# Resonance / Black Magic 101.

Let us assume a circuit with a resistor, a capacitor and an inductor in series with each other. We will use small numbers here for simplicity.

If the value of the resistor is 4 ohms, the value of the inductor is 3 ohms, and the value of the capacitor is -3 ohms. (Remember that capacitors are negative in nature). The 3 ohms of capacitive reactance (X

_{ C })will negate the 3 ohms of inductive reactance (X

_{ L }), and the overall resistance is figured as follows:

R

^{ Total }= R + X

_{ L }- X

_{ C }

R

^{ Total }= 4 + ( 3 - 3 )

Whenever a circuit has both inductors and capacitors, there is a given frequency at which X

_{ L }is mathematically equal, but opposite to X

_{ C }. In this case, X

_{ L }is +3 and X

_{ C }is - 3.

When this happens, the Total Resistance is equal to the pure resistance of the resistor, and the capacitor and inductor cancel each other out for all intents and purposes. We say then, that the circuit is in

**RESONANCE**.

When a circuit is resonant, it is at its lowest point in resistance. Any increase, or decrease in frequency will cause the circuit to have greater resistance.

But because a circuit has less resistance at it resonant frequency, it will allow more of a signal to pass through at resonance than at a higher or lower frequancy than the resonant frequency.

The frequency at which the circuit becomes resonant is (for our purposes) completely dependant on the inductance and capacitance of the circuit. The "pure" resistance of the circuit does not affect the resonant frequency of the circuit.

Circuits which are resonant at a given frequency are said to be TUNED to that frequency. These are sometimes called TUNED CIRCUITS .

They may also be called FILTERS , because they are used to "filter" one set of frequencies apart from all the others within a given band of frequencies. In some circles, tuned or resonant circuits are referred to as TANK CIRCUITS , although I'm not exactly certain why. It has always been my belief that this referred to Tuned Cavities in waveguide, which resemble a tin can or tank in nature. But I have yet to substantiate this idea. Just keep in mind that if you hear someone refer to a tank circuit, they are talking about a tuned filter.