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 V), a resistor (labeled R), and some wires to connect the battery to the resistor. When connected in this way, the voltage across the battery will cause a current (labeled I) to flow through the circuit. Voltage (V), current (I), and resistance (R) are the three basic parameters of an electric circuit.
Voltage is the force that causes electrons to flow in a circuit. Voltage is measured in volts, and we use the letter V to represent both the force and the units.
T5A05
What is the electrical term for the force that causes electron flow?
A. Voltage
B. Ampere-hours
C. Capacitance
D. Inductance
Current is the flow of electrons in a circuit. In Figure 1, 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.
T5A03
What is the name for the flow of electrons in an electric circuit?
A. Voltage
B. Resistance
C. Capacitance
D. Current
T5A01
Electrical current is measured in which of the following units?
A. Volts
B. Watts
C. Ohms
D. Amperes
Because the polarity of the battery voltage in the circuit never changes, the current will flow in only one direction through the circuit. We call this direct current, or DC. 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. We call it alternating current because the voltage and current are constantly changing.
Figure 2 shows an alternating current waveform. That is to say it shows how the voltage changes over time. For this particular waveform, the voltage starts at 0 V, increases to a positive peak voltage, then decreases to a negative peak voltage, and then begins increasing again, until it once again reaches 0 V. This process repeats over and over.
T5A09
Which of the following describes alternating current?
A. Current that alternates between a positive direction and zero
B. Current that alternates between a negative direction and zero
C. Current that alternates between positive and negative directions
D. All these answers are correct
One of the most important parameters of an alternating current is its frequency. The frequency of an alternating current is the number of times per second that an alternating current makes a complete cycle, where a cycle is the portion of an alternating current waveform that repeats over and over. The frequency of the alternating current that you get from a wall socket in your home is 60 cycles per second, or in engineering terms, 60 hertz (Hz). 1 Hz is equal to one cycle per second.
T5A12
What describes the number of times per second that an alternating current makes a complete cycle?
A. Pulse rate
B. Speed
C. Wavelength
D. Frequency
T5A06
What is the unit of frequency?
A. Hertz
B. Henry
C. Farad
D. Tesla
Resistance is the third basic parameter of an electric circuit. As the name implies, resistance opposes the flow of current in a circuit. The higher the resistance, the smaller the current, for a given voltage. This applies to direct current, alternating current, and RF current, which is alternating current with a high frequency. 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.
T5A04
What are the units of electrical resistance?
A. Siemens
B. Mhos
C. Ohms
D. Coulombs
T5A11
What type of current flow is opposed by resistance?
A. Direct current
B. Alternating current
C. RF current
D. All these choices are correct
To connect components in an electric circuit, we generally use copper wires because they conduct electrical current well or, in other words, have a low resistance. Metals generally are good conductors because they have many free electrons, and as a result offer low resistance to current flow.
T5A07
Why are metals generally good conductors of electricity?
A. They have relatively high density
B. They have many free electrons
C. They have many free protons
D. All these choices are correct
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 gold 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.
T5A08
Which of the following is a good electrical insulator?
A. Copper
B. Glass
C. Aluminum
D. Mercury
Ohm’s Law: formulas and usage
Hams obey Ohm’s Law!
Ohm’s Law is the relationship between voltage, current, and resistance in an electrical circuit. When you know any two of these values, you can calculate the third.
The most basic equation for Ohm’s Law is V = I × R. In other words, when you know the current (I) flowing through a circuit and the resistance (R) of the circuit, you can calculate the voltage across the circuit by multiplying these two values.
T5D02
What formula is used to calculate voltage in a circuit?
A. V = I x R
B. V = I / R
C. V = I + R
D. V = I – R
Using simple algebra, you can derive the other two forms of this equation: R = V / I and I = V / R. 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.
T5D03
What formula is used to calculate resistance in a circuit?
A. R = V x I
B. R = V / I
C. R = V + I
D. R = V – I
T5D01
What formula is used to calculate current in a circuit?
A. I = V x R
B. I = V / R
C. I = V + R
D. I = V – R
Now, let’s look at some examples of how to apply Ohm’s Law.
T5D04
What is the resistance of a circuit in which a current of 3 amperes flows when connected to 90 volts?
A. 3 ohms
B. 30 ohms
C. 93 ohms
D. 270 ohms
Here’s how to calculate this answer: R = V / I = 90 V / 3 A = 30 Ω
T5D05
What is the resistance of a circuit for which the applied voltage is 12 volts and the current flow is 1.5 amperes?
A. 18 ohms
B. 0.125 ohms
C. 8 ohms
D. 13.5 ohms
R = V / I = 12 V / 1.5 A = 8 Ω
T5D06
What is the resistance of a circuit that draws 4 amperes from a 12-volt source?
A. 3 ohms
B. 16 ohms
C. 48 ohms
D. 8 ohms
R = V / I = 12 V / 4 A = 3 Ω.
Now, let’s look at another form of the Ohm’s Law equation, I = V / R to calculate the current in a circuit.
T5D07
What is the current in a circuit with an applied voltage of 120 volts and a resistance of 80 ohms?
A. 9600 amperes
B. 200 amperes
C. 0.667 amperes
D. 1.5 amperes
I = V / R = 120 V / 80 Ω = 1.5 A
T5D08
What is the current through a 100-ohm resistor connected across 200 volts?
A. 20,000 amperes
B. 0.5 amperes
C. 2 amperes
D. 100 amperes
I = V / R = 200 V / 100 Ω = 2 A
T5D09
What is the current through a 24-ohm resistor connected across 240 volts?
A. 24,000 amperes
B. 0.1 amperes
C. 10 amperes
D. 216 amperes
I = V / R = 240 V / 24 Ω = 10 A
Now, let’s look at the third form of the Ohm’s Law equation, E = I × R to calculate the voltage across a circuit.
T5D10
What is the voltage across a 2-ohm resistor if a current of 0.5 amperes flows through it?
A. 1 volt
B. 0.25 volts
C. 2.5 volts
D. 1.5 volts
V = I × R = 0.5 A × 2 Ω = 1 V
T5D11
What is the voltage across a 10-ohm resistor if a current of 1 ampere flows through it?
A. 1 volt
B. 10 volts
C. 11 volts
D. 9 volts
V = I × R = 1 A × 10 Ω = 10 V
T5D12
What is the voltage across a 10-ohm resistor if a current of 2 amperes flows through it?
A. 8 volts
B. 0.2 volts
C. 12 volts
D. 20 volts
V = 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. Figure 3 shows a series circuit.
There is only one path for the current to flow, so the same current flows through both resistors. If R1 = R2, then the voltage will be the same across both resistors, because the same current flows through 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.
T5D13
In which type of circuit is DC current the same through all components?
A. Series
B. Parallel
C. Resonant
D. Branch
In a parallel circuit, shown in Figure 4, 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.
T5D14
In which type of circuit is voltage the same across all components?
A. Series
B. Parallel
C. Resonant
D. Branch
DC power
Power is the rate at which electrical energy is generated or consumed. Power is measured in watts. We use the letter P to stand for power and the letter W to stand for watts.
T5A10
Which term describes the rate at which electrical energy is used?
A. Resistance
B. Current
C. Power
D. Voltage
T5A02
Electrical power is measured in which of the following units?
A. Volts
B. Watts
C. Watt-hours
D. Amperes
To calculate power, we multiply the voltage across a circuit by the current flowing through the circuit. We write this equation P = V × I.
T5C08
What is the formula used to calculate electrical power (P) in a DC circuit?
A. P = V x I
B. P = V / I
C. P = V – I
D. P = V + I
Here are some examples:
T5C09
How much power is delivered by a voltage of 13.8 volts DC and a current of 10 amperes?
A. 138 watts
B. 0.7 watts
C. 23.8 watts
D. 3.8 watts
The calculation for this question is P = V × I = 13.8 V × 10 A = 138 W.
T5C10
How much power is delivered by a voltage of 12 volts DC and a current of 2.5 amperes?
A. 4.8 watts
B. 30 watts
C. 14.5 watts
D. 0.208 watts
The calculation for this question is P = V × 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 / V.
T5C11
How much current is required to deliver 120 watts at a voltage of 12 volts DC?
A. 0.1 amperes
B. 10 amperes
C. 12 amperes
D. 132 amperes
The calculation for this question is I = P / V = 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:
T5B01
How many milliamperes is 1.5 amperes?
A. 15 milliamperes
B. 150 milliamperes
C. 1500 milliamperes
D. 15,000 milliamperes
To convert amperes to milliamperes, you multiply by 1,000.
T5B02
Which is equal to 1,500,000 hertz?
A. 1500 kHz
B. 1500 MHz
C. 15 GHz
D. 150 kHz
To convert from hertz (Hz) to kHz, you divide by 1,000.
T5B03
Which is equal to one kilovolt?
A. One one-thousandth of a volt
B. One hundred volts
C. One thousand volts
D. One million volts
T5B04
Which is equal to one microvolt?
A. One one-millionth of a volt
B. One million volts
C. One thousand kilovolts
D. One one-thousandth of a volt
To convert from kilovolts to volts, you multiply by 1,000. To convert from microvolts to volts, you divide by one million.
T5B05
Which is equal to 500 milliwatts?
A. 0.02 watts
B. 0.5 watts
C. 5 watts
D. 50 watts
To convert from milliwatts to watts, you divide by 1,000. 500 / 1000 = ½ or 0.5.
T5B08
Which is equal to 1,000,000 picofarads?
A. 0.001 microfarads
B. 1 microfarad
C. 1000 microfarads
D. 1,000,000,000 microfarad
The farad is the unit of capacitance. There are 1 million picofarads in a microfarad.
T5B06
Which is equal to 3000 milliamperes?
A. 0.003 amperes
B. 0.3 amperes
C. 3,000,000 amperes
D. 3 amperes
There are a thousand milliamperes in an ampere, so to convert from milliamperes to amperes, you divide by 1,000.
T5C13
What is the abbreviation for kilohertz?
A. KHZ
B. khz
C. khZ
D. kHz
1 kHz is 1,000 Hz or 1,000 cycles per second. Note that the “H” in Hz is capitalized.
T5B07
Which is equal to 3.525 MHz?
A. 0.003525 kHz
B. 35.25 kHz
C. 3525 kHz
D. 3,525,000 kHz
T5B12
Which is equal to 28400 kHz?
A. 28.400 kHz
B. 2.800 MHz
C. 284.00 MHz
D. 28.400 MHz
T5B13
Which is equal to 2425 MHz?
A. 0.002425 GHz
B. 24.25 GHz
C. 2.425 GHz
D. 2425 GHz
To convert from MHz to kHz, you multiply by 1,000. To convert from kHz to MHz, or to convert from MHz to GHz, you divide by 1,000.
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.
T5B09
Which decibel value most closely represents a power increase from 5 watts to 10 watts?
A. 2 dB
B. 3 dB
C. 5 dB
D. 10 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.
T5B10
Which decibel value most closely represents a power decrease from 12 watts to 3 watts?
A. -1 dB
B. -3 dB
C. -6 dB
D. -9 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.
T5B11
Which decibel value represents a power increase from 20 watts to 200 watts?
A. 10 dB
B. 12 dB
C. 18 dB
D. 28 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.
Dave New, N8SBE says
Missing Figure 2 alternating current waveform. You’ll then need to renumber the following figures.
Dave New, N8SBE says
In T5D05 through T5D12, you have E instead of V in the discussion and/or example solution.
In the following figures in the next section, the battery is not labled ‘V”.
Dave New, N8SBE says
In T5C09 through T5C11, the example solutions use E instead of V.
Dan KB6NU says
Thanks, Dave. I thought I’d gotten them all. Proofreading your own work is next to impossible. :) Should be all fixed now.