The electrical theory is a bit more complicated. First, although
almost all dynamos are rated 6V 3W, that's an oversimplification
that's approximately valid only when they're fitted with the load
(i.e. bulbs) for which they were designed. It's more accurate to say
they put out half an Amp. The physics of the design causes it to
automatically adjust the voltage to whatever value is needed to push
out half an amp.
Second, a resistor's characteristic property (called "resistance"_) is
measured in Ohms, not Volts. The number of volts you'd drop through a
resistor depends on its rating in Ohms, but also on the amount of
current measured in Amps. So that part is a bit more complicated.
Look up "Ohm's Law," which is a very simple equation, to see how the
variables tie together.
Now about the practicalities: I don't know much about the design of
the light you're using. But there's a (small?) chance you could get
by much more simply. If the light naturally drew about half an amp
out of the battery, you could expect the dynamo to put about half an
amp into the battery, and you might be done. But a bike dynamo puts
out AC, while the battery both produces DC, and needs DC for
charging. So you need a full-wave rectifier, which costs maybe $3
from Radio Shack.
For a little more explanation, see Sheldon's explanation of his
system, at
http://sheldonbrown.com/dynohubs.html It's mostly correct. He was
talking about antique Sturmey-Archer Dynohubs but it applies to almost
any dynamo.
Here's a partial quote of the pertinent part:
"I used to have a Dynohub on a tandem, and the bulb consumption was
unacceptable. I solved the problem (and some others) by running the
Dyno's output through a full-wave bridge rectifier and then hooking
the DC in parallel with a 6 volt (5 x 1.2v cell) nickel cadmium
battery. This not only provided light when I was stopped, the Dyno
would re-charge the nicads, and, when we went so fast that the voltage
rose above 6 volts, the low internal resistance of the nicads sucked
up the excess, gaining a bit of extra charge and saving the bulb.
"The rectified output of the Dynohub was always connected to the
lights. There was no way to turn the light off while you were in
motion. It would have been easy enough to rig a switch for that
purpose, but I didn't see the need. The Dynohub has _very_ low drag.
"I had a three way switch connecting the battery pack to the lights.
In the "night" position, the nicads were in parallel with the
rectified output of the Dynohub, as described above..."
But I think you'll find your headlight draws more current than half an
amp. If so, engaging the dynamo/rectifier system might extend running
time, but not make it infinite, as with a proper generator system.
There may be ways around that (e.g. reducing current to the headlamp)
but I suspect that's more than you'd want to attempt.
If the battery is a Ni-Cad or lead acid, I wouldn't worry about the
difference between the supposed 6V dynamo output and the 4.8V of the
battery. To charge a battery, you need a bit of excess voltage. But
if it's lithium or Ni-MH, I think recharging needs more
sophistication. Look up accounts of laptop batteries catching fire.
(I've never seen a bicycle fire, but you wouldn't want to be the
first!)
Those are initial thoughts. If you could post more technical details
on your lights, we could probably give further advice. How many watts
do they claim? What's the amp-hour capacity of the stock battery?
How many hours does the battery actually last? What chemistry is it?
Oh, and how much do you want to learn about working with electricity?
It would be simpler just to buy a good dynamo and headlight. But the
tinkering and the challenge can be fun.
- Frank Krygowski