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All about LEDs
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LED...Light Emitting Diode.  LEDs are not difficult to use but it is useful to have some basic understanding of DC (direct current) electrical circuits.  There are four things that are usually considered in a DC circuit. They are: Voltage (E) expressed as volts, Current (I) expressed as Amps, Resistance (R) expressed as Ohms and Power (P) expressed as watts.  In our model trains the Voltage comes from a battery or from the power pack down the rails.   I'm going to limit the rest of this topic to just considering battery power, since that's all I use but what I show here can be considered valid for track power.  Just remember that with a battery my Voltage is pretty constant until the battery begins to get to the end of its charge and with a power pack the Voltage can go from 0 to 24 or more.

One thing you can do to help visualize electrical circuits is to think of it as you would water in a hose or pipe.
Voltage is like water pressure.
Current is like the flow of the water...gallons per minute.
Resistance is like the size of the hose or pipe... it's harder to get water through a small pipe than a big pipe.
So the water pressure (E) helps determine how fast the water will flow (I) through any given size (R) of hose or pipe.

E = voltage       I = Current      R= Resistance

Ohm's Law states that  E = IR, which means that  I = E/R  and   R = E/I  are also true.  Why do I care?...I used to ask that question a lot.  Answer, because when you buy an LED the package material will tell you what Current (I) and what Voltage (E) you need to use to run it without destroying it.  The thing with LEDs is that they appear to have very, very little resistance so you must use a resister.  If you don't, the Current (I) will go so high as to burn out the LED. 

So here's an example.  I have an LED that says it runs on a current of 20mA.  The mA means milliamps, which is the same as 0.020Amps. And the LED will use 3.5V...which is 3.5 Volts.  The LED will always use 3.5V so I need to find a resistor that will limit the current to 20mA using Ohm's law. Here's the tricky part.  I know the current I want is .020 Amps but what's the voltage?  It's not 3.5...that's the voltage the LED is using and I need to know the voltage the resistor is using.  The answer is that I take my battery voltage and subtract 3.5 (what the LED is using) from that number.   I use 14.4 volt batteries in all my engines, but a freshly charged battery will be closer to 16.2 volts. So to be safe I'll use that number. The resistor voltage will then be 16.2 - 3.5  which is 12.7.

So if ... R = E/I ....I can plug in the numbers  R = 12.7volts / 0.020Amps.
R = 12.7 / 0.020.....therefore  R = 635ohms

So now I know I need a 635ohm resistor but there's one more thing I need to know and that's how much power is used so I can buy the resistor with a correct power rating.  Power has it's own formula, which is P = IE.

So if.....P = IE.....then .....P = 0.020Amps x 12.7Volts.....therefore P = 0.22watts

Resistors come in all sizes but at Radio Shack and similar stores the resistors are most often sold in 1/4 watt and 1/2 watt sizes.  A 1/4 watt can be shown as 0.250 so our example needs a 1/4watt resistor.

The minimum size resistor I need is a 635 Ohm, 1/4Watt resistor. Anything that size or a little bigger will be fine.