# 6: Resonance

• 6.1: An Electric Pendulum
Capacitors store energy in the form of an electric field, and electrically manifest that stored energy as a potential: static voltage. Inductors store energy in the form of a magnetic field, and electrically manifest that stored energy as a kinetic motion of electrons: current. When these two types of reactive components are directly connected together, their complementary tendencies to store energy will produce an unusual result.
• 6.2: Simple Parallel (Tank Circuit) Resonance
A condition of resonance will be experienced in a tank circuit when the reactances of the capacitor and inductor are equal to each other. Because inductive reactance increases with increasing frequency and capacitive reactance decreases with increasing frequency, there will only be one frequency where these two reactances will be equal.
• 6.3: Simple Series Resonance
A similar effect happens in series inductive/capacitive circuits. When a state of resonance is reached (capacitive and inductive reactances equal), the two impedances cancel each other out and the total impedance drops to zero!
• 6.4: Applications of Resonance
So far, the phenomenon of resonance appears to be a useless curiosity, or at most a nuisance to be avoided (especially if series resonance makes for a short-circuit across our AC voltage source!). However, this is not the case. Resonance is a very valuable property of reactive AC circuits, employed in a variety of applications.
• 6.5: Resonance in Series-Parallel Circuits
In simple reactive circuits with little or no resistance, the effects of radically altered impedance will manifest at the resonance frequency. In a parallel (tank) LC circuit, this means infinite impedance at resonance. In a series LC circuit, it means zero impedance at resonance
• 6.6: Q Factor and Bandwidth of a Resonant Circuit
The Q, or quality, factor of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a more narrow bandwith, which is desirable in many applications. More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistance.