Quoted from rolf_martin_062:I do have a cheap, simple meter - I measured Ohms on a 44 bulb and on a 47 bulb - same reading. I do not know if it is 1.6 Ohms or 16 Ohms or 160 Ohms or what.
I made the same mistake. Then I was reminded recently that you can't reliably measure the resistance of an incandescent bulb when it's cold because the resistance of the bulb filament increases as the bulb heats up. So for bulbs it's more reliable to use their ratings to figure out their operating resistance.
A 44 bulb is rated at .25 amps when running at 6.3 volts while a 47 bulb is rated at .15 amps.
Using Ohm's law (V = I * R or, voltage = current * resistance) the resistance of the bulbs at temperature is:
- about 25 ohms for a 44 bulb (6.3 volts = .25 amps * 25 ohms)
- about 42 ohms for a 47 bulb (6.3 volts = .15 amps * 42 ohms)
The purpose of the large resistor in series with the bulb is to drop the voltage from the 25-30 volt relay supply voltage down to the 6.3 volts that the bulb is designed for. How much voltage is dropped across the large resistor depends on the resistor value and on the current that passes through it (V = I * R again).
An 85 ohm resistor would have a voltage drop across it of 21.25 volts when .25 amps pass through it. The same resistor would drop only 12.75 volts across it when .15 amps pass through it, leaving the 47 bulb with more than double the voltage it was designed for.
So while 75-85 ohms is about right to drop the voltage to 6.3 volts for a #44 bulb that draws .25 amps, a larger resistance of 140-150 ohms or so is required to drop the voltage to 6.3 volts for a #47 bulb that draws .15 amps. (LED fans beware: an even larger resistance would be needed if using an LED bulb in this circuit.)
Note that none of these figures is precise. That's not an oversight. Supply voltages vary depending on the transformer and on the voltage supplied by your utility. Resistances can vary 5-10% unless otherwise specified. And I'm sure there's variability in the bulbs too due to manufacturing and other differences. The good news is that 5-10% is usually good enough unless you're dealing with precision equipment (test equipment, audio, etc.).