stoven said:
One last question -
As the batteries drain their voltage decreases right? So as the voltage decreases the change in voltage across the resistor decreases causing a reduction in current right?
Yes, that's correct. Now, let's see just how much it'll decrease. All you need to know is Ohm's law to follow it.
For simplicity, I'm going to consider the LED to have a voltage that doesn't change with current. It does, of course, but not much. At around 1 amp, a 200 mA current change causes only about a 0.1 volt change in LED voltage. So we'll consider it constant at 3.7 volts for this analysis.
Your fresh cells will have a voltage of around 3.0 volts at one amp, although they won't stay at that level very long. Suppose you chose a 2.2 ohm series resistor. The initial current would be (6.0 - 3.7) / 2.2 = 1.05 amp. In a short time, the voltage will drop to around 2.5 volt per cell, and stay close to that for most of the discharge period. Then your current will be (5.0 - 3.7) / 2.2 = 590 mA. When the cells are just about dead, their voltage will be about 2.0 volts, so the current wil be (4.0 - 3.7) / 2.2 = 140 mA. That drop will occur, though, only very near the end of the discharge period. Also, at that low current the LED voltage will be significantly lower, so the current drop won't be this bad. If you had used Li-Ion cells with voltage of around 4.0 - 3.5 volts per cell during discharge and chosen a 4.3 ohm resistor, you'd have (8 - 3.7) / 4.3 = 1.0 amp at 4.0 volts/cell and (7 - 3.7) / 4.3 = 770 mA at 3.5 volts/cell. The higher the resistor value, the more constant the current. But the efficiency is lower with the Li-Ion cells and higher resistor value.
You won't find a very good zener with a drop around 2 volts, but let's say you did, and you used it and 0.33 ohms instead of just the resistor. Then when the battery voltage is 6.0 volts (3.0 volt/cell), the current will be (6.0 (battery) - 2.0 (zener) - 3.7 (LED)) / .33 = 910 mA. It'll decrease from 910 mA to zero as the cell voltage drops from 3.0 volts to 2.85 volts, which will take only minutes.
In practice, the internal resistance of the cell and other stray resistances will alter things a bit, but this will give you an idea of what's happening. You can improve the current regulation with a linear current regulator circuit, but it'll have the same or less efficiency than the resistor.
c_c