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**Amateur Extra License Class**

Chapter 4 Electrical Principles

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**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.

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**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

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**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.

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**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.

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**E5D04 -- What unit measures electrical energy stored in an electrostatic field?**

Coulomb Joule Watt Volt

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**E5D05 -- Which of the following creates a magnetic field?**

Potential differences between two points in space Electric current A charged capacitor A battery

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**E5D08 -- What type of energy is stored in an electromagnetic or electrostatic field?**

Electromechanical energy Potential energy Thermodynamic energy Kinetic energy

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**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.

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**Electrical Principles**

RC and RL Time Constants

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**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.

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**Electrical Principles**

RC and RL Time Constants

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**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

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**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.

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**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

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**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

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**Electrical Principles**

RL and RC Time Constants

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**Electrical Principles**

RL and RC Time Constants Charging Discharging Time Constants Percentage of Applied Voltage Percentage of Starting Voltage 1 63.20% 36.80% 2 86.50% 13.50% 3 95.00% 5.00% 4 98.20% 1.80% 5 99.30% 0.70%

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**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.”

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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

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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

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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%

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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

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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

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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

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**E5D03 -- What device is used to store electrical energy in an electrostatic field?**

A battery A transformer A capacitor An inductor

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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

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**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

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**Electrical Principles**

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

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**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.

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**Electrical Principles**

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

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**Electrical Principles**

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

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**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.

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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

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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

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**Radio Mathematics Basic Trigonometry Sine Cosine Tangent**

sin(θ) = a/c Cosine cos(θ) = b/c Tangent tan(θ) = a/b ArcSin, ArcCos, ArcTan c a θ b

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**Radio Mathematics Complex Numbers Represented by**

X + jY where j = Also called “imaginary” numbers. “X” is the “real” part. “jY” is the “imaginary” part.

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**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.

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**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.

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**Radio Mathematics Rectangular Coordinates**

Also called Cartesian coordinates.

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**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.

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**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.

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**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.

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**Radio Mathematics Vectors Line with BOTH length and direction.**

Represented by a single-headed arrow.

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**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

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**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)

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**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

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**Radio Mathematics Working with Polar and Rectangular Coordinates**

Converting from rectangular coordinates to polar coordinates. r = x2 + y2 θ = ArcTan (y/x)

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**Radio Mathematics Working with Polar and Rectangular Coordinates**

Converting from polar coordinates to rectangular coordinates. x = r x cos(θ) y = r x sin(θ)

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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

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**Electrical Principles**

Complex Impedance Capacitive Reactance 1 2πfC Reactance decreases with increasing frequency. Capacitor looks like open circuit at 0 Hz (DC). Capacitor looks like short circuit at very high frequencies. XC = /-90°

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**Electrical Principles**

Complex Impedance Inductive Reactance XL = 2πfL /90º Reactance increases with increasing frequency. Inductor looks like short circuit at 0 Hz (DC). Inductor looks like open circuit at very high frequencies.

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**Electrical Principles**

Complex Impedance When resistance is combined with reactance the result is called impedance. Z = R + jXL – jXC Z = R2 + (XL - XC)2 θ = ArcTan (X/R) where: X = XL - XC

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**Electrical Principles**

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.

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**Electrical Principles**

Plotting Impedance R = 600 Ω XL = j600 Ω Z = Ω /45º R = 600Ω Z = 848.5Ω X = j600Ω Θ = 45º

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**Electrical Principles**

Plotting Impedance R = 600 Ω XC = -j600 Ω Z = Ω /-45º Θ = -45º X = -j600Ω Z = 848.5Ω R = 600Ω

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**Electrical Principles**

Plotting Impedance R = 600 Ω XL = j600 Ω XC = -j1200 Ω X = -j600 Ω Z = Ω /-45º XL = j600Ω Θ = -45º Z = 848.5Ω XC = -j1200Ω X = -j600Ω R = 600Ω

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**Electrical Principles**

Other Units Conductance = 1 / Resistance Admittance = 1 / Impedance Unit of measurement = siemens (S) Formerly “mho”. Example: An impedance of /45° is equivalent to 7.09 /-45°

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E5C09 -- When using rectangular coordinates to graph the impedance of a circuit, what does the horizontal axis represent? Resistive component Reactive component The sum of the reactive and resistive components The difference between the resistive and reactive components

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E5C10 -- When using rectangular coordinates to graph the impedance of a circuit, what does the vertical axis represent? Resistive component Reactive component The sum of the reactive and resistive components The difference between the resistive and reactive components

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E5C12 -- If you plot the impedance of a circuit using the rectangular coordinate system and find the impedance point falls on the right side of the graph on the horizontal axis, what do you know about the circuit? It has to be a direct current circuit It contains resistance and capacitive reactance It contains resistance and inductive reactance It is equivalent to a pure resistance

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E5C13 -- What coordinate system is often used to display the resistive, inductive, and/or capacitive reactance components of an impedance? Maidenhead grid Faraday grid Elliptical coordinates Rectangular coordinates

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E5C14 -- What coordinate system is often used to display the phase angle of a circuit containing resistance, inductive and/or capacitive reactance? Maidenhead grid Faraday grid Elliptical coordinates Polar coordinates

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E5B07 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms? 68.2 degrees with the voltage leading the current 14.0 degrees with the voltage leading the current 14.0 degrees with the voltage lagging the current 68.2 degrees with the voltage lagging the current

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EE5B08 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 100 ohms, R is 100 ohms, and XL is 75 ohms? 14 degrees with the voltage lagging the current 14 degrees with the voltage leading the current 76 degrees with the voltage leading the current 76 degrees with the voltage lagging the current

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E5B11 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 50 ohms? 14 degrees with the voltage lagging the current 14 degrees with the voltage leading the current 76 degrees with the voltage lagging the current 76 degrees with the voltage leading the current

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EE5B12 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 75 ohms, R is 100 ohms, and XL is 50 ohms? 76 degrees with the voltage lagging the current 14 degrees with the voltage leading the current 14 degrees with the voltage lagging the current 76 degrees with the voltage leading the current

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E5B13 -- What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 250 ohms, R is 1 kilohm, and XL is 500 ohms? 81.47 degrees with the voltage lagging the current 81.47 degrees with the voltage leading the current 14.04 degrees with the voltage lagging the current 14.04 degrees with the voltage leading the current

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E5C01 -- In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance inductor in series with a 100-ohm resistor? 121 ohms at an angle of 35 degrees 141 ohms at an angle of 45 degrees 161 ohms at an angle of 55 degrees 181 ohms at an angle of 65 degrees

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**100 ohms at an angle of 90 degrees 10 ohms at an angle of 0 degrees **

E5C02 -- In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance inductor, a 100-ohm-reactance capacitor, and a 100-ohm resistor, all connected in series? 100 ohms at an angle of 90 degrees 10 ohms at an angle of 0 degrees 10 ohms at an angle of 90 degrees 100 ohms at an angle of 0 degrees

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**500 ohms at an angle of 37 degrees 900 ohms at an angle of 53 degrees **

E5C03 -- In polar coordinates, what is the impedance of a network consisting of a 300-ohm-reactance capacitor, a 600-ohm-reactance inductor, and a 400-ohm resistor, all connected in series? 500 ohms at an angle of 37 degrees 900 ohms at an angle of 53 degrees 400 ohms at an angle of 0 degrees 1300 ohms at an angle of 180 degrees

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E5C04 -- In polar coordinates, what is the impedance of a network consisting of a 400-ohm-reactance capacitor in series with a 300-ohm resistor? 240 ohms at an angle of 36.9 degrees 240 ohms at an angle of degrees 500 ohms at an angle of 53.1 degrees 500 ohms at an angle of degrees

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E5C05 -- In polar coordinates, what is the impedance of a network consisting of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor? 240 ohms at an angle of 36.9 degrees 240 ohms at an angle of degrees 500 ohms at an angle of 53.1 degrees 500 ohms at an angle of degrees

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E5C06 -- In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance capacitor in series with a 100-ohm resistor? 121 ohms at an angle of -25 degrees 191 ohms at an angle of -85 degrees 161 ohms at an angle of -65 degrees 141 ohms at an angle of -45 degrees

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E5C07 -- In polar coordinates, what is the impedance of a network comprised of a 100-ohm-reactance capacitor in parallel with a 100-ohm resistor? 31 ohms at an angle of -15 degrees 51 ohms at an angle of -25 degrees 71 ohms at an angle of -45 degrees 91 ohms at an angle of -65 degrees

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E5C08 -- In polar coordinates, what is the impedance of a network comprised of a 300-ohm-reactance inductor in series with a 400-ohm resistor? 400 ohms at an angle of 27 degrees 500 ohms at an angle of 37 degrees 500 ohms at an angle of 47 degrees 700 ohms at an angle of 57 degrees

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**E5C15 -- In polar coordinates, what is the impedance of a circuit of 100 -j100 ohms impedance?**

141 ohms at an angle of -45 degrees 100 ohms at an angle of 45 degrees 100 ohms at an angle of -45 degrees 141 ohms at an angle of 45 degrees

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E5C16 -- In polar coordinates, what is the impedance of a circuit that has an admittance of 7.09 millisiemens at 45 degrees? 5.03 E–06 ohms at an angle of 45 degrees 141 ohms at an angle of -45 degrees 19,900 ohms at an angle of -45 degrees 141 ohms at an angle of 45 degrees

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E5C17 -- In rectangular coordinates, what is the impedance of a circuit that has an admittance of 5 millisiemens at -30 degrees? 173 -j100 ohms 200 +j100 ohms 173 +j100 ohms 200 -j100 ohms

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E5C18 -- In polar coordinates, what is the impedance of a series circuit consisting of a resistance of 4 ohms, an inductive reactance of 4 ohms, and a capacitive reactance of 1 ohm? 6.4 ohms at an angle of 53 degrees 5 ohms at an angle of 37 degrees 5 ohms at an angle of 45 degrees 10 ohms at an angle of -51 degrees

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E5C19 -- Which point on Figure E5-2 best represents that impedance of a series circuit consisting of a 400 ohm resistor and a 38 picofarad capacitor at 14 MHz? Point 2 Point 4 Point 5 Point 6

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E5C20 -- Which point in Figure E5-2 best represents the impedance of a series circuit consisting of a 300 ohm resistor and an 18 microhenry inductor at MHz? Point 1 Point 3 Point 7 Point 8

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E5C21 -- Which point on Figure E5-2 best represents the impedance of a series circuit consisting of a 300 ohm resistor and a 19 picofarad capacitor at MHz? Point 1 Point 3 Point 7 Point 8

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E5C22 -- In rectangular coordinates, what is the impedance of a network consisting of a 10-microhenry inductor in series with a 40-ohm resistor at 500 MHz? 40 + j31,400 40 - j31,400 31,400 + j40 31,400 - j40

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**Point 1 Point 3 Point 5 Point 8**

E5C23 -- Which point on Figure E5-2 best represents the impedance of a series circuit consisting of a 300-ohm resistor, a 0.64-microhenry inductor and an 85-picofarad capacitor at MHz? Point 1 Point 3 Point 5 Point 8

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Break

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**Electrical Principles**

Reactive Power & Power Factor Power Rate of doing work (using energy) over time. 1 Watt = 1 Joule/second

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**Electrical Principles**

Reactive Power & Power Factor Resistive Power Resistance consumes energy. Voltage & current are in phase (θ = 0°). Work is done. Power is used.

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**Electrical Principles**

Reactive Power & Power Factor Reactive Power Capacitance & inductance only store & return energy, they do not consume it. Voltage & current are 90° out of phase (θ = 90°). No work is done. No power is used.

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**Electrical Principles**

Reactive Power & Power Factor Reactive Power P = I x E only works when voltage & current are in phase. True formula is P = I x E x cos(θ) cos(0°) = 1 cos(90°) = 0 P = I x E apparent power. Expressed as Volt-Amperes (V-A) rather than Watts.

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**Electrical Principles**

Reactive Power & Power Factor Power Factor P = I x E Apparent Power P= I x E x cos(θ) Real Power Power Factor (PF) = (Real Power) / (Apparent Power) PF = cos(θ) Real Power = Apparent Power x PF.

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E5D09 -- What happens to reactive power in an AC circuit that has both ideal inductors and ideal capacitors? It is dissipated as heat in the circuit It is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated It is dissipated as kinetic energy in the circuit It is dissipated in the formation of inductive and capacitive fields

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E5D10 -- How can the true power be determined in an AC circuit where the voltage and current are out of phase? By multiplying the apparent power times the power factor By dividing the reactive power by the power factor By dividing the apparent power by the power factor By multiplying the reactive power times the power factor

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E5D11 -- What is the power factor of an R-L circuit having a 60 degree phase angle between the voltage and the current? 1.414 0.866 0.5 1.73

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E5D12 -- How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-V AC at 4 amperes? 400 watts 80 watts 2000 watts 50 watts

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E5D13 -- How much power is consumed in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere? 70.7 Watts 100 Watts 141.4 Watts 200 Watts

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**E5D14 -- What is reactive power?**

Wattless, nonproductive power Power consumed in wire resistance in an inductor Power lost because of capacitor leakage Power consumed in circuit Q

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E5D15 -- What is the power factor of an RL circuit having a 45 degree phase angle between the voltage and the current? 0.866 1.0 0.5 0.707

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E5D16 -- What is the power factor of an RL circuit having a 30 degree phase angle between the voltage and the current? 1.73 0.5 0.866 0.577

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E5D17 -- How many watts are consumed in a circuit having a power factor of 0.6 if the input is 200V AC at 5 amperes? 200 watts 1000 watts 1600 watts 600 watts

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E5D18 -- How many watts are consumed in a circuit having a power factor of 0.71 if the apparent power is 500 VA? 704 W 355 W 252 W 1.42 mW

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**Electrical Principles**

Resonance Mechanical systems have a natural frequency where they want to vibrate when stimulated. This is called resonance. Electrical circuits containing both capacitors and inductors behave in a similar manner.

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**Electrical Principles**

Resonant Circuits As frequency increases, inductive reactance increases. As frequency increases, capacitive reactance decreases. At some frequency, inductive reactance & capacitive reactance will be equal. This is called the resonant frequency. 1 f = R 2π LC

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**Electrical Principles**

Resonant Circuits At the resonant frequency: XL = XC Inductive & capacitive reactances cancel each other out. Circuit impedance is purely resistive. Voltage & current are in phase. Series L-C circuit impedance = 0 Ω (short circuit). Current is maximum. Parallel L-C circuit impedance = ∞ Ω (open circuit). Current is minimum.

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**Electrical Principles**

Resonant Circuits Series Resonant Circuit Impedance is at the minimum. Z = RS Voltage across resistor equal to applied voltage. Sum of individual voltages greater than applied voltage.

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**Electrical Principles**

Resonant Circuits Series Resonant Circuit Capacitive below resonance. Resistive at resonance. Inductive above resonance.

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**Electrical Principles**

Resonant Circuits Parallel Resonant Circuit Impedance is at the maximum. Z = RP Current through resistor equals current through circuit. Sum of currents through all components greater than current through circuit.

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**Electrical Principles**

Resonant Circuits Parallel Resonant Circuit Inductive below resonance. Resistive at resonance. Capacitive above resonance.

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E5A01 -- What can cause the voltage across reactances in series to be larger than the voltage applied to them? Resonance Capacitance Conductance Resistance

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**E5A02 -- What is resonance in an electrical circuit?**

The highest frequency that will pass current The lowest frequency that will pass current The frequency at which the capacitive reactance equals the inductive reactance The frequency at which the reactive impedance equals the resistive impedance

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**E5A03 -- What is the magnitude of the impedance of a series RLC circuit at resonance?**

High, as compared to the circuit resistance Approximately equal to capacitive reactance Approximately equal to inductive reactance Approximately equal to circuit resistance

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E5A04 -- What is the magnitude of the impedance of a circuit with a resistor, an inductor and a capacitor all in parallel, at resonance? Approximately equal to circuit resistance Approximately equal to inductive reactance Low, as compared to the circuit resistance Approximately equal to capacitive reactance

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E5A05 -- What is the magnitude of the current at the input of a series RLC circuit as the frequency goes through resonance? Minimum Maximum R/L L/R

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E5A06 -- What is the magnitude of the circulating current within the components of a parallel LC circuit at resonance? It is at a minimum It is at a maximum It equals 1 divided by the quantity 2 times Pi, multiplied by the square root of inductance L multiplied by capacitance C It equals 2 multiplied by Pi, multiplied by frequency "F", multiplied by inductance "L”

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**E5A07 -- What is the magnitude of the current at the input of a parallel RLC circuit at resonance?**

Minimum Maximum R/L L/R

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E5A08 -- What is the phase relationship between the current through and the voltage across a series resonant circuit at resonance? The voltage leads the current by 90 degrees The current leads the voltage by 90 degrees The voltage and current are in phase The voltage and current are 180 degrees out of phase

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E5A09 -- What is the phase relationship between the current through and the voltage across a parallel resonant circuit at resonance? The voltage leads the current by 90 degrees The current leads the voltage by 90 degrees The voltage and current are in phase The voltage and current are 180 degrees out of phase

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E5A14 -- What is the resonant frequency of a series RLC circuit if R is 22 ohms, L is 50 microhenrys and C is 40 picofarads? 44.72 MHz 22.36 MHz 3.56 MHz 1.78 MHz

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E5A15 -- What is the resonant frequency of a series RLC circuit if R is 56 ohms, L is 40 microhenrys and C is 200 picofarads? 3.76 MHz 1.78 MHz 11.18 MHz 22.36 MHz

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E5A16 -- What is the resonant frequency of a parallel RLC circuit if R is 33 ohms, L is 50 microhenrys and C is 10 picofarads? 23.5 MHz 23.5 kHz 7.12 kHz 7.12 MHz

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E5A17 -- What is the resonant frequency of a parallel RLC circuit if R is 47 ohms, L is 25 microhenrys and C is 10 picofarads? 10.1 MHz 63.2 MHz 10.1 kHz 63.2 kHz

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Quality factor (Q). Ratio of power stored (PS) in circuit to power dissipated (PD) in circuit. Q = PS / PD PS = I2 x X PD = I2 x R Q = X / R

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Quality factor (Q). Q always goes down when resistance is added in series with a component. Internal series resistance of an inductor is almost always greater than internal series resistance of a capacitor. Resistance of inductor is primarily responsible for Q of circuit.

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Quality factor (Q). Q affects bandwidth & efficiency of circuit. Higher Q Higher efficiency (lower losses). Higher Q Narrower bandwidth.

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Quality factor (Q). Same rules apply to parallel resonant circuits, but underlying math is a little more messy. Q = PS / PD

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Bandwidth. Half-power bandwidth (BW). Frequency difference between -3dB points (BW = f2-f1). BW = f0 / Q

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Bandwidth. BW = -3 dB points. Δf = fR / Q

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**Electrical Principles**

“Q” and Bandwidth of Resonant Circuits Skin effect and Q. As frequency is increased, current flow is concentrated at the outer surface of conductor Effective cross-sectional area is reduced. Effective resistance is increased. Q is reduced. As frequency is increased, Q of an inductor increases until skin effect takes over & Q is reduced.

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E4B15 -- Which of the following can be used as a relative measurement of the Q for a series-tuned circuit? The inductance to capacitance ratio The frequency shift The bandwidth of the circuit's frequency response The resonant frequency of the circuit

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E5A10 -- What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 1.8 MHz and a Q of 95? 18.9 kHz 1.89 kHz 94.5 kHz 9.45 kHz

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E5A11 -- What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150? 157.8 Hz 315.6 Hz 47.3 kHz 23.67 kHz

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E5A12 -- What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118? 436.6 kHz 218.3 kHz 31.4 kHz 15.7 kHz

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E5A13 -- What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of MHz and a Q of 187? 38.1 kHz 76.2 kHz 1.332 kHz 2.665 kHz

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**E5D01 -- What is the result of skin effect?**

As frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface As frequency decreases, RF current flows in a thinner layer of the conductor, closer to the surface Thermal effects on the surface of the conductor increase the impedance Thermal effects on the surface of the conductor decrease the impedance

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**E5D02 -- Why is the resistance of a conductor different for RF currents than for direct currents?**

Because the insulation conducts current at high frequencies Because of the Heisenburg Effect Because of skin effect Because conductors are non-linear devices

136
**Electrical Principles**

Magnetic Cores Core is whatever material wire is wound around. Coil can be wound on: Non-ferrous material. Air. Plastic. Cardboard. Iron. Powdered Iron. Ferrite.

137
**Electrical Principles**

Magnetic Cores Adding a core of magnetic material concentrates magnetic field in the core. Higher inductance. More efficient. Permeability (µ) Measurement of amount of concentration. µ = HC / HA (H = magnetic field strength) Permeability of air = 1.

138
**Electrical Principles**

Magnetic Cores Core Materials Air Lowest inductance. Iron Low frequency (power supplies, AF). Higher losses.

139
**Electrical Principles**

Magnetic Cores Core Materials Powdered Iron. Fine iron powder mixed with non-magnetic binding material. Lower losses. Better temperature stability. Ferrite Nickel-zinc or magnesium-zinc added to powdered iron. Higher permeability.

140
**Electrical Principles**

Magnetic Cores Core Materials Choice of proper core material allows inductor to perform well over the desired frequency range. AF to UHF.

141
**Electrical Principles**

Magnetic Cores Core shapes. Solenoid Coil. Inductance determined by: Number of turns. Diameter of turns. Distance between turns (turn spacing). Permeability (µ) of core material. Book says solenoidal coil fairly uncommon in electronics – WRONG! Very common in low inductance, high-power applications such as RF amplifier tank circuits.

142
**Electrical Principles**

Magnetic Cores Core shapes. Solenoid Coil. Magnetic field not confined within coil. Mutual Inductance & coupling. Book says solenoidal coil fairly uncommon in electronics – WRONG! Very common in low inductance, high-power applications such as RF amplifier tank circuits.

143
**Electrical Principles**

Magnetic Cores Toroidal Coil Magnetic field almost completely confined within coil. No stray coupling. <20 Hz to about 300 MHz with proper material choice.

144
**Electrical Principles**

Calculating Inductance Inductance Index (AL) Value provided by manufacturer of core. Accounts for permeability of core. Powdered Iron Cores L = AL x N2 / 10,000 L = Inductance in uH AL = Inductance Index in uH/(100 turns). N = Number of Turns

145
**Electrical Principles**

Calculating Inductance Powdered Iron Cores L = AL x N2 / 10,000 N = 100 x L / AL L = Inductance in uH AL = Inductance Index in uH/(100 turns). N = Number of Turns

146
**Electrical Principles**

Calculating Inductance Ferrite Cores L = AL x N2 / 1,000,000 N = 1000 x L / AL L = Inductance in mH AL = Inductance Index in mH/(1000 turns). N = Number of Turns

147
**Electrical Principles**

Ferrite Beads RF suppression at VHF & UHF.

148
**E6D06 -- What core material property determines the inductance of a toroidal inductor?**

Thermal impedance Resistance Reactivity Permeability

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E6D07 -- What is the usable frequency range of inductors that use toroidal cores, assuming a correct selection of core material for the frequency being used? From a few kHz to no more than 30 MHz From less than 20 Hz to approximately 300 MHz From approximately 10 Hz to no more than 3000 kHz From about 100 kHz to at least 1000 GHz

150
E6D08 -- What is one important reason for using powdered-iron toroids rather than ferrite toroids in an inductor? Powdered-iron toroids generally have greater initial permeability Powdered-iron toroids generally maintain their characteristics at higher currents Powdered-iron toroids generally require fewer turns to produce a given inductance value Powdered-iron toroids have higher power handling capacity

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E6D09 -- What devices are commonly used as VHF and UHF parasitic suppressors at the input and output terminals of transistorized HF amplifiers? Electrolytic capacitors Butterworth filters Ferrite beads Steel-core toroids

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E6D10 -- What is a primary advantage of using a toroidal core instead of a solenoidal core in an inductor? Toroidal cores confine most of the magnetic field within the core material Toroidal cores make it easier to couple the magnetic energy into other components Toroidal cores exhibit greater hysteresis Toroidal cores have lower Q characteristics

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E6D11 -- How many turns will be required to produce a 1-mH inductor using a ferrite toroidal core that has an inductance index (A L) value of 523 millihenrys/1000 turns? 2 turns 4 turns 43 turns 229 turns

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E6D12 -- How many turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A L) value of 40 microhenrys/100 turns? 35 turns 13 turns 79 turns 141 turns

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E6D16 -- What is one reason for using ferrite toroids rather than powdered-iron toroids in an inductor? Ferrite toroids generally have lower initial permeabilities Ferrite toroids generally have better temperature stability Ferrite toroids generally require fewer turns to produce a given inductance value Ferrite toroids are easier to use with surface mount technology

156
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Fundamentals of Electric Circuits Chapter 11

Fundamentals of Electric Circuits Chapter 11

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