Electrical Principles Flashcards
Reactance; inductance; capacitance; impedance; impedance transformation; resonance
What happens when inductive and capacitive reactance are equal in a series LC circuit?
A. Resonance causes impedance to be very high
B. Impedance is equal to the geometric mean of the inductance and capacitance
C. Resonance causes impedance to be very low
D. Impedance is equal to the arithmetic mean of the inductance and capacitance
C. Resonance causes impedance to be very low
Capacitive reactance is a negative imaginary component and inductive reactance is a positive imaginary component–thus, when they are equal, they cancel each other out, leaving the impedance equal to the resistance with no imaginary component. This is the minimum impedance, and thus the condition for resonance.
What is reactance?
A. Opposition to the flow of direct current caused by resistance
B. Opposition to the flow of alternating current caused by capacitance or inductance
C. Reinforcement of the flow of direct current caused by resistance
D. Reinforcement of the flow of alternating current caused by capacitance or inductance
B. Opposition to the flow of alternating current caused by capacitance or inductance
Reactance is the opposition to the flow of alternating current caused by capacitance or inductance. Reactance changes with both the capacitance and inductance of the current to act along with resistance as components of the impedance.
Note: Reactance (either from changes in capacitance and/or inductance) is going to make the circuit “react” and block (oppose) current flow in the AC circuit.
Hint: Reactance includes the letters “AC”
Which of the following is opposition to the flow of alternating current in an inductor?
A. Conductance
B. Reluctance
C. Admittance
D. Reactance
D. Reactance
Reactance is the factor listed which causes opposition to the flow of alternating current (AC) in an inductor. Both inductive (from an inductor) and capacitive (from a capacitor) reactances act with resistance to oppose the flow of current as components of impedance.
Which of the following is opposition to the flow of alternating current in a capacitor?
A. Conductance
B. Reluctance
C. Reactance
D. Admittance
C. Reactance
The Reactance is the factor which causes opposition to the flow of alternating current (AC) in a capacitor. Both capacitive (from a capacitor) and inductive (from an inductor) reactances along with resistance combine as the impedance causing the opposition to the flow of AC current through the circuit.
How does an inductor react to AC?
A. As the frequency of the applied AC increases, the reactance decreases
B. As the amplitude of the applied AC increases, the reactance increases
C. As the amplitude of the applied AC increases, the reactance decreases
D. As the frequency of the applied AC increases, the reactance increases
D. As the frequency of the applied AC increases, the reactance increases
Reactance — whether inductive or capacitive — opposes the flow of current. Inductive reactance varies proportionately with the frequency, so as frequency increases, the inductive reactance also increases.
(Capacitive reactance varies inversely with frequency.)
Notice that the equation for inductive reactance is defined with frequency, not amplitude.
The amplitude of the applied AC has no effect on reactance, eliminating two distractors.
Silly way to help remember: How does an IN-ductor react to AC? As freq IN-creases, reACtance IN-creases. It’s an IN-IN-IN! Also, indUctor goes up (capacitor goes down)
How does a capacitor react to AC?
A. As the frequency of the applied AC increases, the reactance decreases
B. As the frequency of the applied AC increases, the reactance increases
C. As the amplitude of the applied AC increases, the reactance increases
D. As the amplitude of the applied AC increases, the reactance decreases
A. As the frequency of the applied AC increases, the reactance decreases
As the frequency of the AC current applied to a capacitor increases, the reactance of the capacitor decreases.
The capacitive reactance is inversely proportional to the frequency. The higher the frequency of the AC current, the less charge can accumulate in the capacitor, and so the opposition to the current decreases.
SILLY HINT: the band AC/DC - Frequency increases - CapACitor - DeCreases
From Wikipedia:
Reactance is the opposition of a circuit element to a change of electric current or voltage, due to that element’s inductance or capacitance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current. The notion of reactance is similar to electrical resistance, but they differ in several respects.
What is the term for the inverse of impedance?
A. Conductance
B. Susceptance
C. Reluctance
D. Admittance
D. Admittance
This is just a definition. To address the distractors:
Conductance is the REAL part of the true answer. In other words, conductance is the inverse of Resistance, not impedance.
Susceptance is the IMAGINARY part of the true answer. That is, it is the inverse of Reactance as it relates to impedance.
Reluctance is the opposition to creating magnetic fields. It really has nothing to do with impedance at all.
The answer is Admittance, which is the vector of both Conductance and Susceptance - two of the distractors.
Hint: Impedance impedes, and the opposite of impeding is admitting.
What is impedance?
A. The ratio of current to voltage
B. The product of current and voltage
C. The ratio of voltage to current
D. The product of current and reactance
C. The ratio of voltage to current
Impedance is the opposition to the flow of current in an AC circuit. Impedance is composed of resistance and reactance (both capacitive and inductive).
Note: Think that “impedance” is going to “impede” or get in the way of current flow… kinda like Resistance, except it changes with frequency.
You might think of it as resistance due to inductance and capacitance on alternating current. As such, just like with Ohm’s law (R=E/I) the impedance is the ratio of voltage to current (E/I).
SILLY HINT: The correct choice is the only one with VOLTAGE following OF in the wording.
What unit is used to measure reactance?
A. Farad
B. Ohm
C. Ampere
D. Siemens
B. Ohm
The ohm (Ω) is the unit used to measure Reactance. The ohm is also the unit for electrical Impedance and Resistance, as these are all related properties that impede the flow of current in an AC circuit.
Resistance This is essentially friction against the flow of current. It is present in all conductors to some extent (except superconductors!), most notably in resistors. When the alternating current goes through a resistance, a voltage drop is produced that is in phase with the current. Resistance is mathematically symbolized by the letter “R” and is measured in the unit of ohms (Ω).
Reactance This is essentially inertia against the flow of current. It is present anywhere electric or magnetic fields are developed in proportion to an applied voltage or current, respectively; but most notably in capacitors and inductors.
When the alternating current goes through a pure reactance, a voltage drop is produced that is 90° out of phase with the current. Reactance is mathematically symbolized by the letter “X” and is measured in the unit of ohms (Ω).
Impedance This is a comprehensive expression of any and all forms of opposition to current flow, including both resistance and reactance. It is present in all circuits, and in all components.
When the alternating current goes through an impedance, a voltage drop is produced that is somewhere between 0° and 90° out of phase with the current. Impedance is mathematically symbolized by the letter “Z” and is measured in the unit of ohms (Ω), in complex form.
Perfect resistors possess resistance, but not reactance. Perfect inductors and perfect capacitors possess reactance but no resistance. All components possess impedance, and because of this universal quality, it makes sense to translate all component values (resistance, inductance, capacitance) into common terms of impedance as the first step in analyzing an AC circuit.
Which of the following devices can be used for impedance matching at radio frequencies?
A. A transformer
B. A Pi-network
C. A length of transmission line
D. All these choices are correct
D. All these choices are correct
All of the listed devices are ones that can be used to match the impedances of the circuit frequency. Impedance matching is important as it allows for maximum transfer of power from the source to the load.
What letter is used to represent reactance?
A. Z
B. X
C. B
D. Y
B. X
Mnemonic: If you pronounce reactance with an extended southern drawl, re-act-taance sounds just a little bit more like X than the other possible choices.
What occurs in an LC circuit at resonance?
A. Current and voltage are equal
B. Resistance is cancelled
C. The circuit radiates all its energy in the form of radio waves
D. Inductive reactance and capacitive reactance cancel
D. Inductive reactance and capacitive reactance cancel
Think of inductive reactance as having a positive sign and capacitive reactance having a negative sign. If they are equal, they add to zero (they cancel).
Silly hint: deCAPitate a snake by slicing horizontally (-) across the ground
IndUct (+) goes Up ^
What dB change represents a factor of two increase or decrease in power?
A. Approximately 2 dB
B. Approximately 3 dB
C. Approximately 6 dB
D. Approximately 9 dB
B. Approximately 3 dB
A two-times increase or decrease in power results in a change of approximately 3 decibels.
The logarithmic decibel scale is used to measure changes in power or signal strength.
Note: Formula to calculate change in Power in Decibels:
Δ dB=10×log10(P2/P1)
Where:
P1= reference power
P2= power being compared.
If we plug in the values given in this question we get:
Δ dB=10×log10(P2/P1)=10×log10(2/1)=10×log10(2)=10×0.3=3 dB
Hint: Watch out for (C). Amateur radio uses an S scale to measure signal strength, and a change of 1 S unit corresponds to a four-times increase in power or a 6 dB change, but this is NOT what they are asking for in this question. Don’t get fooled.
How does the total current relate to the individual currents in a circuit of parallel resistors?
A. It equals the average of the branch currents
B. It decreases as more parallel branches are added to the circuit
C. It equals the sum of the currents through each branch
D. It is the sum of the reciprocal of each individual voltage drop
C. It equals the sum of the currents through each branch
urrent doesn’t get lost. It gets split up across all of the branches of the circuit, but all the currents in all the branches add up to the total current.
The equation for the total current of a parallel circuit is:
I total = I1+I2+…+In
For an excellent, intuitive explanation of this, see the video from the Khan Academy on Kirchhoff’s current law.
Hint: The question asks about “individual currents” and while two answers mention current, only one answer–the correct one–uses the plural “currents”.
How many watts of electrical power are consumed if 400 VDC is supplied to an 800-ohm load?
A. 0.5 watts
B. 200 watts
C. 400 watts
D. 3200 watts
B. 200 watts
To solve for power use Ohm’s Law I=E/R and Watt’s Law P=I∗E, where I = current in amperes, E = voltage, R = resistance in ohms, and P = power in watts.
We know E=400V, and R=800Ω.
Method 1:
First solve for I, using I=E/R:
400/800=.5A
Then solve for P, using P=I∗E:
.5∗400=200 watts.
Method 2:
Combining the two equations gives us P=(E/R)∗E, or P=E^2/R.
Solving for the given values:
400^2/800=200 watts.
How many watts of electrical power are consumed by a 12 VDC light bulb that draws 0.2 amperes?
A. 2.4 watts
B. 24 watts
C. 6 watts
D. 60 watts
A. 2.4 watts
The amount of power (watts) used by a 12-VDC (volts direct current) light bulb that draws 0.2 amperes is 2.4 watts. The power circle equation based on Ohm’s law shows that P = I x E, where P is power in Watts, I is current in Amperes, and E is energy in Volts.
So for this question: P = I x E
P = (0.2 amperes) x (12 volts) = 2.4 watts
How many watts are consumed when a current of 7.0 milliamperes flows through a 1,250-ohm resistance?
A. Approximately 61 milliwatts
B. Approximately 61 watts
C. Approximately 11 milliwatts
D. Approximately 11 watts
A. Approximately 61 milliwatts
Approximately 61 milliwatts are dissipated when a current of 7.0 milliamperes flows through 1.25 kilohms.
By combining the Ohm’s Law equations and the power circle equations we can solve the problem.
P = Power in Watts
I = Current in Amperes
E = Energy in Volts
R = Resistance in Ohms
We are given:
Icurrent = 7.0milliamperes = 0.007Amperes
Rresistance = 1.25kilohms = 1250Ohms
To solve for P, use the power equation P=I×E and combine it with the equation from Ohm’s Law E=I×R.
This gives us: P=I×(I×R) = I^2 × R
So for this question:
P=0.007A×(0.007A×1250Ω) = 0.061Watts = 61milliwatts, or
P=(0.007A)^2×1250Ω=0.061Watts=61milliwatts
What is the PEP produced by 200 volts peak-to-peak across a 50-ohm dummy load?
A. 1.4 watts
B. 100 watts
C. 353.5 watts
D. 400 watts
B. 100 watts
Silly hint: Even a dummy knows that 50 percent of 200 is 100.
What value of an AC signal produces the same power dissipation in a resistor as a DC voltage of the same value?
A. The peak-to-peak value
B. The peak value
C. The RMS value
D. The reciprocal of the RMS value
C. The RMS value
The RMS (root mean square) value of an AC signal results in the same power dissipation as a DC voltage of the same value. The RMS value is useful as an average value for the voltage in an AC circuit throughout the alternating wave cycle, as if the current were a constant as in DC.
What is the peak-to-peak voltage of a sine wave with an RMS voltage of 120 volts?
A. 84.8 volts
B. 169.7 volts
C. 240.0 volts
D. 339.4 volts
D. 339.4 volts
The RMS voltage of a sine wave is approximately 0.7×peak voltage.
Looking at the possible answers, which are all peak-to-peak: divide them in half to know the peak voltage, and only one answer is still high enough to be correct – 339.4/2=169.7. Multiply that by 0.7 to get approximately 120V.
What is the RMS voltage of a sine wave with a value of 17 volts peak?
A. 8.5 volts
B. 12 volts
C. 24 volts
D. 34 volts
B. 12 volts
12 volts is the RMS (i.e. Root Mean Square) voltage of a sine wave with a value of 17 volts peak.
To find the RMS voltage, multiply the peak voltage by 0.707, which is the same as dividing by the square root of 2.
What percentage of power loss is equivalent to a loss of 1 dB?
A. 10.9 percent
B. 12.2 percent
C. 20.6 percent
D. 25.9 percent
C. 20.6 percent
What is the ratio of PEP to average power for an unmodulated carrier?
A. 0.707
B. 1.00
C. 1.414
D. 2.00
B. 1.00
The key word here is “unmodulated.”
A modulation envelope shows how a carrier wave’s amplitude changes over time, the envelope power is the power value of that envelope, and the peak envelope power is the highest power value within some timeframe.
However, if a carrier is unmodulated, its power isn’t changing, which means its modulation envelope is flat. And as with any unchanging value, its peak equals its average, and the ratio of two equal values is
1:1=1/1=1.00
(Note that as power varies directly with amplitude2, it’s convenient to think of the envelope as representing both.)
(Note also that the question asks about the ratio of two power values, not the values themselves, so RMS calculations aren’t involved here.)
Hint: There’s only one (1.00) answer.
What is the RMS voltage across a 50-ohm dummy load dissipating 1200 watts?
A. 173 volts
B. 245 volts
C. 346 volts
D. 692 volts
B. 245 volts
What is the output PEP of an unmodulated carrier if the average power is 1060 watts?
A. 530 watts
B. 1060 watts
C. 1500 watts
D. 2120 watts
B. 1060 watts
1060 watts is the output PEP (Peak Envelope Power) of an unmodulated carrier if an average reading wattmeter connected to the transmitter output indicates 1060. The average power and the PEP are the same value for an unmodulated carrier, so the values are the same.
Silly hint: 1060 is both in the question and answer
What is the output PEP of 500 volts peak-to-peak across a 50-ohm load?
A. 8.75 watts
B. 625 watts
C. 2500 watts
D. 5000 watts
B. 625 watts
What causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across its primary winding?
A. Capacitive coupling
B. Displacement current coupling
C. Mutual inductance
D. Mutual capacitance
C. Mutual inductance
Mutual Inductance is what causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across the transformer’s primary winding. A transformer is made up of two wire windings (coils) on either side of a common core. When a current flows through the first or primary winding, it causes a magnetic field to be generated in the core. As the magnetic field fluctuates in strength and polarity with the input AC cycle, it induces a current to be generated in the secondary winding.
What is the output voltage if an input signal is applied to the secondary winding of a 4:1 voltage step-down transformer instead of the primary winding?
A. The input voltage is multiplied by 4
B. The input voltage is divided by 4
C. Additional resistance must be added in series with the primary to prevent overload
D. Additional resistance must be added in parallel with the secondary to prevent overload
A. The input voltage is multiplied by 4
Reversing a step-down transformer yields a step-up transformer of the same ratio (or more properly, its reciprocal).
What is the total resistance of a 10-, a 20-, and a 50-ohm resistor connected in parallel?
A. 5.9 ohms
B. 0.17 ohms
C. 17 ohms
D. 80 ohms
A. 5.9 ohms
What is the approximate total resistance of a 100- and a 200-ohm resistor in parallel?
A. 300 ohms
B. 150 ohms
C. 75 ohms
D. 67 ohms
D. 67 ohms
Why is the primary winding wire of a voltage step-up transformer usually a larger size than that of the secondary winding?
A. To improve the coupling between the primary and secondary
B. To accommodate the higher current of the primary
C. To prevent parasitic oscillations due to resistive losses in the primary
D. To ensure that the volume of the primary winding is equal to the volume of the secondary winding
B. To accommodate the higher current of the primary
A step up transformer does exactly as the name implies: it “steps up” voltage. The output voltage on the secondary is higher than the input voltage. However, the Conservation of Energy means that the input power on the primary must be higher or equal to the output power on the secondary.
Recall that
Power=Current×Voltage
Which we usually write as
P=IV or P=IE
Since the voltage is stepped up, you need extra current to “balance out” the higher voltage on the secondary – you are trading extra current for the higher voltage.
Higher current means there is more loss over resistive wire. Therefore, to prevent transformer winding wires from overheating, transformer manufacturers make high current winding wire thicker.
What is the voltage output of a transformer with a 500-turn primary and a 1500-turn secondary when 120 VAC is applied to the primary?
A. 360 volts
B. 120 volts
C. 40 volts
D. 25.5 volts
A. 360 volts
What transformer turns ratio matches an antenna’s 600-ohm feed point impedance to a 50-ohm coaxial cable?
A. 3.5 to 1
B. 12 to 1
C. 24 to 1
D. 144 to 1
A. 3.5 to 1
The impedance ratio of a transformer is equal to the square of its turn ratio.
This means the square root of the impedance ratio of the transformer is equal to its turn ratio.
What is the equivalent capacitance of two 5.0-nanofarad capacitors and one 750-picofarad capacitor connected in parallel?
A. 576.9 nanofarads
B. 1,733 picofarads
C. 3,583 picofarads
D. 10.750 nanofarads
D. 10.750 nanofarads
When capacitors are in parallel, you can add the individual capacitances together to get the total equivalent capacitance.
Recall that 1000 picofarads are equivalent to 1 nanofarad.
Converting all the values to the same unit yields:
5.0 nF + 5.0 nF + 0.75 nF = 10.75 nF
For an intuitive explanation of this phenomenon check out Khan Academy’s video about capacitors in parallel.
Note that capacitors and resistors behave in opposite ways in this regard: you sum up resistors in series and capacitors in parallel.
Silly hint: “750” is in both the question and the answer. “750” is not used in any of the other distractors.
What is the capacitance of three 100-microfarad capacitors connected in series?
A. 0.33 microfarads
B. 3.0 microfarads
C. 33.3 microfarads
D. 300 microfarads
C. 33.3 microfarads
What is the inductance of three 10-millihenry inductors connected in parallel?
A. 0.30 henries
B. 3.3 henries
C. 3.3 millihenries
D. 30 millihenries
C. 3.3 millihenries
What is the inductance of a circuit with a 20-millihenry inductor connected in series with a 50-millihenry inductor?
A. 7 millihenries
B. 14.3 millihenries
C. 70 millihenries
D. 1,000 millihenries
C. 70 millihenries
What is the capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor?
A. 0.07 microfarads
B. 14.3 microfarads
C. 70 microfarads
D. 1,000 microfarads
B. 14.3 microfarads
Which of the following components should be added to a capacitor to increase the capacitance?
A. An inductor in series
B. An inductor in parallel
C. A capacitor in parallel
D. A capacitor in series
C. A capacitor in parallel
Capacitors act in an almost opposite manner than inductors and resistors. The total capacitance of capacitors in PARALLEL is the SUM of the individual capacitance values, therefore adding additional capacitors in PARALLEL will result in a larger total capacitance.
Which of the following components should be added to an inductor to increase the inductance?
A. A capacitor in series
B. A capacitor in parallel
C. An inductor in parallel
D. An inductor in series
D. An inductor in series
Inductors act in the same manner as resistors in series and parallel circuits. The total inductance in SERIES is the SUM of the individual inductance values. Therefore, adding more inductors in SERIES will increase the total inductance.
