I found this great diagram (below) on the Web about how to read the value of a resistor (one resistance value is called an "ohm"). Within model railroading resistors are needed when you are wanting to use an LED (light emitting diode). That kind of resistor is called a current-limiting resistor. This is because if you just hook up an LED directly to a power source and turn the circuit on, the LED will show a bright flash before it self-destructs. The LED takes all the current it can get and does so very quickly. A resistor is necessary to be able to control the amount of current the LED gets. This directly controls the LED's brightness. Resistors can also be used to encourage a certain amount of current to go down one path of a split design, and an other amount of current down the other path (think: relative turns of a valve on either side of a garden-hose splitter).
Resistors are only available in these common values:
1.0, 10, 100, 1.0K, 10K, 100K, 1.0M, 10M ohm
1.1, 11, 110, 1.1K, 11K, 110K, 1.1M, 11M ohm
1.2, 12, 120, 1.2K, 12K, 120K, 1.2M, 12M ohm
1.3, 13, 130, 1.3K, 13K, 130K, 1.3M, 13M ohm
1.5, 15, 150, 1.5K, 15K, 150K, 1.5M, 15M ohm
1.6, 16, 160, 1.6K, 16K, 160K, 1.6M, 16M ohm
1.8, 18, 180, 1.8K, 18K, 180K, 1.8M, 18M ohm
2.0, 20, 200, 2.0K, 20K, 200K, 2.0M, 20M ohm
2.2, 22, 220, 2.2K, 22K, 220K, 2.2M, 22M ohm
2.4, 24, 240, 2.4K, 24K, 240K, 2.4M ohm
2.7, 27, 270, 2.7K, 27K, 270K, 2.7M ohm
3.0, 30, 300, 3.0K, 30K, 300K, 3.0M ohm
3.3, 33, 330, 3.3K, 33K, 330K, 3.3M ohm
3.6, 36, 360, 3.6K, 36K, 360K, 3.6M ohm
3.9, 39, 390, 3.9K, 39K, 390K, 3.9M ohm
4.3, 43, 430, 4.3K, 43K, 430K, 4.3M ohm
4.7, 47, 470, 4.7K, 47K, 470K, 4.7M ohm
5.1, 51, 510, 5.1K, 51K, 510K, 5.1M ohm
5.6, 56, 560, 5.6K, 56K, 560K, 5.6M ohm
6.2, 62, 620, 6.2K, 62K, 620K, 6.2M ohm
6.8, 68, 680, 6.8K, 68K, 680K, 6.8M ohm
7.5, 75, 750, 7.5K, 75K, 750K, 7.5M ohm
8.2, 82, 820, 8.2K, 82K, 820K, 8.2M ohm
9.1, 91, 910, 9.1K, 91K, 910K, 9.1M ohm
The tolerance value indicates how close to the indicated value the resistor actually might be (the smaller the tolerance, the more accurate, but also the more expensive it is).
Using Two or More Resistors Together
So what do you do if your calculations require you to use a 340 ohm resistor, which is not available? If you solder two resistors back to back (also known as "in series"), the total value is added together. So, to get a 340 ohm resistor, you solder a 330 ohm resistor to a 10 ohm one.
Calculating the total resistance value of two resistors in parallel (i.e. both of their leads are soldered together) is more complex. To do so, multiply the two values together. Then, separately, add the two values together. Now divide the result of the multiplication by the result of the addition, to yield the final number.
Use either or these two methods to come up with a specific resistance value that you need for your circuit.
Calculating the Wattage Rating
These common resistors come in several diameters. When current flows through a resistor, the energy to hold back the current going through the resistor is dissipated by creating heat. The larger the diameter of the resistor, the more heat it can handle. This is expressed in the wattage rating of the resistor.
You will need to know the amount of current (determined by the value of the resistor) flowing through the resistor, and the amount of voltage that the circuit applies to the resistor. With these numbers, you can calculate the diameter of the resistor you need by calculating its wattage using this formula:
P = I x I x R
where I is the current through the resistor (in amps), R is the value of the resistor (in ohms).
So, if we have a 300 ohm resistor, a 12 volt power supply, and the current through the resistor is 0.040 amps (40mA), then the wattage is 0.48 watts.
Resistors only come in standard wattage ratings of 1/8W (0.125W), 1/4W (0.25W), 1/2W (0.5W), and 1W. So, in our example, we go to the next higher available rating, which is 1/2W for the resistor. Wattage is not indicated via any of the bands on a resistor, but rather its diameter determines the wattage that it is designed to handle. The diameter of a resistor is measured in millimeters:
1/8W --> 1.8mm (left in the photo)
1/4W --> 2.5mm (center in the photo)
1/2W --> 3.2mm (right in the photo)
1W --> 5mm
2W --> 5.5mm
If your circuit exceeds the wattage of the resistor, the resistor will, at best, get extremely hot (possibly melting things around it), or it will crack, break, or explode. Because they are of a mechanical nature, a temporary spike of current through a resistor should be OK if the resistor is of a good quality, but that is not guaranteed. So, in our above example where we calculated 0.48W and we chose a 0.5W resistor, we're getting close. If the tolerance of the resistor is such (i.e. slightly under the indicated value) that it allows more current through, it could easily exceed the 1/2W rating on a continuous basis. The resistor will be very warm most of the time, thereby possibly shortening its life. Since 1W resistors are quite a bit larger, it might be better to choose a resistor that is slightly higher in its ohm resistance value, thereby going below the near maximum wattage rating. This is the type of analysis that circuit designers do to come up with a functional design which also has a good lifespan.
If you have a circuit that offers 10mA of current through a 900ohm resistor, the power dissipated by the resistor is:
0.01 x 0.01 x 900 = 0.09 watts,
so a 1/8W-rated resistor will be plenty.
Larger than 1-watt ratings are available as well, but they are hardly ever needed in model railroading electronics. You'll tend to find these in audio circuitry and cabinet-style speakers. If you get above 5 watts, these resistors are called "power resistors" and they usually have a rectangular shape to them and can be quite big. The one shown in the photo is a 100 ohm, 10 watt power resistor, and is a bit over two inches long.
What is SMD?
On the other end of the size spectrum is "SMD". SMD stands for Surface-Mount Device. These are tiny rectangularly-shaped electronic components that don't have the conventional wire leads. Instead, the package has tiny metal pads which are designed to make contact with a printed-circuit board (PCB). This reduces the overall space requirement, thus allowing for small circuits.
Resistors can be had in this SMD format as well (also called "chip resistors"). Be aware, they are very, very small parts and may be hard the handle. Their intended use is for automated circuit construction machines to place them on a circuit board, melt the solder between the part and the circuit board, and quickly move on to the next part. That is why they are, typically, sold in plastic bands, such as shown in the photo; tiny capsules that hold the resistor in such a manner that a suction device can grab it, and know that its pads are on the bottom. This allows for very rapid construction, but makes the parts hard to use manually and individually. Due to their construction, SMD resistors don't come in various diameters or dimensions, as they are much better able to dissipate heat.
Due to their tiny size, the value of the resistor is marked using numbers and a possible letter. These must be deciphered to determine what its value is. For those marked with three numbers, the left two numbers indicate the value, and the third number indicates how many zeroes to add to the right of that number. So, for example, "392" means "39" and "00", or 3900 ohms, or 3.9K ohms. Resistors of less than 10 ohms use the letter "R" to indicate the position of the decimal. So, for example, "3R9" is "3" "." "9", or 3.9 ohms.
The photo is of a set of SMD resistors I bought to use as current-limiting resistors for LEDs that I place in structures. The number printed on them is "102", which means 10-plus-2-zeroes, or 1,000 ohms (1K). For the sake of size-perspective, to show how tiny these parts are, the metal weight is a 3-2-1 block, with the 1-inch side facing the camera.
Four-digit numbers are very similar, except that the first three digits indicate the value, and the fourth one indicates the number of zeroes to add. For example, "4700" is "470" and add zero zeroes to it, so it is 470 ohms. The "R" works in the same manner. "15R5" is 15.5 ohms.
Since they are so hard to handle, why use them? Well, their tiny size makes them perfect for fitting them in locomotives, signals, model vehicles, and even structures. Locomotives, signals, and vehicles are obvious, in that they usually don't have much available space left. For structures, there usually is plenty of space, but you may want to have the interior fully detailed. You don't want to see wires or bulky resistors when looking through a door or a window. These parts are so small that they can be easily glued to a wall or a ceiling so that they are not visible. I typically use magnet wire to hook them up, which can be easily routed in corners between walls and ceilings and not be noticeable. To solder on the magnet wires, I push the tiny part into a modeling clay or that blue tacky stuff used to temporarily hang pictures on the wall; this holds the part in place while applying solder, and yet they can be easily removed. Use tweezers when working with these parts.
There are also electro-mechanical devices that offer a range of resistance values. These are called potentiometers (a.k.a. "pots"). They have some sort of means to turn the internal slider which changes the resistance value across its leads based on the position of that slider. Pots have three leads. The left and right leads are effectively the same as any of the above-mentioned fixed-value resistors. Like those resistors, pots come with a built-in resistance value. The one shown in this photo is marked as 1M ohm (one million ohms). So, while it is a waste of space and money to use just the two outside leads for a fixed-value resistor, it is theoretically possible.
The interesting lead is the center one. If you connect the left lead and the center lead to your circuit, the further toward the left lead you turn the mechanical method by which the pot is adjusted (this small one, which is usually mounted directly on a circuit board, requires the use of a screwdriver), the lower the resistance value of the pot. Conversely, moving the "dial" to the right lead (i.e. the one not connected), increases the resistance value.
Or, you can connect the right lead and the center lead to your circuit, to obtain the same effective, other than the fact that the "dial" has to be rotated in the opposite direction. So, which leads you want to use depends on the "user interface" of the circuit you are building. On an audio amplifier, for example, to increase the volume, you typically turn the knob clockwise, which means that it offers less and less resistance, i.e. the sound gets louder, so that means the pot is likely connected via the center and right leads.
Any of the model railroading power packs or throttles use some version of a potentiometer to control the speed of the train. On the S-CAB system's throttle, shown in the photo, the speed is controlled by a vertical slider (to the right of the LED display). This works in the same manner as a rotating potentiometer does, except that the resistance value is increased or decreased by moving the slider up and down, or left and right.
Finally, some throttles, such as the Digitrax ones, have what appears to be an infinitely-turning knob. These don't have a mechanical stop at either end of the range. These are not called potentiometers, but rather are "encoders". They operate in the digital domain, rather than in the electro-mechanical domain. You can rotate them in either direction as much as is desired, but the throttle will digitally interpret the movement and will eventually reach its minimum and maximum value, and then the value goes no further in either direction, unless you turn it back. Encoders are used to keep the signal in the digital space, but they feel weird in that there is no way to physically feel when you have reached zero speed, for example; you always have to look at the throttle to verify it visually. Not everybody enjoys that; I am one of those.