This is the most finicky step in the project. Your choice of capacitor will determine how well (if at all) your coil works.
Use a film capacitor rated for at least 100 volts and 1uF. 100v may seem low, but the cap I used with greatest success is rated at 100v, while higher voltage rated caps only made the coil buzz.
DO NOT USE ELECTROLYTIC CAPACITORS! These are the ones that look like little metal cans. Even high voltage, high capacitance types failed on me *every* time. They got very hot, they bulged, and one even exploded. No joke--leave them alone! Stick with film types. There may be others that will work as well, but my best result came with a cap salvaged from a computer monitor circuit board.
It is marked:
I measured the capacitance of this cap with a multimeter and got a reading of 2.178 microfarads. With this cap I get good long sparks, cool operation, and no overheating of the coil, the switch, or the cap, although I have not run the coil for long periods. The longest I have let it run was for 60 seconds.
I mount the cap in the jaws of the clothespin. The lower lead goes to the output cord alligator clip, and the upper lead to the dimmer switch. Update as of 3/23/09:
I obtained some metalized polyester capacitors rated at 2.2 uF at 250V from an eBay seller . They work very well, and give a greater range of output on the dimmer (by this I mean I get more sparks at higher settings than I did with the 100v cap). The new caps are marked:
Tolerance is rated at 10%. Update as of 4/22/09
While tearing down a surplus microwave oven, I came across an array of capacitors I thought I would try in the coil driver. (These are not the usual metal can capacitors associated with microwaves; they are high voltage film-type caps). A couple of 3KV caps did not work, but a 4.5 uF, 250 volt cap gives much greater sparks than anything I have used before. Discharges are longer, thicker, and louder. They are no longer blue-white, as with the previous caps, but a kind of vivid orange. Does this indicate a lower temperature, I wonder?
The cap is marked:
Update as of 4/18/10:
Even better results have been obtained using a 10 uF, 330 volt VIOT motor start-run capacitor. This is a large, oval metal-bodied cap I found on eBay. With the motor start capacitor the coil produces much more powerful arcs. I have used this coil and cap combination to power my Tabletop Tesla Coil
with success. If you can get a motor start cap like this, by all means use it.