I may not know the technical definition of a
Tank Circuit, but I have built one. As far as I can tell, a "Tank Circuit" is one where a capacitor is discharged through an inductor, such that the circuit
resonates. This is based on how the tank circuit of a
Tesla Coil works. Others should be the same.
The basic idea is that the capacitor is charged (from some outside source). When current begins flowing through the inductor (a coil), a magnetic feild is setup around the inductor.
As the capacitor's charge aproaches zero, the magnetic feild in the inductor gets smaller. The changing magnetic feild causes more current to flow, thus recharging the capacitor in the oposite direction (the plate that was positive is now negative).
Once the feild, and thus the current, is gone, the capacitor discharges through the inductor once again, but in the opposite direction now.
Thus the circuit "rings" back and forth until all of the energy is lost to resistance and other imperfections of the physical system (or is stolen away by another circuit that is being powered by the tank circuit - or until the circuit is broken)
The frequency of the alternation is determined entirely by the capacitance and inductance of the circuit. As they go up, each cycle takes longer, and thus the frequency goes down.
These are also called "LC Circuits" as the symbols used for Inductance and Capacitance are L and C respectively. The formula for finding the resonant frequency of the circuit is:
F = 1 / (2pi(LC)1/2)