Amateur%20Extra%20Licensing%20Class

1
Amateur Extra Licensing Class
Circuits Resonance for All!

• Lake Area Radio Klub
• Spring 2012

2
Amateur Radio Extra ClassElement 4 Course
Presentation

• ELEMENT 4 Groupings
• Rules Regs
• Skywaves Contesting
• Outer Space Comms
• Visuals Video Modes
• Digital Excitement with Computers Radios
• Modulate Your Transmitters
• Amps Power Supplies
• Receivers with Great Filters

3
Amateur Radio Extra ClassElement 4 Course
Presentation

• ELEMENT 4 Groupings
• Oscillate Synthesize This!
• Circuits Resonance for All!
• Components in Your New Rig
• Logically Speaking of Counters
• Optos OpAmps Plus Solar
• Test Gear, Testing, Testing 1,2,3
• Antennas
• Feedlines Safety

4
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A01 Resonance can cause the voltage across
  reactances in series to be larger than the
  voltage applied to them.

Lets go through the math step by step
5
Amateur Radio Extra ClassCircuits Resonance
for All!
Resonance occurs in a circuit when XL is equal to
XC.
Therefore..
What we do to the left side of the equation, we
must do to the right side, and what we do to the
numerator we must do to the denominator, to
maintain equality
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Amateur Radio Extra ClassCircuits Resonance
for All!
This is the resonant frequency formula.
7
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A02 Resonance in an electrical circuit is the
  frequency at which the capacitive reactance
  equals the inductive reactance.
• E5A03 The magnitude of the impedance of a series
  R-L-C circuit at resonance is approximately equal
  to circuit resistance.
• E5A04 The magnitude of the impedance of a
  circuit with a resistor, an inductor and a
  capacitor all in parallel, at resonance is
  approximately equal to circuit resistance.

At resonance, a series resonant circuit L and C
present a low impedance so the circuit resistance
is set by the resistor.
At resonance, a parallel resonant circuit
presents a very high impedance across the
resistor.
8
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A05The magnitude of the current at the input
  of a series R-L-C circuit as the frequency goes
  through resonance is Maximum.
• At resonance a series circuit presents a low
  impedance and current would be limited by the
  resistor Tuning to either side of resonance
  would cause additional reactive resistance and
  therefore lower current flow in the circuit.

Series and Parallel Resonant Circuits.
9
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A06 The magnitude of the circulating current
  within the components of a parallel L-C circuit
  at resonance is at a maximum.

Variation of Inductive and capacitive reactance
with frequency (graph not to exact log-log scale)
10
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A07 The magnitude of the current at the input
  of a parallel R-L-C circuit at resonance is at a
  Minimum.
• E5A08 The voltage and the current through and
  the voltage across a series resonant circuit are
  in phase.
• E5A09 The current through and the voltage across
  a parallel resonant circuit are in phase.

(also true for a series circuit at resonance)
11
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B07 The phase angle between the voltage across
  and the current through a series R-L-C circuit if
  XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms
  is 14.0 degrees with the voltage lagging the
  current.

? 14.04
Tangent of ? .25
Tangent of ? 250/1000
Tangent of ? Y / X
Series RLC Circuits for Phase angle Calculations
12
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B08 The phase angle between the voltage across
  and the current through a series R-L-C circuit if
  XC is 100 ohms, R is 100 ohms, and XL is 75 ohms
  is 14 degrees with the voltage lagging the
  current.
• Rules for calculating impedances and phase
  angles
• 1) Impedances in series add together
• 2) Admittance is the reciprocal of impedance
• 3) Admittances in parallel add together
• 4) Inductive and capacitive reactance in
  series cancel
• 5) 1/j-j

? -14.04
Tangent of ? Y / X
Tangent of ? (75-100)/100
Tangent of ? -.25
Complex number axis diagram.
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Amateur Radio Extra ClassCircuits Resonance
for All!

• Here is more detail. In an ac circuit, when
  calculating the impedance of the circuit, the
  reactance and resistance must be added
  vectorially rather than algebraically. This
  vector addition can be understood best by looking
  at the following diagram

Vector Addition
14
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B09 The relationship between the current
  through and the voltage across a capacitor is
  that the current leads the voltage by 90 degrees.
  
• E5B10 The relationship between the current
  through an inductor and the voltage across an
  inductor is that the voltage leads current by 90
  degrees.
• E5B11 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
  is 14 degrees with the voltage leading the
  current.

Remember ELI the ICE man.
? 14.04
Tangent of ? Y / X
Tangent of ? (50-25)/100
Tangent of ? .25
j 50
- j 25
100 O
15
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B12 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
  is 14 degrees with the voltage lagging the
  current.

? -14.04
Tangent of ? Y / X
Tangent of ? (50-75)/100
Tangent of ? -.25
100 O
j50
- j 75
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B13 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
  is 14.04 degrees with the voltage leading the
  current.

? 14.04
Tangent of ? (500-250)/1000
Tangent of ? 0.25
Tangent of ? Y / X
j 500
- j 250
1000 O
17
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C13 The Rectangular coordinate system is often
  used to display the resistive, inductive, and/or
  capacitive reactance components of impedance.
• E5C09 When using rectangular coordinates to
  graph the impedance of a circuit, the horizontal
  axis represents the voltage or current associated
  with the resistive component.

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Amateur Radio Extra ClassCircuits Resonance
for All!
Rectangular Coordinates
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Amateur Radio Extra ClassCircuits Resonance
for All!
Polar Coordinates
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C22 In rectangular coordinates, what is the
  impedance of a network comprised of a
  10-microhenry inductor in series with a 40-ohm
  resistor at 500 MHz?
• R 40O
• Remember Inductive Reactance is positive so the
  answer is
• 40 j 31,400
• E5C17 In rectangular coordinates, the impedance
  of a circuit that has an admittance of 5
  millisiemens at -30 degrees is 173 j100 ohms.

XL (6.28 x 500 x 106 x 10 x 10-6)
XL 31,416 O
XL (2 p FL)
Polar Impedance (Z) 1/admittance
Z 1/.005
Z 200O
Polar angle 1/admittance angle
1/- 30
30
Cos ? resistance (R) / Impedance (Z)
R 200O x Cosine 30
R 200O x .866
173.2 O
Sin ? reactance (j) / Impedance (Z)
j 200 x Sine 30
j 200O x .50
j100O
Dont be tempted to use a -j in front of the
reactance with the admittance given initially
with -30o angle.
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C10 When using rectangular coordinates to
  graph the impedance of a circuit, the vertical
  axis represents the voltage or current associated
  with the reactive component.
• E5C11 The two numbers used to define
• 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 line, you know the
  circuit is equivalent to a pure resistance.

a point on a graph using rectangular
coordinates represent the coordinate values along
the horizontal and vertical axes.
22
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C19 In Figure E5-2, point 4 best represents
  that impedance of a series circuit consisting of
  a 400 ohm resistor and a 38 picofarad capacitor
  at 14 MHz.
• R 400 O
• XC 1/ (2 p FC)
• XC 1/(6.28 x 14 x .000038)
• XC -300 O
• Remember
• Capacitive reactance is negative.

Figure E5-2
23
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C20 In Figure E5-2, Point 3 best represents
  the impedance of a series circuit consisting of a
  300 ohm resistor and an 18 microhenry inductor at
  3.505 MHz.
• R 300 O
• XL (2 p FL)
• XL (6.28 x 3.505 x 18)
• XL 396.4 O
• Remember
• Inductive reactance is positive
• Answer is 300 O j 395 O

Figure E5-2
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C21 In Figure E5-2, Point 1 best represents
  the impedance of a series circuit consisting of a
  300 ohm resistor and a 19 picofarad capacitor at
  21.200 MHz.
• R 300 O
• XC 1/ (2 p FC)
• XC 1/(6.28 x 21.2 x .000019)
• XC -395.1 O
• Remember
• Capacitive reactance is negative
• Answer is 300 O j 395

Figure E5-2
25
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C23 On Figure E5-2, Point 8 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 24.900 MHz.
• R 300 O
• XC 1/ (2 p FC)
• XC 1/(6.28 x 24.9 x .000085)
• XC -75.19 O (XC is negative)
• XL (2 p FL)
• XL (6.28 x 24.9 x .64)
• XL 100.12 O (XL is positive)
• Net reactance is the sum of XC and XL
• -75.19 100.12 24.9
• Answer is 300 O j 24.9

Figure E5-2
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C14 The Polar coordinate system is often used
  to display the phase angle of a circuit
  containing resistance, inductive and/or
  capacitive reactance.
• E5C04 In polar coordinates, the impedance of a
  network consisting of a 400-ohm-reactance
  capacitor in series with a 300-ohm resistor is
  500 ohms at an angle of -53.1 degrees.

Z v(X² (XL XC)²) Z v( 300² (0-400)²) Z
v(250,000) Z 500 O ? arc tan
(reactance/resistance) arc tan (-400/300) arc
tan (- 1.33) -53.13
300O
-j400
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Amateur Radio Extra ClassCircuits Resonance
for All!
Complex Numbers (Real and Imaginary and Operator j
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Amateur Radio Extra ClassCircuits Resonance
for All!
j Operator as Vector Rotator
29
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C01 In polar coordinates, the impedance of a
  network consisting of a 100-ohm-reactance
  inductor in series with a 100-ohm resistor is 141
  ohms at an angle of 45.
• Z v(X² Y²)
• Z v(100² 100²)
• Z v( 20,000)
• Z 141.42 O
• ? arc tan (reactance/resistance)
• arc tan 100/100
• arc tan 1 or 45

j 100
100 O
30
Amateur Radio Extra ClassCircuits Resonance
for All!

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

Impedance

120,000 / 500 240 O
? arctan 1/ (Reactance/Resistance) ? arctan
1/ (400 / 300) ? arctan 1/ 1.333 arctan .750 ?
36.87
31
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C02 In polar coordinates, 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 is 100
  ohms at an angle of 0 degrees.

Z v( R² (XL XC)²)
Z v( 100² (100-100)²)
j 100
Z v( 10,000)
100 O
Z 100 O
? arc tan (reactance/resistance)
- j 100
arc tan 0/100
arc tan 0
0
Note- the Y side is the vector sum of the
inductive reactance and capacitive reactance or
(XL Xc) j 100-j 100100 O
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C03 In polar coordinates, 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 is 500
  ohms at an angle of 37 degrees.
• Z v(R² (XL Xc)²)
• Z v( 400² (600-300)²)
• Z v( 250,000)
• Z 500 O
• ? arc tan (reactance/resistance)
• 300/400
• arc tan .75
• 36.9

j 600
400O
- j300
33
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C06 In polar coordinates, the impedance of a
  network consisting of a 100-ohm-reactance
  capacitor in series with a 100-ohm resistor is
  141 ohms at an angle of -45 degrees.
• E5C07 In polar coordinates, the impedance of a
  network comprised of a 100-ohm-reactance
  capacitor in parallel with a 100-ohm resistor is
  71 ohms at an angle of -45 degrees.

Angle is arctan 1/ (reactance/resistance) arctan
1/ (100/100) arc tan (- 1) -45
Z v(X² (XL Xc)²) Z v( 100² (-100)²) Z
v(20,000) Z 141.4 O
Admittance 1/100 ( -j/100) 0.01 j 0.01
Angle arc tan .01/.01 45 (-45 in polar
coordinates)
Impedance 1/ (v ( (.01)² x (.01)²
)) 1/(.0141) 70.71 ?
34
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C07 In polar coordinates, the impedance of a
  network comprised of a 100-ohm-reactance
  capacitor in parallel with a 100-ohm resistor is
  71 ohms at an angle of -45 degrees.
• E5C08 In polar coordinates, the impedance of a
  network comprised of a 300-ohm-reactance inductor
  in series with a 400-ohm resistor is 500 ohms at
  an angle of 37 degrees.

Admittance 1/100 (-j/100) 0.01 j 0.01 Angle
arc tan .01/.01 45 (-45 in polar
coordinates)
Impedance 1/ (v ( (.01)² x (.01)²
)) 1/(.0141) 70.71 ?
Angle is arc tan (X/R) arc tan (300/400) arc tan
(.75) 36.86
Z v(X² (XL XC)²) Z v( 400² (0-300)²) Z
v(250,000) Z 500 O
j300
400O
35
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C15 In polar coordinates, the impedance of a
  circuit of 100 -j100 ohms impedance is 141 ohms
  at an angle of -45 degrees.
• E5C16 In polar coordinates, the impedance of a
  circuit that has an admittance of 7.09
  milli-siemens at 45 degrees is 141 ohms at an
  angle of -45 degrees.

Angle is arc tan (X/R) arc tan (-100/100) arc tan
(-1) -45
Z v(X² (XL XC)²) Z v( 100² ( -100)²) Z
v(20,000) Z 141.42 O
Polar Impedance (Z) 1/admittance Z 1/.00709
Z 141.04O
Polar angle 1 / j (admittance angle) 1/j(45)
-j45
36
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5C18 In polar coordinates, 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 is 5 ohms at an
  angle of 37 degrees.
• Z v(X² (XL Xc)²)
• Z v( 4² (4-1)²)
• Z v(25) or Z 5 O
• Angle is arc tan (X/R)
• arc tan (3/4)
• arc tan (.75)
• 36.86

- j 1
j 4
4O
37
Amateur Radio Extra ClassCircuits Resonance
for All!

• E4B17 The bandwidth of the circuit's frequency
  response can be used as a relative measurement of
  the Q for a series-tuned circuit.
• The Narrower the bandwidth the higher the Q of
  the circuit.

A large loading coil on a mobile whip helps
antennas achieve high Q resonance.
38
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A10 The half-power bandwidth of a parallel
  resonant circuit that has a resonant frequency of
  1.8 MHz and a Q of 95 is 18.9 kHz.

B/W Frequency/Q
1,800 KHz/95
18.94 KHz
For tuned circuits the quality factor, Q, is
For tuned circuits with Q greater than 10
39
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A11 The half-power bandwidth of a parallel
  resonant circuit that has a resonant frequency of
  7.1 MHz and a Q of 150 is 47.3 kHz.

B/W Frequency/Q
7,100 KHz/150
47.3 KHz
An amplifiers voltage gain will vary with
frequency. At the cutoff frequencies, the
voltage gain drops to 0.070 of what is in the
mid-band. These frequencies f1 and f2 are called
the half-power frequencies.
If the output voltage is 10 volts across a
100-ohm load when the gain is A at the mid-band,
then the power output, PO at mid-band is
40
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A12 The half-power bandwidth of a parallel
  resonant circuit that has a resonant frequency of
  3.7 MHz and a Q of 118 is 31.4 kHz.

Power Ratio in dB
At the cutoff frequency, the output voltage will
be 0.707 of what is at the mid-band therefore,
7.07 volts. The power output is
The power output at the cutoff frequency points
is one-half the mid-band power. The half-power
bandwidth is between the frequencies f1 and f2.
The power output at the 0.707 frequencies is 3 dB
down from the mid-band power.
B/W Frequency/Q
3,700 KHz/118
31.36 KHz
41
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A13 The half-power bandwidth of a parallel
  resonant circuit that has a resonant frequency of
  14.25 MHz and a Q of 187 is 76.2 kHz.
• E5A14 The resonant frequency of a series RLC
  circuit with R of 22 ohms, L of 50 microhenrys
  and C of 40 picofarads is 3.56 MHz.
• The equation can be solved with
• L in Henries or Micro Henries and
• C in Farads or Micro Farads

B/W Frequency/Q
14,250 KHz/187
76.20 KHz
50 mh
22 ohms
40 pf
42
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5A15 The resonant frequency of a series RLC
  circuit with R of 56 ohms, L of 40 microhenrys
  and C of 200 picofarads is 1.78 MHz.
• E5A16 The resonant frequency of a parallel RLC
  circuit with R of 33 ohms, L of 50 microhenrys
  and C of 10 picofarads is 7.12 MHz.
• E5A17 The resonant frequency of a parallel RLC
  circuit with R of 47 ohms, L of 25 microhenrys
  and C of 10 picofarads is 10.1 MHz.

43
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B01 One time constant is the term for the
  time required for the capacitor in an RC circuit
  to be charged to 63.2 of the supply voltage.

Schematics
Curves
44
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B02 One time constant is the time it takes for
  a charged capacitor in an RC circuit to discharge
  to 36.8 of its initial value of stored charge.
• Conversely a time constant is the time it takes
  a discharged capacitor to reach 63.2 of the
  applied voltage.

Time Constants Charge of applied voltage Discharge 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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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B03 The capacitor in an RC circuit is
  discharged to 13.5 percentage of the starting
  voltage after two time constants.
• (100-((100 x .632)) (100 (100 x.632) x
  .632))
• 100(- 63.2 23.25)
• 13.54
• E5B04 The time constant of a circuit having two
  220-microfarad capacitors and two 1-megohm
  resistors all in parallel is 220 seconds.
• TC (seconds) R (megohms) x C (microfarads)
• TC (1/2) x (220 x 2)
• 0.5 x 440
• 220 seconds
• Remember that capacitors in parallel add and
  resistors of equal value in parallel are equal
  to one resistor divided by the number of
  resistors.

46
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5B05 It will take .020 seconds (or 20
  milliseconds) 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.
• To discharge to 7.36 VDC would take one time
  constant
• 20V (.632 x 20V)
• 7.36 Volts
• E5B06 It takes 450 seconds 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.
• To discharge to 294 VDC would take one time
  constant
• 800V (.632 x 800V) 294.4V

0.02 seconds
20 milliseconds
TC 2 x .01
TC 1 x 450
450 seconds
47
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D01 As frequency increases, RF current flows
  in a thinner layer of the conductor, closer to
  the surface this is called skin effect.
• E5D02 The resistance of a conductor is
  different for RF currents than for direct
  currents because of skin effect.
• E5D03 A capacitor is a device that is used to
  store electrical energy in an electrostatic
  field.
• E5D04 The Joule is the unit of electrical energy
  stored in an electrostatic field.
• A Joule is defined as a quantity of energy equal
  to one Newton of force acting over 1 meter

48
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D05 The region surrounding a magnet through
  which a magnetic force acts is a magnetic field.
• E5D06 The direction of the magnetic field
  oriented about a conductor in relation to the
  direction of electron flow is in a direction
  determined by the left-hand rule.

Direction of Magnetic Field
Magnetic Field surrounding wire
Wire or Conductor with current through it
Left-Hand Rule
49
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D07 The amount of current determines the
  strength of a magnetic field around a conductor.
• E5D08 Potential energy is the term for energy
  that is stored in an electromagnetic or
  electrostatic field.
• E5D09 Reactive power is the term for an
  out-of-phase, nonproductive power associated with
  inductors and capacitors.
• E5D10 In a circuit that has both inductors and
  capacitors the reactive power is repeatedly
  exchanged between the associated magnetic and
  electric fields, but is not dissipated.
• E5D11 The true power can be determined in an AC
  circuit where the voltage and current are out of
  phase by multiplying the apparent power times the
  power factor.
• Apparent power is the voltage times the current
  into the circuit
• True Power is the apparent power times the
  power factor
• The only time true power and apparent power are
  the same is if the power factor is 1.00 (the
  phase angle is zero)

(assuming perfect lossless components)
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Amateur Radio Extra ClassCircuits Resonance
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Apparent and True Power
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Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D12 The power factor (PF) of an R-L circuit
  having a 60 degree phase angle between the
  voltage and the current is 0.5.
• PF is the cosine function of the voltage to
  current angle
• ?PF cosine of 60
• PF 0.5
• E5D13 80 watts are consumed in a circuit having
  a power factor of 0.2 if the input is 100-V AC at
  4 amperes.

Power Consumed V x I x PF
100 x 4 x .2
80 watts
52
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D14 The power is consumed in a circuit
  consisting of a 100 ohm resistor in series with a
  100 ohm inductive reactance drawing 1 ampere is
  100 Watts.
• Power (real) I² x R
• Power (real) (1)² x 100
• 100 watts. (Only the circuit resistance
  consumes power)
• E5D15 Wattless, nonproductive power is reactive
  power.
• E5D16 The power factor of an RL circuit having a
  45 degree phase angle between the voltage and the
  current is 0.707.
• PF Cosine of 45
• PF 0.707

53
Amateur Radio Extra ClassCircuits Resonance
for All!

• E5D17 The power factor of an RL circuit having a
  30 degree phase angle between the voltage and the
  current is 0.866.
• PF Cosine of 30
• PF 0.866
• E5D18 600 watts are consumed in a circuit having
  a power factor of 0.6 if the input is 200V AC at
  5 amperes.
• Power Consumed V x I x PF
• 200 x 5 x .6
• 600 watts
• E5D19 The power consumed in a circuit having a
  power factor of 0.71 if the apparent power is 500
  watts is 355 W.
• Power Consumed Apparent power x PF
• 500 x .71
• 355 watts

54
Amateur Radio Extra ClassCircuits Resonance
for All!

• E4E04 Conducted and radiated noise caused by an
  automobile alternator can be suppressed by
  connecting the radio's power leads directly to
  the battery and by installing Feed Through
  capacitors in line with the alternator leads.
• E4E05 Noise from an electric motor can be
  suppressed by installing a brute-force AC-line
  filter in series with the motor leads.
• E6D08 Core permeability (for a given size core)
  is the property that determines the inductance of
  a toroidal inductor with a 10-turn winding.

55
Amateur Radio Extra ClassCircuits Resonance
for All!

• E6D09 The usable frequency range of inductors
  that use toroidal cores, assuming a correct
  selection of core material for the frequency
  being used is from less than 20 Hz to
  approximately 300 MHz.
• E6D10 One important reason for using
  powdered-iron toroids rather than ferrite toroids
  in an inductor is that powdered-iron toroids
  generally have better temperature stability.
• Applications for powdered Iron toroids would be
  oscillator and filter circuits where inductance
  stability with temperature is important.
• E6D12 A primary advantage of using a toroidal
  core instead of a solenoidal core in an inductor
  is that toroidal cores contain most of the
  magnetic field within the core material.

56
Amateur Radio Extra ClassCircuits Resonance
for All!

• E6D13 Forty three turns of wire will be required
  to produce a 1-mH inductor using a ferrite
  toroidal core that has an inductance index (AL)
  value of 523 millihenrys/1000 turns.
• N turns 1000 x (v (L / AL))
• N turns 1000 x (v (1 / 523))
• 43.7 turns
• E6D14 Thirty five turns of wire 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.
• N turns 100 x (v (L / AL))
• N turns 100 x (v (5 / 40))
• 35.35 turns
• E6D18 One reason for using ferrite toroids
  rather than powdered-iron toroids in an inductor
  is that Ferrite toroids generally require fewer
  turns to produce a given inductance value.

57
Element 4 Extra Class Question Pool
Circuits Resonance for All!
Valid July 1, 2008 Through June 30, 2012
58
E5A01 What can cause the voltage across
reactances in series to be larger than the
voltage applied to them?

1. Resonance
2. Capacitance
3. Conductance
4. Resistance

59
E5A02 What is resonance in an electrical circuit?

1. The highest frequency that will pass current
2. The lowest frequency that will pass current
3. The frequency at which the capacitive reactance
   equals the inductive reactance
4. The frequency at which the reactive impedance
   equals the resistive impedance

60
E5A03 What is the magnitude of the impedance of a
series R-L-C circuit at resonance?

1. High, as compared to the circuit resistance
2. Approximately equal to capacitive reactance
3. Approximately equal to inductive reactance
4. Approximately equal to circuit resistance

61
E5A04 What is the magnitude of the impedance of a
circuit with a resistor, an inductor and a
capacitor all in parallel, at resonance?

1. Approximately equal to circuit resistance
2. Approximately equal to inductive reactance
3. Low, as compared to the circuit resistance
4. Approximately equal to capacitive reactance

62
E5A05 What is the magnitude of the current at the
input of a series R-L-C circuit as the frequency
goes through resonance?

1. Minimum
2. Maximum
3. R/L
4. L/R

63
E5A06 What is the magnitude of the circulating
current within the components of a parallel L-C
circuit at resonance?

1. It is at a minimum
2. It is at a maximum
3. It equals 1 divided by the quantity 2
   multiplied by Pi, multiplied by the square root
   of ( inductance "L" multiplied by capacitance "C"
   )
4. It equals 2 multiplied by Pi, multiplied by
   frequency "F", multiplied by inductance "L"

64
E5A07 What is the magnitude of the current at the
input of a parallel R-L-C circuit at resonance?

1. Minimum
2. Maximum
3. R/L
4. L/R

65
E5A08 What is the phase relationship between the
current through and the voltage across a series
resonant circuit?

1. The voltage leads the current by 90 degrees
2. The current leads the voltage by 90 degrees
3. The voltage and current are in phase
4. The voltage and current are 180 degrees out of
   phase

66
E5A09 What is the phase relationship between the
current through and the voltage across a parallel
resonant circuit?

1. The voltage leads the current by 90 degrees
2. The current leads the voltage by 90 degrees
3. The voltage and current are in phase
4. The voltage and current are 180 degrees out of
   phase

67
E5B07 What is the phase angle between the voltage
across and the current through a series R-L-C
circuit if XC is 500 ohms, R is 1 kilohm, and XL
is 250 ohms?

1. 68.2 degrees with the voltage leading the current
2. 14.0 degrees with the voltage leading the current
3. 14.0 degrees with the voltage lagging the current
4. 68.2 degrees with the voltage lagging the current

68
E5B08 What is the phase angle between the voltage
across and the current through a series R-L-C
circuit if XC is 100 ohms, R is 100 ohms, and XL
is 75 ohms?

1. 14 degrees with the voltage lagging the current
2. 14 degrees with the voltage leading the current
3. 76 degrees with the voltage leading the current
4. 76 degrees with the voltage lagging the current

69
E5B09 What is the relationship between the
current through and the voltage across a
capacitor?

1. Voltage and current are in phase
2. Voltage and current are 180 degrees out of phase
3. Voltage leads current by 90 degrees
4. Current leads voltage by 90 degrees

70
E5B10 What is the relationship between the
current through an inductor and the voltage
across an inductor?

1. Voltage leads current by 90 degrees
2. Current leads voltage by 90 degrees
3. Voltage and current are 180 degrees out of phase
4. Voltage and current are in phase

71
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?

1. 14 degrees with the voltage lagging the current
2. 14 degrees with the voltage leading the current
3. 76 degrees with the voltage lagging the current
4. 76 degrees with the voltage leading the current

72
E5B12 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?

1. 76 degrees with the voltage lagging the current
2. 14 degrees with the voltage leading the current
3. 14 degrees with the voltage lagging the current
4. 76 degrees with the voltage leading the current

73
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?

1. 81.47 degrees with the voltage lagging the
   current
2. 81.47 degrees with the voltage leading the
   current
3. 14.04 degrees with the voltage lagging the
   current
4. 14.04 degrees with the voltage leading the current

74
E5C13 What coordinate system is often used to
display the resistive, inductive, and/or
capacitive reactance components of an impedance?

1. Maidenhead grid
2. Faraday grid
3. Elliptical coordinates
4. Rectangular coordinates

75
E5C09 When using rectangular coordinates to graph
the impedance of a circuit, what does the
horizontal axis represent?

1. The voltage or current associated with the
   resistive component
2. The voltage or current associated with the
   reactive component
3. The sum of the reactive and resistive components
4. The difference between the resistive and reactive
   components

76
E5C22 In rectangular coordinates, what is the
impedance of a network comprised of a
10-microhenry inductor in series with a 40-ohm
resistor at 500 MHz?

1. 40 j31,400
2. 40 - j31,400
3. 31,400 j40
4. 31,400 - j40

77
E5C17 In rectangular coordinates, what is the
impedance of a circuit that has an admittance of
5 millisiemens at -30 degrees?

1. 173 - j100 ohms
2. 200 j100 ohms
3. 173 j100 ohms
4. 200 - j100 ohms

78
E5C10 When using rectangular coordinates to graph
the impedance of a circuit, what does the
vertical axis represent?

1. The voltage or current associated with the
   resistive component
2. The voltage or current associated with the
   reactive component
3. The sum of the reactive and resistive components
4. The difference between the resistive and reactive
   components

79
E5C11 What do the two numbers represent that are
used to define a point on a graph using
rectangular coordinates?

1. The magnitude and phase of the point
2. The sine and cosine values
3. The coordinate values along the horizontal and
   vertical axes
4. The tangent and cotangent values

80
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 line, what do you
know about the circuit?

1. It has to be a direct current circuit
2. It contains resistance and capacitive reactance
3. It contains resistance and inductive reactance
4. It is equivalent to a pure resistance

81
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?

1. Point 2
2. Point 4
3. Point 5
4. Point 6

82
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
3.505 MHz?

1. Point 1
2. Point 3
3. Point 7
4. Point 8

83
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
21.200 MHz?

1. Point 1
2. Point 3
3. Point 7
4. Point 8

84
E5C23 Which point on Figure E5-2 best represents
the impedance of a series circuit consisting of a
300-ohm resistor, a 0.64-micro-henry inductor and
an 85-picofarad capacitor at 24.900 MHz?

1. Point 1
2. Point 3
3. Point 5
4. Point 8

85
E5C14 What coordinate system is often used to
display the phase angle of a circuit containing
resistance, inductive and/or capacitive reactance?

1. Maidenhead grid
2. Faraday grid
3. Elliptical coordinates
4. Polar coordinates

86
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?

1. 240 ohms at an angle of 36.9 degrees
2. 240 ohms at an angle of -36.9 degrees
3. 500 ohms at an angle of 53.1 degrees
4. 500 ohms at an angle of -53.1 degrees

87
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?

1. 121 ohms at an angle of 35 degrees
2. 141 ohms at an angle of 45 degrees
3. 161 ohms at an angle of 55 degrees
4. 181 ohms at an angle of 65 degrees

88
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?

1. 240 ohms at an angle of 36.9 degrees
2. 240 ohms at an angle of -36.9 degrees
3. 500 ohms at an angle of 53.1 degrees
4. 500 ohms at an angle of -53.1 degrees

89
E5C02 In polar coordinates, what is the impedance
of a net-work consisting of a 100-ohm-reactance
inductor, a 100-ohm-reactance capacitor, and a
100-ohm resistor, all connected in series?

1. 100 ohms at an angle of 90 degrees
2. 10 ohms at an angle of 0 degrees
3. 10 ohms at an angle of 90 degrees
4. 100 ohms at an angle of 0 degrees

90
E5C03 In polar coordinates, what is the impedance
of a net-work consisting of a 300-ohm-reactance
capacitor, a 600-ohm-reactance inductor, and a
400-ohm resistor, all connected in series?

1. 500 ohms at an angle of 37 degrees
2. 900 ohms at an angle of 53 degrees
3. 400 ohms at an angle of 0 degrees
4. 1300 ohms at an angle of 180 degrees

91
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?

1. 121 ohms at an angle of -25 degrees
2. 191 ohms at an angle of -85 degrees
3. 161 ohms at an angle of -65 degrees
4. 141 ohms at an angle of -45 degrees

92
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?

1. 31 ohms at an angle of -15 degrees
2. 51 ohms at an angle of -25 degrees
3. 71 ohms at an angle of -45 degrees
4. 91 ohms at an angle of -65 degrees

93
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?

1. 400 ohms at an angle of 27 degrees
2. 500 ohms at an angle of 37 degrees
3. 500 ohms at an angle of 47 degrees
4. 700 ohms at an angle of 57 degrees

94
E5C15 In polar coordinates, what is the impedance
of a circuit of 100 -j100 ohms impedance?

1. 141 ohms at an angle of -45 degrees
2. 100 ohms at an angle of 45 degrees
3. 100 ohms at an angle of -45 degrees
4. 141 ohms at an angle of 45 degrees

95
E5C16 In polar coordinates, what is the impedance
of a circuit that has an admittance of 7.09
millisiemens at 45 degrees?

1. 5.03 x 10 E05 ohms at an angle of 45 degrees
2. 141 ohms at an angle of -45 degrees
3. 19,900 ohms at an angle of -45 degrees
4. 141 ohms at an angle of 45 degrees

96
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?

1. 6.4 ohms at an angle of 53 degrees
2. 5 ohms at an angle of 37 degrees
3. 5 ohms at an angle of 45 degrees
4. 10 ohms at an angle of -51 degrees

97
E4B17 Which of the following can be used as a
relative measurement of the Q for a series-tuned
circuit?

1. The inductance to capacitance ratio
2. The frequency shift
3. The bandwidth of the circuit's frequency response
4. The resonant frequency of the circuit

98
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?

1. 18.9 kHz
2. 1.89 kHz
3. 94.5 kHz
4. 9.45 kHz

99
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?

1. 157.8 Hz
2. 315.6 Hz
3. 47.3 kHz
4. 23.67 kHz

100
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?

1. 436.6 kHz
2. 218.3 kHz
3. 31.4 kHz
4. 15.7 kHz

101
E5A13 What is the half-power bandwidth of a
parallel resonant circuit that has a resonant
frequency of 14.25 MHz and a Q of 187?

1. 38.1 kHz
2. 76.2 kHz
3. 1.332 kHz
4. 2.665 kHz

102
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?

1. 44.72 MHz
2. 22.36 MHz
3. 3.56 MHz
4. 1.78 MHz

103
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?

1. 3.76 MHz
2. 1.78 MHz
3. 11.18 MHz
4. 22.36 MHz

104
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?

1. 23.5 MHz
2. 23.5 kHz
3. 7.12 kHz
4. 7.12 MHz

105
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?

1. 10.1 MHz
2. 63.2 MHz
3. 10.1 kHz
4. 63.2 kHz

106
E5B01 What is the term for the time required for
the capacitor in an RC circuit to be charged to
63.2 of the supply voltage?

1. An exponential rate of one
2. One time constant
3. One exponential period
4. A time factor of one

107
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 value of stored charge?

1. One discharge period
2. An exponential discharge rate of one
3. A discharge factor of one
4. One time constant

108
E5B03 The capacitor in an RC circuit is
discharged to what percentage of the starting
voltage after two time constants?

1. 86.5
2. 63.2
3. 36.8
4. 13.5

109
E5B04 What is the time constant of a circuit
having two 220-microfarad capacitors and two
1-megohm resistors all in parallel?

1. 55 seconds
2. 110 seconds
3. 440 seconds
4. 220 seconds

110
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?

1. 0.02 seconds
2. 0.04 seconds
3. 20 seconds
4. 40 seconds

111
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?

1. 4.50 seconds
2. 9 seconds
3. 450 seconds
4. 900 seconds

112
E5D01 What is the result of skin effect?

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

113
E5D02 Why is the resistance of a conductor
different for RF currents than for direct
currents?

1. Because the insulation conducts current at high
   frequencies
2. Because of the Heisenburg Effect
3. Because of skin effect
4. Because conductors are non-linear devices

114
E5D03 What device is used to store electrical
energy in an electrostatic field?

1. A battery
2. A transformer
3. A capacitor
4. An inductor

115
E5D04 What unit measures electrical energy stored
in an electrostatic field?

1. Coulomb
2. Joule
3. Watt
4. Volt

116
E5D05 What is a magnetic field?

1. Electric current through the space around a
   permanent magnet
2. The region surrounding a magnet through which a
   magnetic force acts
3. The space between the plates of a charged
   capacitor, through which a magnetic force acts
4. The force that drives current through a resistor

117
E5D06 In what direction is the magnetic field
oriented about a conductor in relation to the
direction of electron flow?

1. In the same direction as the current
2. In a direction opposite to the current
3. In all directions omnidirectional
4. In a direction determined by the left-hand rule

118
E5D07 What determines the strength of a magnetic
field around a conductor?

1. The resistance divided by the current
2. The ratio of the current to the resistance
3. The diameter of the conductor
4. The amount of current

119
E5D08 What is the term for energy that is stored
in an electromagnetic or electrostatic field?

1. Amperes-joules
2. Potential energy
3. Joules-coulombs
4. Kinetic energy

120
E5D09 What is the term for an out-of-phase,
non-productive power associated with inductors
and capacitors?

1. Effective power
2. True power
3. Peak envelope power
4. Reactive power

121
E5D10 In a circuit that has both inductors and
capacitors, what happens to reactive power?

1. It is dissipated as heat in the circuit
2. It is repeatedly exchanged between the associated
   magnetic and electric fields, but is not
   dissipated
3. It is dissipated as kinetic energy in the circuit
4. It is dissipated in the formation of inductive
   and capacitive fields

122
E5D11 How can the true power be determined in an
AC circuit where the voltage and current are out
of phase?

1. By multiplying the apparent power times the power
   factor
2. By dividing the reactive power by the power
   factor
3. By dividing the apparent power by the power
   factor
4. By multiplying the reactive power times the power
   factor

123
E5D12 What is the power factor of an R-L circuit
having a 60 degree phase angle between the
voltage and the current?

1. 1.414
2. 0.866
3. 0.5
4. 1.73

124
E5D13 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?

1. 400 watts
2. 80 watts
3. 2000 watts
4. 50 watts

125
E5D14 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?

1. 70.7 Watts
2. 100 Watts
3. 141.4 Watts
4. 200 Watts

126
E5D15 What is reactive power?

1. Wattless, nonproductive power
2. Power consumed in wire resistance in an inductor
3. Power lost because of capacitor leakage
4. Power consumed in circuit Q

127
E5D16 What is the power factor of an RL circuit
having a 45 degree phase angle between the
voltage and the current?

1. 0.866
2. 1.0
3. 0.5
4. 0.707

128
E5D17 What is the power factor of an RL circuit
having a 30 degree phase angle between the
voltage and the current?

1. 1.73
2. 0.5
3. 0.866
4. 0.577

129
E5D18 How many watts are consumed in a circuit
having a power factor of 0.6 if the input is 200V
AC at 5 amperes?

1. 200 watts
2. 1000 watts
3. 1600 watts
4. 600 watts

130
E5D19 How many watts are consumed in a circuit
having a power factor of 0.71 if the apparent
power is 500 watts?

1. 704 W
2. 355 W
3. 252 W
4. 1.42 mW

131
E4E04 How can conducted and radiated noise caused
by an automobile alternator be suppressed?

1. By installing filter capacitors in series with
   the DC power lead and by installing a blocking
   capacitor in the field lead
2. By connecting the radio to the battery by the
   longest possible path and installing a blocking
   capacitor in both leads
3. By installing a high-pass filter in series with
   the radio's power lead and a low-pass filter in
   parallel with the field lead
4. By connecting the radio's power leads directly to
   the battery and by installing coaxial capacitors
   in line with the alternator leads

132
E4E05 How can noise from an electric motor be
suppressed?

1. By installing a ferrite bead on the AC line used
   to power the motor
2. By installing a brute-force AC-line filter in
   series with the motor leads
3. By installing a bypass capacitor in series with
   the motor leads
4. By using a ground-fault current interrupter in
   the circuit used to power the motor

133
E6D08 What material property determines the
inductance of a toroidal inductor with a 10-turn
winding?

1. Core load current
2. Core resistance
3. Core reactivity
4. Core permeability

134
E6D09 What is the usable frequency range of
inductors that use toroidal cores, assuming a
correct selection of core material for the
frequency being used?

1. From a few kHz to no more than 30 MHz
2. From less than 20 Hz to approximately 300 MHz
3. From approximately 1000 Hz to no more than 3000
   kHz
4. From about 100 kHz to at least 1000 GHz

135
E6D10 What is one important reason for using
powdered-iron toroids rather than ferrite toroids
in an inductor?

1. Powdered-iron toroids generally have greater
   initial permeabilities
2. Powdered-iron toroids generally have better
   temperature stability
3. Powdered-iron toroids generally require fewer
   turns to produce a given inductance value
4. Powdered-iron toroids have the highest power
   handling capacity

136
E6D12 What is a primary advantage of using a
toroidal core instead of a solenoidal core in an
inductor?

1. Toroidal cores contain most of the magnetic field
   within the core material
2. Toroidal cores make it easier to couple the
   magnetic energy into other components
3. Toroidal cores exhibit greater hysteresis
4. Toroidal cores have lower Q characteristics

137
E6D13 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?

1. 2 turns
2. 4 turns
3. 43 turns
4. 229 turns

138
E6D14 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?

1. 35 turns
2. 13 turns
3. 79 turns
4. 141 turns

139
E6D18 What is one reason for using ferrite
toroids rather than powdered-iron toroids in an
inductor?

1. Ferrite toroids generally have lower initial
   permeabilities
2. Ferrite toroids generally have better temperature
   stability
3. Ferrite toroids generally require fewer turns to
   produce a given inductance value
4. Ferrite toroids are easier to use with surface
   mount technology