Basic Electricity Lesson E
The metric system
Most Americans are familiar with our standard system of measurements. When discussing distances, there are inches, feet, yards, rods, fulongs, and miles.
12 inches = 1 foot
3 feet = 1 yard
5 1/2 yards = 1 rod
40 rods = 1 furlong
8 furlongs (1,760 yards or 5,280 feet) = 1 mile
This system can become very complicated because it is necessary to remember several conversion factors (x12, x3, x5.5, x40, x8, x1,760, x5,280) in order to get any converting accomplished.
The beauty of the metric system is that there is only one number (with slight variations) you need to remember. That number is 1. The variations are the number of zeros added to or subtracted from that one... or where the decimal point is placed in relation to that number.
Now let's take a look at some basic conversions of metric prefixes.
Centi- (one one-hundedth; 0.01)
Most people are aware of the centimeter because it is usually found on the opposite side of the same foot long rulers. How do we convert from the centimeter to the meter? How about from the meter back to the centimeter? What does "centi" mean?
Centi- is a prefix meaning "one one-hundredth" or one part out of one hundred. It also sounds like the word "cent" which is used to describe our smallest denomination of money - the one cent (or "penny"). It takes 100 cents to make 1 dollar. It also takes 100 centimeters to make 1 meter.
Lets say that your antenna is 400 centimeters long. How long is this antenna in meters? All you have to do is know that there are one hundred centimeters in one meter. Since it is 400 centimeters long, it must be 4 meters. Written in another form...
100 cm = 1 meter || 400 cm = 4 meters
(Since 100 centimeters equals 1 meter, then 400 centimeters equals 4 meters)
Kilo- (one thousand; 1,000)
Mega- (one million; 1,000,000)
The prefix enables us to reduce the amount of zeros that are used in writing out large numbers. For example... instead of saying that the frequency of my signal is 1,000,000 Hz (Hertz or cycles per second) I can say that it is 1,000 kilohertz (kHz) or even 1 Megahertz (MHz). The prefix enables us to write the number in a shorter form. This especially becomes useful when we need to measure VERY large or VERY small numbers.
Just to make certain that this stuff makes sense, lets go back and look at large frequencies again.
1,000 Hz = 1 kHz
"One thousand Hertz equals one kilohertz"
1,000,000 Hz = 1 Mhz
"One million Hertz equal one megahertz"
So how many kilohertz are in one megahertz? 1000 kHz = 1 MHz
"One thousand kilohertz equals one megahertz"
So if your radio was tuned to 7125 kHz, how would you express that same frequency in megahertz?
1000 kHz = 1 MHz || 7125 kHz = 7.125 MHz
(It takes 1000 kilohertz to equal 1 megahertz, so 7125 kilohertz would equal 7.125 megahertz.)
There are a few things you may have surmised by now, but I'll explain them anyways.
centi = 1 one-hundredth (1/100)
kilo = 1 thousand (1,000)
mega = 1 million (1,000,000)
Lets do another frequency problem. This time, your dial reads 3525 kHz. What is the same frequency when expressed in Hertz? This should be simple...
1 kHz = 1000 Hz || 3525 kHz = 3,525,000 Hz
(Notice that since we have to add three zeros to go from 1 kHz to 1000 Hz, we must also do the same to go from 3525 kHz to 3,525,000 Hz.)
Now, let's work another frequency problem, except we're going to do it backwards. Your displays shows a frequency of 3.525 MHz. What is that same frequency in kilohertz?
1 MHz = 1000 kHz || 3.525 MHz = 3525 kHz
(See how the 1 became 1000? To go from megahertz to kilohertz, you multiply by 1000. Try multiplying 3.525 MHz by 1000 to get your frequency in kilohertz.)
Giga- (one billion; 1,000,000,000)
Now we're going to deal with an even larger frequency. Remember, kilo equals one thousand, and mega equals one million. What equals one billion? There is a prefix for one billion - Giga. One billion Hertz is one gigahertz (GHz). What if you were transmitting on 1.265 GHz? What would your frequency be in megahertz? How many millions equals one billion? 1 billion is 1000 millions, so 1 gigahertz (GHz) is 1000 megahertz (MHz).
1 GHz = 1000 MHz || 1.265 GHz = 1265 MHz
As you begin to see how these metric prefixes relate to each other, it will become easier to express these large and small numbers commonly used in radio and electronics.
Speaking of electronics, lets see how metric prefixes is used to measure the values of electricity and electronic devices.
Milli- (one one-thousandth; 0.001)
Remember when you learned about voltage and current. These terms described the electromotive force ("the force that moves electrons") and the resulting electric current flowing through a circuit. Also, in a previous lesson, we dealt with power (how quickly a circuit uses electrical energy). In review, voltage is measured in volts, current in amperes (or amps), and power is measured in watts.
If you were to take an ammeter (a meter that measures current) marked in amperes and measure a 3,000 milliampere current, what would your ammeter read? First, what does milli- mean? Milli might be familiar to those of you who were already familiar with the ever popular centimeter. The millimeter is the next smallest measurement. There are 100 centimeters in 1 meter... there are also 1000 millimeters in 1 meter. So milli must mean 1 one-thousandth. If your circuit has 3,000 milliamps (mA), how many amps (A) is that?
1,000 mA = 1 A || 3,000 mA = 3 A
Now lets say, on a different circuit, you were using a voltmeter marked in volts (V), and you were measuring a voltage of 3,500 millivolts (mV). How many volts would your meter read?
1,000 mV = 1 V || 3,500 mV = 3.5 V
How about one of those new pocket sized, micro handheld radio you're itching to buy once you get your license? One manufacturer says that their radio puts out 500 milliwatts (mW) , while the other manufacturer's radio will put out 250 milliwatts (mW). How many watts (W) do these radios really put out?
1000 mW = 1 W || 500 mW = 0.5 W
1000 mW = 1 W || 250 mW = 0.25 W
Micro- (one one-millionth; 0.000001)
Pico- (one one-trillionth; 0.000000000001)
Capacitors are devices that usually have very small values. A one farad capacitor is seldom ever used in commercial electronics (however I understand that they are sometimes used when a lot of stored up energy is needed for an instant). Usually, your run of the mill capacitor will have a value of 1 thousandth of a farad to 1 trillionth of a farad. This is the other end of the scale compared with kilo, mega, and giga. Now we'll learn about micro and pico.
If you had a capacitor which had a value of 500,000 microfarads, how many farads would that be? Since it takes one million microfarads to equal one farad...
1,000,000 uF = 1 F || 500,000 uF = 0.5 F
What if we had a capacitor with a value of 1,000,000 picofarads? Pico is a very, very small number, so to have 1 million pico farads is saying that the value is just very small instead of very, very small. One picofarad is one trillionth of a farad. One picofarad is also one millionth of a microfarad. So it takes one million picofarads (pF) to equal one microfarad (uF)...
1,000,000 pF = 1 uF
By the way, just so you get a grasp of just how small a picofarad really is, remember, it would take one trillion (i.e. one million-million) picofarads (pF) to equal one farad (F), or...
1,000,000,000,000 pF = 1 F
To sum up the metric prefixes you'll need to know ...
1 Giga (G) = 1 billion = 1,000,000,000
1 Mega (M) = 1 million = 1,000,000
1 kilo (k) = 1 thousand = 1,000
1 centi (c) = 1 one-hundredth = 0.01
1 milli (m) = 1 one-thousandth = 0.001
1 micro (u) = 1 one-millionth = 0.000001
1 pico (p) = 1 one-trillionth = 0.000000000001
... and a few you might want to know ...
1 Tera (T) = 1trillion = 1,000,000,000,000
1 hecto (h) = ten = 10
1 deci (d) = 1 tenth = 0.1
1 nano (n) = 1 one-billionth = 0.000000001