads the voltage by 90°. Blue = Voltage Red = Current

32. Electrical Principles • Phase Angle • AC Voltage-Current Relationship in Inductors • In an inductor, the current lags the voltage by 90°. Blue = Voltage Red = Current

33. Electrical Principles • Phase Angle • Combining reactance with resistance. • In a resistor, the voltage and the current are always in phase. • In a circuit with both resistance and capacitance, the current will lead the voltage by less than 90°. • In a circuit with both resistance and inductance, the current will lag the voltage by less than 90°. • The size of the phase angle depends on the relative sizes of the resistance to the inductance or capacitance.

34. E5B09 -- What is the relationship between the current through a capacitor and the voltage across a capacitor? Voltage and current are in phase Voltage and current are 180 degrees out of phase Voltage leads current by 90 degrees Current leads voltage by 90 degrees

35. E5B10 -- What is the relationship between the current through an inductor and the voltage across an inductor? Voltage leads current by 90 degrees Current leads voltage by 90 degrees Voltage and current are 180 degrees out of phase Voltage and current are in phase

36. Radio Mathematics • Basic Trigonometry • Sine • sin(θ) = a/c • Cosine • cos(θ) = b/c • Tangent • tan(θ) = a/b • ArcSin, ArcCos, ArcTan c a θ b

37. Radio Mathematics • Complex Numbers • Represented by X + jY where j = • Also called “imaginary” numbers. • “X” is the “real” part. • “jY” is the “imaginary” part.

38. Radio Mathematics • Coordinate Systems • Mathematical tools used to plot numbers or a position. • 2-dimensional & 3-dimensional coordinate systems are the most common. • Latitude & Longitude = 2-dimensional. • Latitude, Longitude, & Altitude = 3-dimensional.

39. Radio Mathematics • Coordinate Systems • Complex impedances can be plotted using a 2-dimensional coordinate system. • There are two primary types of coordinate systems used for plotting impedances. • Rectangular. • Polar.

40. Radio Mathematics • Rectangular Coordinates • Also called Cartesian coordinates.

41. Radio Mathematics • Rectangular Coordinates • A pair of numbers specifies a position on the graph. • 1st number (x) specifies position along horizontal axis. • 2nd number (y) specifies position along vertical axis.

42. Radio Mathematics • Plotting Impedance • Resistance along positive x-axis (right). • Inductive reactance along positive y-axis (up). • Capacitive reactance along negative y-axis (down). • Negative x-axis (left) not used.

43. Radio Mathematics • Polar Coordinates • A pair of numbers specifies a position on the graph. • 1st number (r) specifies distance from the origin. • 2nd number (θ) specifies angle from horizontal axis.

44. Radio Mathematics • Vectors • Line with BOTH length and direction. • Represented by a single-headed arrow.

45. Radio Mathematics • Polar Coordinates • Specify a vector. • Length of vector is impedance. • Angle of vector is phase angle. • Angle always between +90º and -90º. 90º 4/30º 0º 5/-45º -90º

46. Radio Mathematics • Working with Polar and Rectangular Coordinates • Complex numbers can be expressed in either rectangular or polar coordinates. • Adding/subtracting complex numbers more easily done using rectangular coordinates. • (a + jb) + (c + jd) = (a+c) + j(b+d) • (a + jb) - (c + jd) = (a-c) + j(b-d)

47. Radio Mathematics • Working with Polar and Rectangular Coordinates • Multiplying/dividing complex numbers more easily done using polar coordinates. • a/θ1 x b/θ2 = a x b /θ1 + θ2 • a/θ1 / b/θ2 = a / b /θ1 - θ2

48. Radio Mathematics • Working with Polar and Rectangular Coordinates • Converting from rectangular coordinates to polar coordinates. r =x2 + y2 θ= ArcTan (y/x)

49. Radio Mathematics • Working with Polar and Rectangular Coordinates • Converting from polar coordinates to rectangular coordinates. x = r xcos(θ) y= r x sin(θ)

50. E5C11 -- What do the two numbers represent that are used to define a point on a graph using rectangular coordinates? The magnitude and phase of the point The sine and cosine values The coordinate values along the horizontal and vertical axes The tangent and cotangent values