124CHAPTER 6. RESONANCEcurrent has earned it the name tank circuit. Its property of maintaining a single, natural frequencyregardless of how much or little energy is actually being stored in it gives it special signiﬁcance inelectric circuit design.However, this tendency to oscillate, or resonate, at a particular frequency is not limited tocircuits exclusively designed for that purpose. In fact, nearly any AC circuit with a combination ofcapacitance and inductance (commonly called an “LC circuit”) will tend to manifest unusual eﬀectswhen the AC power source frequency approaches that natural frequency. This is true regardless ofthe circuit’s intended purpose.If the power supply frequency for a circuit exactly matches the natural frequency of the circuit’sLC combination, the circuit is said to be in a state of resonance. The unusual eﬀects will reachmaximum in this condition of resonance. For this reason, we need to be able to predict what theresonant frequency will be for various combinations of L and C, and be aware of what the eﬀects ofresonance are.• REVIEW:• A capacitor and inductor directly connected together form something called a tank circuit,which oscillates (or resonates) at one particular frequency. At that frequency, energy is alter-nately shuﬄed between the capacitor and the inductor in the form of alternating voltage andcurrent 90 degrees out of phase with each other.• When the power supply frequency for an AC circuit exactly matches that circuit’s naturaloscillation frequency as set by the L and C components, a condition of resonance will havebeen reached.6.2Simple parallel (tank circuit) resonanceA condition of resonance will be experienced in a tank circuit (Figure 133,6.11) when the reactancesof the capacitor and inductor are equal to each other. Because inductive reactance increases withincreasing frequency and capacitive reactance decreases with increasing frequency, there will onlybe one frequency where these two reactances will be equal.10 µF100 mHFigure 6.11: Simple parallel resonant circuit (tank circuit).In the above circuit, we have a 10 µF capacitor and a 100 mH inductor. Since we know theequations for determining the reactance of each at a given frequency, and we’re looking for that