How we get from a led that runs at 20 mA, to 60 hours of life? I may be dumb (may? likely am), but 200/20 = 10 hours for a single LED. Confused about "rated discharge current" vs the power of the LEDs.
Batteries, honestly, get tired if you suck power out too fast. Every battery in the world has a rating called "Capacity," which is in Amp-hours. They are tested at some rate (amps) and will last for some time (hours) at that rate. If I have a battery that can give me 1 amp for 1 hour, I have a 1 amp*hour battery. I could take the same power out of the battery in half that time, or have 2 amps for half an hour.
However, if I take that battery and drain it dry at 20 amps, it won't last even 3 minutes (1/20th of an hour), because batteries get tired. If you drain a battery faster than its "rated current," you won't have as much power. Since these CR2032 cells have 200 mAh in them at 3 mA, you can run them for about 60 hours. Higher drain rates will reduce how much power you have. At 20 mA, I would conservatively estimate five to six hours runtime.
Secondly, if the light maxes out at 20mA, how do we tell it to drop to 10-15, to use less of the battery?
Sorry for the dumb questions, but you guys have been super helpful already.
Edit: The LEDs don't max out at 20 mA, really. They are "rated" for 20 mA, which means they last a reasonable while (Several hundred hours, we hope) without getting too much dimmer. Like all machines, you can "overdrive" the LED with a bit more current. But even doubling the current won't look very much brighter, but it greatly cuts battery life and LED life.
Using resistors, we play with voltage. Imagine the electrons in the circuit. If they went long enough, they would go in a loop from the (+) end of the battery, through the wires, LED, and resistor, to the (-) end of the battery, and move back "up" from 0 volts to about 3 volts. The voltage of the whole circuit as a loop amounts to 0, a closed loop.
If I had a resistor and a battery, the resistor would have the opposite voltage as the battery, and current would flow through the resistor following Ohm's Law: V=IR (Volts equals Amps (I) times Resistance in ohms). Resistors predictably change their voltage with current.
LEDs are tricky. Being semiconductors, they have a nonlinear response (A curve, not a line). In general, a white LED may light up very dimly (Low current) at 2.5v, be quite bright at 3.0v, be extremely bright and short-lived at 3.4v, and burn out much over that.
You're combining an LED and a resistor to get 3v at 20 mA. Technically, you are using the voltage of the LED at 20 mA V(led at 20 mA) plus V(resistor at 20 mA) equals 3v. As a rule of thumb, we like to use data-sheets for each LED, but general rules apply:
1.8-2v, Red, Yellow, Orange
2.5-3v, Green, Blue, Purple, White
LED color is based on the voltage needed by a semiconductor part. 'Higher Energy' photons take higher voltage, so we can guess what the LED's voltage is going to be at a reasonable current. The abstract, math-ey way is to plot the LED's voltage response to current and pick a resistor so it all adds up to 3v.
The engineer way is to borrow or use a multimeter on a "milli-amp (mA)" setting, and measure. Connect one leg of the LED to a resistor between 50 and 200 ohms, then touch the free legs to the battery. If it didn't light, turn the battery around and try again. Now tape one "free' leg to the battery, and connect the multimeter probes in. Touch the free leg with one, and the battery with the other. A number should pop up telling you the current draw. Larger resistors in series will decrease this number (Dimmer). Adding resistors in parallel will increase it (Brighter). The current draw will indicate battery life, but nothing replaces a runtime test. The light will gradually dim over time, eventually fading to nothing.
PS: Don't get the lithium coin cells wet! Metals in non-pure water can corrode very fast when they have voltage on them. Nothing exciting is likely to happen, but the lights won't light.