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Two big ideas allow a Tesla coil to function: Induction, and resonance. These two concepts will be explained here, as well as the general description of how a Tesla coil operates.

Induction is a property of circuits defined by Faraday's Law, named after the scientist Michael Faraday. It states that if a coil of wire is in a magnetic field, any change in that magnetic field will produce a voltage in the coil. For example, if you were to wave a permanent magnet near a coil of wire, the coil would be moving through a magnetic field, and a voltage would be induced. Now, since a current in a wire produces a magnetic field, and an alternating current would produce a changing magnetic field, then a coil with an alternating current in it can induce a current in another coil within that changing magnetic field. Tesla coils use this property in the same way that standard transformers do, which is explained in the section on transformers.

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Resonance is a concept that everyone is actually very familiar with; we have used resonance to help ourselves swing on a swing set. When we begin to swing in one direction, we push our legs in the same direction in order to go faster. When we do this for long enough, we end up swinging much higher than we did before. Another example is breaking a wineglass with your voice. When someone yells at the wineglass at the right frequency and volume, the wineglass breaks. This is because of harmonic resonance. When two things vibrate or oscillate at the same frequency, the two things "push" each other in such a way that they they increase their own amplitudes.

http://www.acs.psu.edu/drussell/Demos/SHO/force2.gif

The equations and calculations required to get all of the data required for a proper Tesla coil build are many, and most are not very friendly. I know from hard experience that it is a real pain to do them all by hand, but fortunately there are several resources online that can calculate all of these for you. I personally use a site called Deep Fried Neon to do most of my calculations. The site also includes construction and design guides I find extremely useful. I start with finding the right transformer, then all of the primary circuit components, then all of the secondary circuit components. I put all of these numbers into a Google Sheets file so I had easy access to them.

http://www.tb3.com/tesla/AnimateCoil03.gif

To get a detailed description of the operation of each part of the coil, visit their corresponding pages linked above.

The cycle described here happens in the merest fractions of a second:

1. The power comes out of the mains and is stepped up in voltage by a transformer.


2. The capacitor charges up to full power.


3. The spark gap fires and closes the circuit of the primary coil. The circuit oscillates at a certain predetermined frequency.


4. The primary coil inductively transfers its energy to the secondary coil, their shared resonant frequency causing a sharp increase in voltage.


5. The power is dissipated into the air by the top load, manifesting as sparks.


6. Because the spark gap cannot be perfect, the power is transferred back into the primary coil and back again to the secondary coil until all the energy is dissipated.


7. The spark gap stops firing, and the process starts over again with charging the capacitor.