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I may have messed up direction of LED in diagram so just make sure you put it in the correct way :)
Circuit Diagram
Here's why 22 ohms is great, and won't blow anything. Don't forget that the diode has it's own 'forward voltage' that does not count toward the voltage difference falling on the resistor (which sets the current). The way to figure the resistance is: r = e / i The e = e(source) - e(diode drop). This is 3.6V for the battery and 3.2V or slightly more for the diode. Therefore, only around .5V falls over the resistor. So, .5V/.020A = 20ohms!
A subscript here is that the voltage over the diode actually increases with current; check the datasheet for the diode to see what I mean. because of this, each new current level set by the resistor causes a slightly different voltage level on the LED. Again, check your datasheet to be sure of the final level. Some LEDs drop about 3.6V @ their max current and those LEDs don't even need resistors at all with this sort of lithium battery! They automatically accept the current value associated on the curve with that forward voltage.
Also, as to the 'greater voltages' concern, the battery will keep any higher voltages from being reached. It would actually continue to accept the pulses of current as recharging current and the maximum voltage would not appreciably rise until the battery were completely full or beyond. Check a lithium battery book for the charge/discharge voltage curves - you'll find them quite flat.
So, summary: shake away, and you won't reach dizzying voltages as long as the battery is there... a capacitor might be a different story! And, 22 ohms is the right value because the resistor only limits the voltage it is exposed to... only about .5V or less.
Regards,
David
If you're using a diode that is orange with a black stripe, the black stripe is negative. Most common LED's negative leg is longer than the positive leg. Other diodes will be marked.
If you are unsure about the polarity of your diode, look up the specifications sheet. Good places to do this (as well as price the materials) are Digikey and Mouser.
I think the circle with (-) in it is supposed to be the negative terminal of the battery too, he just didn't label it "battery".