how fast electricyti travel?

The speed of electricity is not due to the individual speed of each electron but the combined movement of all the electrons in a circuit acting together. It's a bit like the links of a bicycle chain where each individual link does not travel that fast the but all of them move almost at once. An electron can only move a tiny distance called 'drift' but they all act as one field. The speed of electricity is really the speed of the electromagnetic field created in an electrical circuit, but this is something for study at a more advanced stage.

what are the scopes in Electrical engineering?

A scope is designed to measure varying voltage signals, which is important when you want to find out if, for example, a particular component in a circuit is working properly. A scope can measure very tiny quantities which would be impossible by other means.

What is the difference between e-engineering and computer science?

Engineering is building or inventing. Computer science is programing objects.

How long would it take for an electrical pole's circuit to blow out when it has an overload of half of its usual input/output of electricity?

Let's clarify your question. Do you mean that there is an electric circuit, like one on an outdoor pole, that is protected by a circuit breaker? And is the question how long the circuit breaker will take to trip? Also, when you say overload of half are you saying that there is 150% of the rated amps? Many circuit breakers have a piece of metal holding the circuit closed. The amount and type of metal is chose so that the metal strip will heat up if more amps of electricity pass through than the circuit breaker is rated for. The heating takes some amount of time and then the piece of metal will deflect and then an internal spring will cause the circuit breaker to flip - meaning open up and no more electricity will flow. The reason that this is important is that many electronic devices are sensitive to the type of voltage fluctuations that cause high current, but the heating is not instantaneous and so the high voltage can reach your computer (or stereo or TV) and destroy it well before the circuit breaker flips. Among electricians there is an adage that circuit breakers protect the electric company, not the customer. For your protection you need a surge suppressor. I'm not sure this is what you asked, but it's important to know ;)

Why do electrical engineers have to deal with such small numbers when they have to build/invent things? You can't build something that you can't see.

Probably the best reason we have for building things really small is that small transistors work better than big transistors. They are faster, and take less power to do the same thing. And every time you make a transistor half as big as the previous generation, you can pack four times as many of them in the same space on an integrated circuit. It's all good. The silicon electronics was invented in the 1950's and has been getting smaller ever since. When we want to make something too small to see, we don't give up, we invent better microscopes to see with!

I'm in fifth grade. Is it okay for me to be learning this type of material?

This engineering topic is fairly challenging for a 5th grader. We use math ideas that you will learn about in Algebra in a few years. However, you will probably enjoy the first several videos that talk about the basic concepts of charge and current and voltage, and how we talk about circuits. In these videos it's perfectly ok to skip past any math parts you don't get just yet. You can learn anything.

In engineering notation, what is the purpose of hopping 3 digits at a time? I noticed that the common prefixes are also 10³ apart from each other: 10⁻³ _milli_- 10⁻⁶ _micro_- 10⁻⁹ _nano_- 10⁻¹² _pico_- Is this related, or just a coincidence?

The names and the group-by-3 are the same idea, and the same as putting commas every 3 digits in big numbers. The thought is that we have a good quick sense of arithmetic and comparisons for numbers between 1 and 1000. You can visualize $1 and $1,000 pretty easy. The same goes for component values, voltages, currents, frequencies.

Does anyone know when and why it came to pass that we're seeing V replacing E in electronics math? Seems pointless, but would be interested to know why someone thought it was necessary. As something of a purist and originalist, it bothers me a bit. But perhaps there's a better reason than, "It's easier for greenies to learn."

Voltage is Energy, hence E can be used instead of V in electronics math. To me, E was helpful to understand definition of voltage during high school. I always found it easier to explain that how energy, i.e. E, (voltage) pushes electrons (current) in a circuit.

How far can we get through this course before calculus is required? Are there sections that would be better to work on at the same time as calculus?

You don't need calculus all the way through DC Circuit Analysis. When you get to Natural and Forced Response we have to solve a differential equation. That's where calc kicks in.

Main content

Course: Electrical engineering > Unit 1

Lesson 1: Getting started

Numbers in electrical engineering

Google Classroom

An overview of engineering notation, large and small numbers, number prefixes, and the grammar for units. Written by Willy McAllister.

Electrical engineers come across very large and very small numbers compared to everyday experience. This article gives you an initial exposure to large and small numbers and has examples of how they show up in engineering applications.

Engineering numbers are written in engineering notation, similar to scientific notation. It helps to get comfortable with engineering notation and the wide, dynamic range of numbers that engineers deal with on a regular basis.

Scientific notation

If you've studied math or science, you have probably run across scientific notation. You can brush up on scientific notation with this video. To express a number in scientific notation, you rewrite it as a number

\geq 1

and

< 10

, multiplied by a power of

10

. It might make more sense if we look at some examples:

Avogadro's Number looks like this in scientific notation: $6.02214082 \times 10^{23}$ ‍. You may see the same number in computer syntax like this: $6.02214082 E 23$ ‍, where "E" for "Exponent" stands in for " $\times 10 to the …$ ‍".
The speed of light is $299792458$ ‍ meters per second. This is expressed in scientific notation as $2.99792458 \times 10^{8} m/s$ ‍ and may be rounded to fewer digits like this: $3.00 \times 10^{8} m/s$ ‍.
The charge on an electron is a tiny, unwieldy number. $0.00000000000000000016021766208$ ‍ coulombs. Rather than writing all those zeros—and getting it wrong most of the time—we can use scientific notation to write the number more simply: $1.6021766208 \times 10^{- 19}$ ‍ coulombs.

Engineering notation

The habit in engineering is to use a slightly modified scientific notation. Engineers like exponents in multiples of three. This means the digits to the left of the decimal point fall in the range of one to 999. Our minds do a pretty good job relating to numbers in this range.

Engineering notation is only slightly different than scientific notation.

It takes light 0.0000333564095 seconds to travel 10 kilometers in a vacuum. Let's convert this small number into engineering notation:

Find the decimal point.
Hop over three digits at a time, going right, until you hop over one, two, or three nonzero digits. In this case, take two hops to the right, until you hop over $33$ ‍.
Write down $33$ ‍.
Add a decimal point: $33.$ ‍
Write down the remaining digits: $33.3564095$ ‍.
Because we hopped right, finish by writing $10$ ‍ raised to the negative number of hops times three: $- 2 hops \times 3 = - 6$ ‍.

33.3564095 \times 10^{- 6}

seconds is the time it takes for light to travel 10 kilometers in a vacuum, in engineering notation.

A few more examples of engineering notation:

Speed of light: $300 \times 10^{6} m/s$ ‍
A blink of an eye: $\sim 350 \times 10^{- 3} s$ ‍

The number format rules are not rigid. As long as the point you are trying to make is clear and unambiguous, you may make exceptions. The blink of an eye may be clearly written 0.350 seconds if you intend the reader to compare the value to one second.

One flaw in engineering notation is that it can mislead about the number of significant figures. Engineers generally deal with wide tolerances of manufactured components, so the number of significant figures in circuit designs is usually small: two to three. If the tolerance is important, it is common to write it next to the number, as shown in this example:

A large resistance value:

33.3 \times 10^{6} Ω \pm 1 %

Over time, you will develop a feel for numerical accuracy and rounding in different situations. When done appropriately, rounding to a few digits is not a sign of laziness, but a realization that real-world components are not all the same—and yet your design still has to work every time. There are other instances, such as during long calculations using computer arithmetic, where even tiny rounding errors are important to anticipate and control. It all depends on the situation. This is the engineering art.

Prefixes

Many numbers have names derived from Greek or Latin. Engineers and scientists use Système International d'Unités (SI) number prefixes.

Some of the most common prefixes in engineering are listed below. Notice that the exponents are multiples of three. These prefixes are shorter and easier to say or abbreviate than the numerical equivalent: "

\times 10 to the …

Number	Prefix	Symbol	Note
$10^{+ 12}$ ‍	tera-	$T$ ‍
$10^{+ 9}$ ‍	giga-	$G$ ‍
$10^{+ 6}$ ‍	mega-	$M$ ‍
$10^{+ 3}$ ‍	kilo-	$k$ ‍	the only > 1 prefix in lower case
$10^{0}$ ‍
$10^{- 3}$ ‍	milli-	$m$ ‍
$10^{- 6}$ ‍	micro-	$μ$ ‍	be careful $μ$ ‍ (mu) doesn't turn into "m"
$10^{- 9}$ ‍	nano-	$n$ ‍
$10^{- 12}$ ‍	pico-	$p$ ‍

The Latin word gigas gives us the number prefix "giga-". It is also the source of our English word giant. In English, the letter "g" can be hard (goat) or soft (giant). So how should "giga-" be pronounced?

The hard "g" is more common these days, but the soft "g" is still acceptable. You might come across someone saying it that way. One such person is Christopher Lloyd's character in the movie Back to the Future

Do engineers really deal with numbers this large and small?

Yes! Below are examples of large, medium and small numbers used in real-world electrical systems. These examples are common occurrences, and you can always find greater extremes.

Frequency: Frequency counts the number of times something happens per second—or another unit of time. The SI unit for frequency is hertz (Hz), which is the same as

1 / s

. You could also say "reciprocal second" or "per second". The internal clock of a modern personal computer runs at a frequency of around 3 GHz

(3 \times 10^{9} Hz)

. This corresponds to a clock period—the amount of time between clock ticks—of

1 / (3 \times 10^{9})

or 333 ps

(333 \times 10^{- 12} s)

. A human heart beats about one time per second (1 Hz), as detected by an electrocardiogram (ECG) machine.

Resistance: Resistance is measured in units of ohms

(Ω)

. The resistance of a wire is often much less than one ohm. Resistance up to tens of megohms

(10 \times 10^{6} Ω)

is not unusual.

Voltage: The unit of electrical potential is the volt (V). A flashlight battery is 1.5 volts. You can hold this battery in your hand without fear of electric shock. Inside a computer, the chips usually operate with 3 to 5 volts. A car battery is 12 volts. A wall socket is 110 or 220 volts, depending on where you live. This voltage can be fatal if you touch it with bare hands. High-tension power lines overhead are hundreds of thousands of volts—tension is the French word for voltage. As for tiny voltages, wireless signals are measured in microvolts

(10^{- 6} V)

when detected by a radio or mobile phone receiver.

Current: Currents are measured in amperes (A). One ampere is a large current. Car batteries momentarily supply 100 amperes or more to start a car. A house may consume 150 amperes if everything is turned on. Currents can also be absurdly small. There are situations where 1 femtoamp

(1 \times 10^{- 15} A)

matters.

Time: Electrical circuits are capable of working at very short time scales. Time intervals in electronics range from 1 second, for the heartbeat example above, down to 1 picosecond

(1 \times 10^{- 12} s)

Capacitance: Capacitance has units of farads (F). A farad is defined as a coulomb per volt. Since a coulomb is such a large amount of charge, a farad is a large unit of capacitance. As a result, capacitance values you come across are tiny numbers. 100 microfarads is a large capacitance. If you twist two 1-inch (2- centimeter) pieces of ordinary insulated hookup wire together, those wires have a capacitance around one picofarad

(1 \times 10^{- 12} F)

Distance and Length: Distance and length have units of meters. We deal with huge distances and tiny lengths on a regular basis. Nature gives us some staggering distances—light travels at

300 \times 10^{6}

meters (300 million meters) in one second. Modern microelectronics blesses us with astoundingly small dimensions inside integrated circuits. Today's most aggressive—and expensive—integrated-circuit processes have dimensions as small as 15 nanometers

(15 \times 10^{- 9} m)

. That's 15 billionths of a meter!

Unit grammar

These are the grammatical guidelines for writing unit names and symbols.

Names of all units start with a lowercase letter, even if the unit is named after a person.
Symbols for units are uppercase if the unit is named after a person, otherwise lowercase.

Symbol name	example names	Symbol	example symbols	Named after
second	1 millisecond	$s$ ‍	$2 ns$ ‍
meter	300 kilometer	$m$ ‍	$35 nm$ ‍
hertz	10 kilohertz	$Hz$ ‍	$100 MHz$ ‍	Hertz
ohm	2 megohm	$Ω$ ‍	$47 k Ω$ ‍	Ohm
farad	10 picofarad	$F$ ‍	$220 pF$ ‍	Faraday
ampere	35 microamp	$A$ ‍	$65 mA$ ‍	Ampère
volt	11 kilovolt	$V$ ‍	$5 μ V$ ‍	Volta

Isn't it cool. Ohm gets a Greek symbol:

Ω

, "Ohm ega."

The short form "amp" is a perfectly acceptable way to abbreviate "ampere".

The numbers you encounter as you study electrical engineering span a huge range. You will come across these numbers on Khan Academy, in textbooks, and in real-world electronic systems.

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sylvester marton
Posted 8 years ago. Direct link to sylvester marton's post “how fast electricyti trav...”
how fast electricyti travel?
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(21 votes)
Answer
- rtownsend_21
  Posted 8 years ago. Direct link to rtownsend_21's post “The speed of electricity ...”
  The speed of electricity is not due to the individual speed of each electron but the combined movement of all the electrons in a circuit acting together. It's a bit like the links of a bicycle chain where each individual link does not travel that fast the but all of them move almost at once. An electron can only move a tiny distance called 'drift' but they all act as one field. The speed of electricity is really the speed of the electromagnetic field created in an electrical circuit, but this is something for study at a more advanced stage.
  Comment on rtownsend_21's post “The speed of electricity ...”
  (79 votes)
sunilkarki320
Posted 8 years ago. Direct link to sunilkarki320's post “what are the scopes in El...”
what are the scopes in Electrical engineering?
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(8 votes)
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- rtownsend_21
  Posted 8 years ago. Direct link to rtownsend_21's post “A scope is designed to me...”
  A scope is designed to measure varying voltage signals, which is important when you want to find out if, for example, a particular component in a circuit is working properly. A scope can measure very tiny quantities which would be impossible by other means.
  Button navigates to signup page
  (12 votes)
Alya
Posted 8 years ago. Direct link to Alya's post “What is the difference be...”
What is the difference between e-engineering and computer science?
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- Isaac
  Posted 8 years ago. Direct link to Isaac's post “Engineering is building ...”
  Engineering is building or inventing. Computer science is programing objects.
  Comment on Isaac's post “Engineering is building ...”
  (12 votes)
patelkhushi757
Posted 8 years ago. Direct link to patelkhushi757's post “Why do electrical enginee...”
Why do electrical engineers have to deal with such small numbers when they have to build/invent things? You can't build something that you can't see.
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(4 votes)
Answer
- Willy McAllister
  Posted 8 years ago. Direct link to Willy McAllister's post “Probably the best reason ...”
  Probably the best reason we have for building things really small is that small transistors work better than big transistors. They are faster, and take less power to do the same thing. And every time you make a transistor half as big as the previous generation, you can pack four times as many of them in the same space on an integrated circuit. It's all good. The silicon electronics was invented in the 1950's and has been getting smaller ever since. When we want to make something too small to see, we don't give up, we invent better microscopes to see with!
  Comment on Willy McAllister's post “Probably the best reason ...”
  (9 votes)
Caleb Fox
Posted 8 years ago. Direct link to Caleb Fox's post “How long would it take fo...”
How long would it take for an electrical pole's circuit to blow out when it has an overload of half of its usual input/output of electricity?
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(5 votes)
Answer
- Martin McEnroe
  Posted 8 years ago. Direct link to Martin McEnroe's post “Let's clarify your questi...”
  Let's clarify your question. Do you mean that there is an electric circuit, like one on an outdoor pole, that is protected by a circuit breaker? And is the question how long the circuit breaker will take to trip? Also, when you say overload of half are you saying that there is 150% of the rated amps? Many circuit breakers have a piece of metal holding the circuit closed. The amount and type of metal is chose so that the metal strip will heat up if more amps of electricity pass through than the circuit breaker is rated for. The heating takes some amount of time and then the piece of metal will deflect and then an internal spring will cause the circuit breaker to flip - meaning open up and no more electricity will flow. The reason that this is important is that many electronic devices are sensitive to the type of voltage fluctuations that cause high current, but the heating is not instantaneous and so the high voltage can reach your computer (or stereo or TV) and destroy it well before the circuit breaker flips. Among electricians there is an adage that circuit breakers protect the electric company, not the customer. For your protection you need a surge suppressor. I'm not sure this is what you asked, but it's important to know ;)
  Button navigates to signup page
  (4 votes)
Hồ Đức Trung
Posted 7 years ago. Direct link to Hồ Đức Trung's post “I'm in fifth grade. Is it...”
I'm in fifth grade. Is it okay for me to be learning this type of material?
Button navigates to signup pageComment on Hồ Đức Trung's post “I'm in fifth grade. Is it...”
(3 votes)
Answer
- Willy McAllister
  Posted 7 years ago. Direct link to Willy McAllister's post “This engineering topic is...”
  This engineering topic is fairly challenging for a 5th grader. We use math ideas that you will learn about in Algebra in a few years. However, you will probably enjoy the first several videos that talk about the basic concepts of charge and current and voltage, and how we talk about circuits. In these videos it's perfectly ok to skip past any math parts you don't get just yet. You can learn anything.
  Button navigates to signup page
  (4 votes)
Polina Vitić
Posted 4 years ago. Direct link to Polina Vitić's post “In engineering notation, ...”
In engineering notation, what is the purpose of hopping 3 digits at a time? I noticed that the common prefixes are also 10³ apart from each other:

10⁻³ milli-
10⁻⁶ micro-
10⁻⁹ nano-
10⁻¹² pico-

Is this related, or just a coincidence?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Willy McAllister
  Posted 4 years ago. Direct link to Willy McAllister's post “The names and the group-b...”
  The names and the group-by-3 are the same idea, and the same as putting commas every 3 digits in big numbers. The thought is that we have a good quick sense of arithmetic and comparisons for numbers between 1 and 1000. You can visualize $1 and $1,000 pretty easy. The same goes for component values, voltages, currents, frequencies.
  Comment on Willy McAllister's post “The names and the group-b...”
  (6 votes)
Renardo James
Posted 7 years ago. Direct link to Renardo James's post “In the "Unit Grammar" sec...”
In the "Unit Grammar" section, shouldn't the example name for ohm be 2 megaohm instead of 2 megohm?
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(3 votes)
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- Willy McAllister
  Posted 7 years ago. Direct link to Willy McAllister's post “Good question. The common...”
  Good question. The common usage is "megohm", I think mostly because "megaohm" has that double vowel thing going on in the middle and is harder to say. a-o has a hole in the middle of it.
  Button navigates to signup page
  (1 vote)
Keith
Posted 8 years ago. Direct link to Keith's post “Does anyone know when and...”
Does anyone know when and why it came to pass that we're seeing V replacing E in electronics math? Seems pointless, but would be interested to know why someone thought it was necessary. As something of a purist and originalist, it bothers me a bit. But perhaps there's a better reason than, "It's easier for greenies to learn."
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Meki
  Posted 8 years ago. Direct link to Meki's post “Voltage is Energy, hence ...”
  Voltage is Energy, hence E can be used instead of V in electronics math. To me, E was helpful to understand definition of voltage during high school. I always found it easier to explain that how energy, i.e. E, (voltage) pushes electrons (current) in a circuit.
  Comment on Meki's post “Voltage is Energy, hence ...”
  (2 votes)
Polina Vitić
Posted 4 years ago. Direct link to Polina Vitić's post “How far can we get throug...”
How far can we get through this course before calculus is required? Are there sections that would be better to work on at the same time as calculus?
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(1 vote)
Answer
- Willy McAllister
  Posted 4 years ago. Direct link to Willy McAllister's post “You don't need calculus a...”
  You don't need calculus all the way through DC Circuit Analysis. When you get to Natural and Forced Response we have to solve a differential equation. That's where calc kicks in.
  Comment on Willy McAllister's post “You don't need calculus a...”
  (4 votes)