How to tune the frequency of a coil? I'm doing a scientific fair project. I want to do it about wireless energy transmission.
In practice consists of two coils NOT physically connected. One is the transmitter of energy, which is connected to a source of energy. The other (s) is the receiver, which receives the energy through magnetic fields. The main characteristic is that both coils are designed to have the same frequency, since this way the amount of energy transferred is maximized. So my question is, how can I do, to equalize its frequencies? Keep in mind that I am a high school student and you could explain it to me in more practical terms to carry out the project.
PD: I investigated, and according to this, I must obtain "the maximum output" to pass the point of resonance, but I have no idea what this means
 A: Normally, the resonant frequency of the antenna can be tuned with a variable capacitor (varactor) using a bias voltage. In direct inductive coupling of coils there is no resonance involved although capacitors may still be used to match the driver amplifier or receiver detector to the coil. The word antenna in this context is probably a misnomer for there is no radiation involved, rather the coils act as a pair of loosely coupled inductive transformer. You can find the details and with design formulas in Umar Azad, Crystal Jing, Ethan Wang: "Link Budget and Capacity Performance of Inductively Coupled Resonant Loops" IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 60, NO. 5, MAY 2012
A: The frequency of the signal is not a property of the coil alone, but of a resonant circuit which includes both the coil and a capacitor. You question is thus about tuning the resonant frequency.
This may be done by varying the value of either the capacitor or the coil.
Usually, varying the capacitance is easier. Most capacitors are basically a pair of plates set close to each other. A variable capacitor will adjust their area of overlap or their distance apart. Both types are commercially available and which you choose will depend on the capacitance value and power level. Alternatively, for higher frequencies you can get solid-state, voltage-controlled capacitors, such as varicap diodes, but these need complicated circuitry to control them.
Sometimes, varying the coil inductance is done instead. This can be done either by squeezing and stretching the coil lengthways, or by leaving a hole through the core and inserting or withdrawing a magnetic or conductive slug. Most variable inductors use small ferrite cores with a ferrite slug you screw in and out. Your magnetic system will need a large-diameter air-cored coil, presumably home made. Simply placing a piece of metal or a hand near it can affect its value. You could rig up some kind of plunger in the middle, but you'd need a long-ish adjusting rod so your hand doesn't get too close.
When the resonant frequency of the receiver is tuned to exactly match the frequency of the transmitter, you will obtain the strongest (maximum) output signal from the receiver.
One problem you will face is drift; as the components warm or cool, their values will change and the frequencies will drift. To keep it in tune you may find that you need to adjust it from time to time during operation.
A: A coil does not have a frequency.  A circuit with a coil, a capacitor, and resistance has a resonant frequency:  $ω^2 = 1/(LC)$.  The frequency in your transmitting coil will depend on the source of power.
A: Ideally you must ensure that,
$$S R F=\frac{1}{2 \pi \sqrt{L C}}$$
The Self Resonant Frequency of the two separated circuits is the same.
Meaning they must have the same inductance L and Capacitance C product (i.e. not necessarily the same discrete L and C values).
Ohmic resistance does not affect the common resonant frequency however it affects the Q factor of the resonance (i.e. how sharp in bandwidth the circuit resonates):
$$Q=R \sqrt{\frac{C}{L}}=\frac{R}{\omega_{0} L}=\omega_{0} R C$$
Here the ohmic resistance of the circuit does matter as shown in the function above. The higher the resistance R the higher the Q factor and thus the resonance is more sharp that translates to less energy loss between the two circuits.
Make sure your coils have a ferrite core. That will greatly increase their inductance L and reduce their size.
Next optimize the mutual inductance M and coupling coefficient K of the two separated coils:
$$M=k \sqrt{L_{1} L_{2}}$$
In this case of wireless transmission - reception the higher k value closer to 1 is the better. Spatial alignment and proximity of the two coils will affect k.
Impedance Z matching, WP, between the two circuits meaning besides inductive and capacitive reactance $X_{L}$ and $X_{C}$, load ohmic resistance in both circuits R should be the same is many times no practically achievable because the different load requirements in the receiving circuit.
In that case use an impedance matching circuit on the receiving end to connect your receiving load (i.e. that would be the combined input resistance of the demodulator circuit and signal amplifier connected).
