I’ve been working on my No Nonsense Technician Class License Study Guide for the past couple of weeks now, and I’m ready to start publishing chapters here on my blog. Here’s Chapter 1: Electrical Principles. They added some questions about series and parallel circuits this time around. Other than that, it’s pretty much unchanged…..Dan
Units and terms: current, voltage, and resistance; alternating and direct current; conductors and insulators
Figure 1 shows a simple electric circuit. It consists of a voltage source (in this case a battery, labeled E), a resistor (labeled R), and some wires to connect the battery to the resistor. When connected in this way, the battery will cause a current (labeled I) to flow through the circuit.
The three basic parameters of this circuit are electromotive force (E), current (I), and resistance (R). Electromotive force, or EMF, is the force that causes electrons to flow in a circuit. We use the letter E to denote electromotive force. Electromotive force is measured in volts, and we use the letter V to denote volts.
QUESTION: What is the electrical term for the electromotive force (EMF) that causes electron flow? (T5A05)
ANSWER: Voltage
QUESTION: What is the unit of electromotive force? (T5A11)
ANSWER: The volt
QUESTION: How much voltage does a mobile transceiver typically require? (T5A06)
ANSWER: About 12 volts
Current is the flow of electrons in a circuit. In the circuit above, the letter I stands for current. Current flows from the positive (+) terminal of the voltage source through the circuit to the negative terminal of the voltage source. Current is measured in amperes, and we use the letter A to stand for amperes.
QUESTION: What is the name for the flow of electrons in an electric circuit? (T5A03)
ANSWER: Current
QUESTION: Electrical current is measured in which of the following units? (T5A01)
ANSWER: Amperes
Because the polarity of the battery voltage never changes, the current will flow in only one direction through the circuit. We call this direct current, or DC.
QUESTION: What is the name for a current that flows only in one direction? (T5A04)
ANSWER: Direct current
Batteries supply direct current, or simply DC.
The type of current you get out of a wall socket is different from the current that you get from a battery. Unlike the battery, the polarity of the voltage changes from positive to negative on a regular basis. In fact, it changes polarity 120 times per second. This means that the current changes direction 120 times per second. Because of this, we call this alternating current, or AC.
QUESTION: What is the name for a current that reverses direction on a regular basis? (T5A09)
ANSWER: Alternating current
One of the most important parameters of an alternating current is its frequency. The frequency of an alternating current is equal to half the number of times it reverses direction.
QUESTION: What describes the number of times per second that an alternating current makes a complete cycle? (T5A12)
ANSWER: Frequency
QUESTION: What is the unit of frequency? (T5C05)
ANSWER: Hertz
1 Hz is equal to one cycle per second. An alternating current reverses polarity twice per cycle, so the frequency of the alternating current available from a wall socket is 60 Hz.
Resistance is the third parameter. As the name implies, resistance opposes the flow of electrons in a circuit. The higher the resistance, the smaller the current. We use the letter R to stand for resistance. Resistance is measured in ohms, and we use the Greek letter omega (Ω) to stand for ohms.
Conductors are materials that conduct electrical current well or, in other words, have a low resistance. We use copper wires to connect a power supply to a radio because copper wires are good conductors.
QUESTION: Which of the following is a good electrical conductor? (T5A07)
ANSWER: Copper
Silver is actually a better conductor than copper, but copper is a lot less expensive than silver. Often, you will see gold used as a conductor. Although it is not as good a conductor as either copper or silver, it doesn’t corrode like copper or silver. That makes it a good choice for switch or connector contacts.
Many times we need a material that does not conduct current very well. We call these materials insulators, and insulators have a high resistance. Plastics and glass are commonly used insulators.
QUESTION: Which of the following is a good electrical insulator? (T5A08)
ANSWER: Glass
Ohm’s Law: formulas and usage
Hams obey Ohm’s Law!
Ohm’s Law is the relationship between voltage, current, and the resistance in a DC circuit. When you know any two of these values, you can calculate the third.
The most basic equation for Ohm’s Law is E = I × R.
In other words, when you know the current flowing through a circuit and the resistance of the circuit, you can calculate the voltage across the circuit.
QUESTION: What formula is used to calculate voltage in a circuit? (T5D02)
ANSWER: Voltage (E) equals current (I) multiplied by resistance (R)
Using simple algebra, you can derive the other two forms of this equation. These two equations let you calculate the resistance in a circuit if you know the voltage and current or the current in a circuit if you know the voltage and resistance.
QUESTION: What formula is used to calculate resistance in a circuit? (T5D03)
ANSWER: Resistance (R) equals voltage (E) divided by current (I)
We can also write this formula as R = E / I.
QUESTION: What formula is used to calculate current in a circuit? (T5D01)
ANSWER: Current (I) equals voltage (E) divided by resistance (R)
This formula is written I = E / R.
Now, let’s look at some examples of how to apply Ohm’s Law.
QUESTION: What is the resistance of a circuit in which a current of 3 amperes flows through a resistor connected to 90 volts? (T5D04)
ANSWER: 30 ohms
Here’s how to calculate this answer: R = E / I = 90 V ÷ 3 A = 30 Ω
QUESTION: What is the resistance in a circuit for which the applied voltage is 12 volts and the current flow is 1.5 amperes? (T5D05)
ANSWER: 8 ohms
R = E / I = 12 V / 1.5 A = 8 Ω
QUESTION: What is the resistance of a circuit that draws 4 amperes from a 12-volt source? (T5D06)
ANSWER: 3 ohms
R = E / I = 12 V / 4 A = 3 Ω
QUESTION: What is the current in a circuit with an applied voltage of 120 volts and a resistance of 80 ohms? (T5D07)
ANSWER: 1.5 amperes
I = E / R = 120 V / 80 Ω = 1.5 A
QUESTION: What is the current through a 100-ohm resistor connected across 200 volts? (T5D08)
ANSWER: 2 amperes
I = E / R = 200 V / 100 Ω = 2 A
QUESTION: What is the current through a 24-ohm resistor connected across 240 volts? (T5D09)
ANSWER: 10 amperes
I = E / R = 240 V / 24 Ω = 10 A
QUESTION: What is the voltage across a 2-ohm resistor if a current of 0.5 amperes flows through it? (T5D10)
ANSWER: 1 volt
E = I × R = 0.5 A × 2 Ω = 1 V
QUESTION: What is the voltage across a 10-ohm resistor if a current of 1 ampere flows through it? (T5D11)
ANSWER: 10 volts
E = I × R = 1 A × 10 Ω = 10 V
QUESTION: What is the voltage across a 10-ohm resistor if a current of 2 amperes flows through it? (T5D12)
ANSWER: 20 volts
E = I × R = 2 A × 10 Ω = 20 V
Series and parallel circuits
Now, let’s consider circuits with two resistors instead of just a single resistor. There are two ways in which the two resistors can be connected: in series or in parallel. A series circuit looks like this:
There is only one path for the current to flow, so the same current flows through both resistors. And, because the voltage across the resistors is equal to I x R, the voltage across each of the resistors will depend on the value of the resistors. If R1 = R2, then the voltage will be the same across both resistors. If R1 does not equal R2, however, the voltages will be different. In either case, the sum of the two voltages will equal the voltage of the voltage source.
QUESTION: In which type of circuit is current the same through all components? (T5A13)
ANSWER: Series
QUESTION: What happens to current at the junction of two components in series? (T5D13)
ANSWER: It is unchanged
QUESTION: What is the voltage across each of two components in series with a voltage source? (T5D15)
ANSWER: It is determined by the type and value of the components
In a parallel circuit, both resistors are connected directly to the voltage source:
Because both components are connected directly to the voltage source, the voltage across them will be the same. This voltage will cause currents to flow in each of the resistors. I1 = V/R1, and I2 = V/R2. The total current, I, is equal to I1 + I2. If R1 = R2, then the same current flows through both resistors. If the resistors have different values, then I1 will be different from I2.
QUESTION: In which type of circuit is voltage the same across all components? (T5A14)
ANSWER: Parallel
QUESTION: What is the voltage across each of two components in parallel with a voltage source? (T5D16)
ANSWER: The same voltage as the source
QUESTION: What happens to current at the junction of two components in parallel? (T5D14)
ANSWER: It divides between them dependent on the value of the components
DC power
Power is the rate at which electrical energy is generated or consumed. Power is measured in watts, and the letter W is the symbol we use for watts.
QUESTION: Which term describes the rate at which electrical energy is used? (T5A10)
ANSWER: Power
QUESTION: What is the formula used to calculate electrical power in a DC circuit? (T5C08)
ANSWER: Power (P) equals voltage (E) multiplied by current (I)
We write this equation P = E × I.
QUESTION: Electrical power is measured in which of the following units? (T5A02)
ANSWER: Watts
Here are some examples:
QUESTION: How much power is being used in a circuit when the applied voltage is 13.8 volts DC and the current is 10 amperes? (T5C09)
ANSWER: 138 watts
The calculation for this question is P = E × I = 13.8 V × 10 A = 138 W.
QUESTION: How much power is being used in a circuit when the applied voltage is 12 volts DC and the current is 2.5 amperes? (T5C10)
ANSWER: 30 watts
The calculation for this question is P = E × I = 12 V × 2.5 A = 30 W.
Just as with Ohm’s Law, you can use algebra to come up with other forms of this equation to calculate the voltage if you know the power and the current, or to calculate the current if you know the power and the voltage. The formula to calculate the current, if you know the power and the voltage is I = P / E.
QUESTION: How many amperes are flowing in a circuit when the applied voltage is 12 volts DC and the load is 120 watts? (T5C11)
ANSWER: 10 amperes
The calculation for this question is I = P / E = 120 W ÷ 12 V = 10 A.
Math for electronics and conversion of electrical units
When dealing with electrical parameters, such as voltage, resistance, current, and power, we use a set of prefixes to denote various orders of magnitude:
- milli- is the prefix used to denote 1 one-thousandth of a quantity. A milliampere, for example, is 1 one-thousandth of an ampere, or 0.001 A. Often, the letter m is used instead of the prefix milli-. 1 milliampere is, therefore, 1 mA.
- micro- is the prefix used to denote 1 one-millionth of a quantity. A microvolt, for example, is 1 one-millionth of a volt, or 0.000001 V. Often, you will see the Greek letter mu, or μ, used to denote the prefix micro-. 1 microvolt is, therefore, 1 μV.
- pico- is the prefix used to denote 1 one-trillionth of a quantity. A picovolt is 1 one-trillionth of a volt, or 0.000001 μV.
- kilo- is the prefix used to denote 1 thousand of a quantity. A kilovolt, for example, is 1000 volts. Often, the letter k is used instead of the prefix kilo-. 1 kilovolt is, therefore, 1 kV.
- mega- is the prefix used to denote 1 million of a quantity. A megahertz, for example, is 1 million Hertz. Often, the letter M is used instead of the prefix mega-. 1 megahertz is, therefore, 1 MHz.
- giga – is the prefix used to denote one billion of a quantity. One gigahertz, or 1 GHz, for example is 1 billion Hertz.
Prefix | Abbreviation | Numerical | Exponential |
giga- | G | 1,000,000,000 | 109 |
mega- | M | 1,000,000 | 106 |
kilo- | k | 1,000 | 103 |
—- | —- | 1 | 100 |
milli- | m | 0.001 | 10-3 |
micro- | μ,u | 0.000001 | 10-6 |
nano- | n | 0.000000001 | 10-9 |
pico- | p | 0.000000000001 | 10-12 |
Here are some examples:
QUESTION: How many milliamperes is 1.5 amperes? (T5B01)
ANSWER: 1500 milliamperes
QUESTION: What is another way to specify a radio signal frequency of 1,500,000 hertz? (T5B02)
ANSWER: 1500 kHz
QUESTION: How many volts are equal to one kilovolt? (T5B03)
ANSWER: One thousand volts
QUESTION: How many volts are equal to one microvolt? (T5B04)
ANSWER: One one-millionth of a volt
QUESTION: Which of the following is equal to 500 milliwatts? (T5B05)
ANSWER: 0.5 watts
QUESTION: How many microfarads are equal to 1,000,000 picofarads? (T5B08)
ANSWER: 1 microfarad
The farad is the unit of capacitance.
QUESTION: If an ammeter calibrated in amperes is used to measure a 3000-milliampere current, what reading would it show? (T5B06)
ANSWER: 3 amperes
QUESTION: What is the proper abbreviation for megahertz? (T5C14)
ANSWER: MHz
QUESTION: If a frequency display calibrated in megahertz shows a reading of 3.525 MHz, what would it show if it were calibrated in kilohertz? (T5B07)
ANSWER: 3525 kHz
QUESTION: Which of the following frequencies is equal to 28,400 kHz? (T5B12)
ANSWER: 28.400 MHz
QUESTION: If a frequency display shows a reading of 2425 MHz, what frequency is that in GHz? (T5B13)
ANSWER: 2.425 GHz
Decibels
When dealing with ratios—especially power ratios—we often use decibels (dB). The reason for this is that the decibel scale is a logarithmic scale, meaning that we can talk about large ratios with relatively small numbers. When the value is positive, it means that there is a power increase. When the value is negative, it means that there is a power decrease.
At this point, you don’t need to know the formula used to calculate the ratio in dB, but you need to know the ratios represented by the values 3 dB, 6 dB, and 10 dB.
QUESTION: What is the approximate amount of change, measured in decibels (dB), of a power increase from 5 watts to 10 watts? (T5B09)
ANSWER: 3 dB
3 dB corresponds to a ratio of 2 to 1, and because going from 5 watts to 10 watts doubles the power, we can also say that there is a gain of 3 dB.
QUESTION: What is the approximate amount of change, measured in decibels (dB), of a power decrease from 12 watts to 3 watts? (T5B10)
ANSWER: −6 dB
6 dB corresponds to a ratio of 4 to 1, and a decrease in power from 12 watts to 3 watts is a ratio of 4 to 1. Because this is a power decrease, the value in dB is negative.
QUESTION: What is the amount of change, measured in decibels (dB), of a power increase from 20 watts to 200 watts? (T5B11)
ANSWER: 10 dB
Increasing the power from 20 watts to 200 watts is a ratio of 10 to 1, and 10 dB corresponds to a ratio of 10 to 1.
Ray says
I think gold has à higher resistivity than copper.
Dan KB6NU says
Well, that’s amazing. I’ve been doing this a long time and never thought to look this up. Here are the resistivities of silver, copper, and gold:
I’ve updated the text.