LED lights on HO scale - Model Railroader Magazine

To understand the biasing of LED's, you have to consider Ohm's law. 

   i = V / R 

In English, this means the current in a circuit is proportional to the voltage driving it and inversely proportional to the resistance of the circuit.  Double the voltage and the current doubles as well. Double the resistance and the current drops by half.

LED's are rectifying diodes that happen to glow when conducting. They have NO resistance, like a short circuit.  When you divide V by zero, you get a huge number meaning the current shoots up without limit until something pops.  "Something" is the LED, which is converted into a darkness emitting diode (DED for short).   To prevent catastrophe, a resistor must be inserted in series with the LED.  

  The resistor must be sized to limit LED current to 20 mA or less.  All LED's will withstand a forward bias current of 20 mA and glow VERY brightly.  Current in excess of 20mA will pop LED's.  It's a heat thing, 20 mA  will heat a LED enough to destroy it.  I usually shoot for a LED current of 10 mA, 'cause LED's glow plenty brightly with 10 mA and it gives some margin should the the resistor value be off a little bit, or the voltage a little bit high.  

   Solve Ohm;s law for resistance  and we have

R = V / 0.02    R = V divided by 20 mA or 0.02 Amps which is the same thing.  Ohms law requires all units to be the same, Volts, Amps and Ohms.   That is an approximation good enough for most work.

There is one simple correction needed here.   You don't get the full supply voltage across the resistor.  A forward biased LED drops about 2.75 volts across itself, so the voltage across the resistor is closer to V - 2.75.  This becomes noticeable if you are using a common 5 volt DC supply to light your LEDs. So:

R = (V-2.75) / 0.02 gives a better approximation

You want to light your LEDS with DC and you want to be careful to hook the LED's up the right way round.  Although LED's are rectifying diodes, they are not very good rectifiers, in that they cannot withstand much reverse bias voltage.  It only takes 5 or 6 volts reverse bias to blow a LED.  If you hook up to 12 volts backward the LED is converted to a DED within microseconds.

Some LEDs are made with a current limiting resistor built into the LED.  These can be identified by the voltage specification that they are sold with.   Other than that, the electrical characteristics of all LEDs are about the same, so you can use the low cost unmarked surplus LED's from places like ALL Electronics. 

With all that said, a good cheap source for structure lighting is the tiny white Christmas lights.  They don't get very hot, they plug right in, no power supply needed.  Just let the extra bulbs hang under the layout.  Try yard sales and the after Christmas sales.