T5: Electrical Principles

Before we touch a single number, let's understand what electricity actually is. The best picture in the whole world for this is water flowing through pipes. Get this picture firmly in your head and almost everything in this chapter will suddenly make sense. Seriously — if you only remember one thing from this lesson, make it the water picture.

The water-in-pipes picture

Imagine water running through a pipe. Three things matter, and we care about each one:

• How hard the water is being pushed — the pressure. A tall water tower pushes water out hard; a little cup tipped on its side barely pushes at all. In electricity, this "push" is called voltage. More voltage means a stronger push.
• How much water is actually flowing — the amount moving past a spot each second. A fire hose moves a huge amount; a thin drinking straw moves just a trickle. In electricity, this flowing amount is called current.
• A narrow, squeezed, or kinked spot in the pipe that makes it harder for water to get through. In electricity, anything that fights the flow is called resistance. More resistance means less flow gets through.

So, said in three short lines you can repeat to yourself: voltage = the push, current = the flow, resistance = the squeeze that fights the flow. Electricity is really just billions of tiny invisible particles called electrons getting pushed through wires, the very same way water gets pushed through pipes.

The words you must know (and the units that go with them)

A "unit" is just the name of the measuring stick. We measure how tall you are in inches; we measure how heavy a bag is in pounds. Electricity has its own measuring sticks too:

Word	What it means (water picture)	Unit (the measuring stick)	Short letter
Voltage	The push / pressure that makes electrons move	volt	E (sometimes V)
Current	The flow — how many electrons move past each second	ampere (we just say "amp")	I
Resistance	The squeeze that fights the flow	ohm	R
Power	How fast electrical energy is being used up	watt	P

That last one, power, means how fast energy is being used. A bright lamp uses more power than a dim night-light. The unit of power is the watt — you have surely seen "60 watt" or "9 watt" printed on a light bulb. And here is a sneaky one to memorize: the short letter for current is I, not C. It comes from an old French word, intensité (intensity). People always expect current to be "C," so burn it into your memory: current = I.

Exam facts, said plainly

• Electrical current is measured in amperes. (How much is flowing.)
• Electrical power is measured in watts. (How fast energy is used.)
• The flow of electrons in a circuit is called current.
• The force that causes electrons to flow is called voltage.
• Power is the word for the rate at which electrical energy is used.
• The unit of frequency is the hertz (more on frequency in a moment).

One small trap to watch for: the exam might offer "watt-hours" as a choice. A watt-hour measures energy — a total amount used up, like how much you owe on the electric bill. But the question "what is the rate at which energy is used?" is asking about speed, not total amount, and the answer to that is plain power, measured in watts.

Conductors and insulators

Some materials let electricity flow through them easily, like a nice wide-open pipe. We call those conductors. Other materials block electricity almost completely, like a pipe stuffed full of a cork. We call those insulators.

Metals are good conductors because they have many free electrons — loose electrons that are not locked tightly to one atom and can hop from atom to atom, carrying the flow along. That is exactly why wires are made of copper, which is a metal. So when the exam asks why metals conduct electricity so well, the answer is "they have many free electrons."

Glass is a good insulator. So are rubber, plastic, and ceramic. That plastic coating wrapped around a lamp cord is an insulator — it keeps the electricity trapped inside the wire so it does not leap out and zap your hand. Be careful, though: salty sea water, stainless steel, and graphite (the gray stuff in a pencil) all actually conduct electricity. Out of the usual list of choices, the one that is a true insulator is glass.

AC and DC: two different styles of flow

Electricity can flow in two different styles, and you need to tell them apart:

• Direct current (DC) flows steadily in one direction only, like a river always running one way downhill. A battery makes DC: the plus end always pushes and the minus end always pulls, and it never switches. Your handheld radio runs on DC from its battery.
• Alternating current (AC) keeps switching directions, back and forth, over and over, many times a second. The exam describes it as current that alternates between positive and negative directions. The electricity coming out of the wall plug in your house is AC, and so are radio signals.

Because AC flips back and forth, we can count how many complete back-and-forth trips it makes each second. That count is the frequency. The exam asks: "the number of times per second that an alternating current makes a complete cycle" — that is the frequency. We measure frequency in hertz (Hz), named after a scientist named Heinrich Hertz. One hertz means one full back-and-forth cycle every second. Radio waves do this millions of times per second, so we will use big-number nicknames for them in the next group.

One more handy fact about resistance

Resistance — that "squeeze" — fights every kind of electrical flow. It fights steady DC, it fights back-and-forth AC, and it fights the super-fast radio-frequency current too. So if the exam asks "what type of current flow is opposed by resistance?" do not get tricked into picking just one type — the answer is all of these choices are correct.

This is the group people fear, so we are going to crawl through it. There is no algebra at all here — just two skills. Skill one: changing a big unit into a small unit (or the other way around) by sliding the decimal point. Skill two: three little decibel facts you memorize once. That is the entire group. Let's build it up from nothing, starting with what a decimal point even is.

First: what is a "decimal point" and how do we slide it?

The decimal point is the little dot you see in a number like 3.5. The digits to the left of the dot are whole things; the digits to the right are little pieces. Here is the one trick we use over and over again:

• To multiply a number by 10, slide the dot one spot to the right. (3.5 becomes 35.)
• To multiply by 1000, slide it three spots to the right, sticking on zeros if you run out of digits. (1.5 becomes 1500.)
• To divide by 1000, slide it three spots to the left. (3000 becomes 3.000, which is just 3.)
• To divide by a million, slide it six spots to the left.

Easy way to remember which direction: sliding the dot to the right makes the number bigger; sliding it to the left makes the number smaller. That single idea is the whole secret behind every unit conversion you will ever see on this test.

Metric prefixes: nicknames for big and small numbers

Writing out 1,000,000 every time is a pain, so scientists invented short nicknames called prefixes that you stick onto the front of a unit. You already know several of them! "Kilo" means a thousand — a kilometer is a thousand meters. "Mega" means a million — a megapixel is a million dots. Here is the full table. The last column shows you exactly how big one of each prefix is.

Prefix	Short letter	What it means	The actual number
giga	G	one billion	1,000,000,000
mega	M	one million	1,000,000
kilo	k	one thousand	1,000
(plain unit)	—	one	1
milli	m	one one-thousandth	0.001
micro	u (a Greek letter named "mu")	one one-millionth	0.000001
nano	n	one one-billionth	0.000000001
pico	p	one one-trillionth	0.000000000001

Everyday examples to make these stick in your memory: a kilogram is 1000 grams (about a bag of sugar). A song file might be 4 megabytes, which is 4 million bytes. A millisecond is one-thousandth of a second, about as quick as a camera flash. The top three (giga, mega, kilo) are the big ones; the bottom four (milli, micro, nano, pico) are the small ones. Notice the small-letter versus big-letter detail too: a little m means milli (small), but a big M means mega (huge) — same letter, very different size.

The golden rule for converting

Before you do any sliding, ask yourself one simple question: should the answer be a bigger pile of smaller pieces, or a smaller pile of bigger pieces?

• Changing a big unit into a smaller unit (like amps into milliamps) means each piece is tinier, so it takes more of them. You multiply (slide the dot to the right).
• Changing a small unit into a bigger unit (like milliamps into amps) means each piece is fatter, so you need fewer. You divide (slide the dot to the left).

Almost every step between neighbors on our list is a jump of 1000: kilo to plain is 1000, plain to milli is 1000, milli to micro is 1000, and so on. Mega to kilo is also 1000. So "slide three spots" is by far your most common move. The two exceptions you might meet are mega to plain (a jump of a million, six spots) and pico to micro (also a jump of a million, six spots).

Worked conversion examples — every single step spelled out

Q: How many milliamperes is 1.5 amperes?
Amps is the big unit, milliamps is the small unit, so we make MORE pieces: multiply by 1000. Slide the dot three spots to the right: 1.5 turns into 1500. Answer: 1500 milliamperes.

Q: What is 3000 milliamperes in amperes?
Going from the small unit (milli) up to the big unit (amps), so we need FEWER pieces: divide by 1000. Slide the dot three spots to the left: 3000 turns into 3.000, which is just 3. Answer: 3 amperes.

Q: What is 500 milliwatts in watts?
Milli up to plain watts means divide by 1000. Slide three spots left: 500 becomes 0.500. Answer: 0.5 watts.

Q: 1,500,000 hertz is equal to how many kilohertz?
We want kilohertz. Kilo means a thousand, so divide the hertz by 1000: slide three spots left, 1,500,000 becomes 1500. Answer: 1500 kHz. (For fun: if we wanted megahertz instead, mega is a million, so divide by a million to get 1.5 MHz.)

Q: What is 3.525 MHz the same as in kilohertz?
Mega is a million; kilo is a thousand. Mega is the bigger unit and kilo is the smaller unit, so we make more pieces: multiply by 1000. Slide three spots right: 3.525 becomes 3525. Answer: 3525 kHz.

Q: What is 28400 kHz the same as in megahertz?
Kilo up to mega is a jump of 1000, going to a bigger unit, so divide by 1000. Slide three left: 28400 becomes 28.400. Answer: 28.400 MHz.

Q: What is 2425 MHz the same as in gigahertz?
Giga is a thousand times bigger than mega. Going up to the bigger unit, divide by 1000. Slide three left: 2425 becomes 2.425. Answer: 2.425 GHz.

Q: What is 1,000,000 picofarads the same as in microfarads?
Micro is a MILLION times bigger than pico (pico is the tiniest one on our whole list). Going up to the bigger unit, divide by a million: slide six spots to the left, 1,000,000 becomes 1. Answer: 1 microfarad. (A "farad" is the unit for a part called a capacitor — you'll meet it in the next group. For now, just treat it like any other unit you slide the dot on.)

Two quick definition ones (no dot-sliding needed, just memory):

• One kilovolt = one thousand volts (kilo = 1000).
• One microvolt = one one-millionth of a volt (micro = a millionth).

Decibels (dB): comparing two powers

A decibel is a way of saying "how many times bigger or smaller" one power is compared to another, instead of stating the exact number of watts. Real engineers work these out with something called a logarithm, but you do not need any of that for this exam. You only need to memorize three magic facts:

Change in dB	What happened to the power
+3 dB	power roughly doubled (became 2 times as big)
-3 dB	power was cut in half (became 1/2 as big)
+10 dB	power became 10 times as big

And one bonus idea that unlocks the trickier question: you can add dB steps together. If the power doubles, then doubles again, that is +3 and another +3 = +6 dB, and the power ended up 4 times bigger. Going down works the exact same way: cut in half and cut in half again is -3 and -3 = -6 dB. A plus sign means the power went up; a minus sign means it went down. With those rules, the exam questions are easy:

Q: Power goes from 5 watts up to 10 watts. How many dB is that change?
10 is double of 5 (because 5 times 2 = 10). Doubling = +3 dB. Answer: 3 dB.

Q: Power goes from 20 watts up to 200 watts. How many dB?
200 is ten times 20 (because 20 times 10 = 200). Ten times = +10 dB. Answer: 10 dB.

Q: Power drops from 12 watts down to 3 watts. How many dB?
Step one: 12 cut in half is 6 (that is -3 dB). Step two: 6 cut in half again is 3 (another -3 dB). Add the steps: -3 and -3 = -6. Answer: -6 dB. The minus sign is important here because the power went down, not up.

This group introduces two new parts you will find living inside radios, a couple of radio abbreviations, and our first real formula — the power formula. We will go slowly through what a formula even is before we use it, so nobody gets lost.

Two parts that store energy: capacitors and inductors

Some electronic parts can hold onto a little energy for a moment and then give it back, like a tiny rechargeable bucket. There are two kinds, and they store their energy in two different invisible ways:

Ability	Stores energy in...	The part is called a...	Its unit
Capacitance	an electric field	capacitor	farad (F)
Inductance	a magnetic field	inductor (a coil of wire)	henry (H)

Said simply for the exam: capacitance is the ability to store energy in an electric field, and its unit is the farad. Inductance is the ability to store energy in a magnetic field, and its unit is the henry. Here is a memory hook: an inductor is a coil of wire, and coiled wire makes a magnet (think of an electromagnet). So inductor goes with the magnetic field, which leaves the capacitor with the electric field.

Radio frequency abbreviations

Remember from the first groups that frequency is measured in hertz. Radio frequencies are enormous numbers, so we always squeeze them down with prefixes and short letters:

• kHz is the abbreviation for kilohertz (thousands of hertz).
• MHz is the abbreviation for megahertz (millions of hertz).

The capital letters genuinely matter here: a little k for kilo, a big M for mega, and the H is always capital because hertz is named after a person (Heinrich Hertz again). Get the capitalization right on the test.

Impedance

Back in the first group, "resistance" was the squeeze that fights DC flow. When the current is AC (flipping back and forth), the total fight against it has a fancier name: impedance. So on the exam, impedance is defined as the opposition to AC current flow. Its unit is the ohm — the very same unit as plain resistance, because impedance is really just the AC cousin of resistance.

What is a "formula," anyway?

A formula is just a tiny recipe written with letters. The letters are nicknames for numbers you are going to fill in. When two letters sit right next to each other, it means multiply them. A line or a slash between letters means divide. "Plugging in" simply means swapping each letter for its number and then doing the arithmetic. That is genuinely all there is to it. Let's do one.

The power formula: P = I x E

To find electrical power in a DC circuit, you multiply the current by the voltage:

P = I × E   (watts = amps × volts)

So on the exam, when it asks "what formula is used to calculate power in a DC circuit?" the answer is P = I × E.

The power triangle — so you never need algebra

Picture a triangle split into three little rooms. P sits up in the top room, all by itself. I and E sit side by side in the bottom row, sharing it. Now just cover the letter you want to find with your finger and read whatever is left:

• Cover P (the top): you see I next to E, side by side, and side-by-side means multiply → P = I × E.
• Cover I (bottom left): you see P sitting on top of E, top-over-bottom, and that means divide → I = P ÷ E.
• Cover E (bottom right): you see P on top of I → E = P ÷ I.

The rule never changes: top-over-bottom always means divide; side-by-side always means multiply. The triangle quietly does all the "algebra" for you, so you never have to.

Worked power examples — every step spelled out

Q: How much power comes from 13.8 volts and 10 amperes?
We want power, so cover P: that gives P = I × E. Plug in the numbers: I is 10, E is 13.8. Multiply: 10 × 13.8 = 138. Answer: 138 watts.

Q: How much power comes from 12 volts and 2.5 amperes?
Cover P: P = I × E. Plug in: 2.5 × 12. Multiply: 2.5 × 12 = 30. Answer: 30 watts.

Q: How much current is needed to deliver 120 watts at 12 volts?
This time we want current, so cover I: that gives I = P ÷ E. Plug in: P is 120, E is 12. Divide: 120 ÷ 12 = 10. Answer: 10 amperes.

Q: How much voltage is needed to deliver 60 watts using 5 amperes? (extra practice)
We want voltage, so cover E: E = P ÷ I. Plug in: 60 ÷ 5. Divide: 60 ÷ 5 = 12. Answer: 12 volts.

That is the whole power story for the test. (For the curious only: there are two extra power formulas, P = E squared ÷ R and P = I squared × R, but the Technician exam never needs them — P = I × E answers every power question you will be asked.)

This is the single most useful formula in all of ham radio, and the good news is it works exactly like the power triangle you just learned. If you understood that one, you already understand this one. Ohm's Law ties together the three water-pipe ideas from the very first group: the push (voltage), the flow (current), and the squeeze (resistance).

Ohm's Law and its three faces

The main recipe is:

E = I × R   (volts = amps × ohms)

The same recipe can be flipped around to find whichever value is missing. The exam asks for all three forms directly by name, so know each one:

Want to find...	Use this formula	In plain words
Voltage (E)	E = I × R	current times resistance
Current (I)	I = E ÷ R	voltage divided by resistance
Resistance (R)	R = E ÷ I	voltage divided by current

So when the exam asks "what formula calculates current?" the answer is I = E ÷ R. "What formula calculates voltage?" is E = I × R. And "what formula calculates resistance?" is R = E ÷ I.

The Ohm's Law triangle

Same triangle trick as the power one. Put E in the top room, all alone, and I and R side by side in the bottom row. Cover the letter you want and read the rest:

• Cover E (top): you see I next to R, side by side → multiply → E = I × R.
• Cover I (bottom left): you see E over R, top-over-bottom → divide → I = E ÷ R.
• Cover R (bottom right): you see E over I → divide → R = E ÷ I.

Remember the unbreakable rule: side-by-side means multiply, top-over-bottom means divide. You never have to "do algebra" — just cover and read. Tip for the test: lightly sketch this triangle on your scratch paper before you start, so it's ready whenever an Ohm's Law question pops up.

Worked examples: finding RESISTANCE (R = E ÷ I)

Q: 3 amperes flow when a circuit is connected to 90 volts. What is the resistance?
We want R, so cover R: R = E ÷ I. Plug in: E is 90, I is 3. Divide: 90 ÷ 3 = 30. Answer: 30 ohms.

Q: 12 volts applied, 1.5 amperes flowing. What is the resistance?
R = E ÷ I. Plug in: 12 ÷ 1.5. Divide: 12 ÷ 1.5 = 8. Answer: 8 ohms.

Q: A circuit draws 4 amperes from a 12-volt source. What is the resistance?
R = E ÷ I. Plug in: 12 ÷ 4. Divide: 12 ÷ 4 = 3. Answer: 3 ohms.

Worked examples: finding CURRENT (I = E ÷ R)

Q: 120 volts applied, resistance is 80 ohms. What is the current?
We want I, so cover I: I = E ÷ R. Plug in: 120 ÷ 80. Divide: 120 ÷ 80 = 1.5. Answer: 1.5 amperes.

Q: A 100-ohm resistor is connected across 200 volts. What is the current?
I = E ÷ R. Plug in: 200 ÷ 100. Divide: 200 ÷ 100 = 2. Answer: 2 amperes.

Q: A 24-ohm resistor is connected across 240 volts. What is the current?
I = E ÷ R. Plug in: 240 ÷ 24. Divide: 240 ÷ 24 = 10. Answer: 10 amperes.

Worked examples: finding VOLTAGE (E = I × R)

Q: 0.5 amperes flows through a 2-ohm resistor. What is the voltage?
We want E, so cover E: E = I × R. Plug in: 0.5 × 2. Multiply: 0.5 × 2 = 1. Answer: 1 volt.

Q: 1 ampere flows through a 10-ohm resistor. What is the voltage?
E = I × R. Plug in: 1 × 10. Multiply: 1 × 10 = 10. Answer: 10 volts.

Q: 2 amperes flows through a 10-ohm resistor. What is the voltage?
E = I × R. Plug in: 2 × 10. Multiply: 2 × 10 = 20. Answer: 20 volts.

Series and parallel circuits

Last thing in the whole chapter, and there is no math at all — just two facts about how parts can be wired together.

• A series circuit is one single loop, with parts lined up end-to-end like train cars on one track. Since there is only one path, the exact same flow must go through every part. So in a series circuit, the current is the same through every component.
• A parallel circuit has parts placed side by side, each one bridging the same two points, like several rungs on a ladder. Because they all connect to the same two points, they all feel the same push. So in a parallel circuit, the voltage is the same across every component.

Memory hook to keep them straight: series goes with same current (one path, so one single flow). Parallel goes with same voltage (every part bridges the same two points, so every part feels the same push).