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Resonance in RLC Circuits
Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies—in an RLC series circuit, it occurs at $\nu_0 = \frac{1}{\sqrt{2 \pi LC}}$ .
Learning Objectives

Determine when resonance occurs in an RLC series circuit

Compare resonance characteristics of higher and lowerresistance circuits
Key Points

Resonance condition of an RLC series circuit can be obtained by equating XL and XC, so that the two opposing phasors cancel each other.

At resonance, the effects of the inductor and capacitor cancel, so that Z=R, and Irms is a maximum.

Higherresistance circuits do not resonate as strongly compared to lowerresistance circuits, nor would they be as selective in, for example, a radio receiver.
Terms

impedance
A measure of the opposition to the flow of an alternating current in a circuit; the aggregation of its resistance, inductive and capacitive reactance. Represented by the symbol Z.

rms
Root mean square: a statistical measure of the magnitude of a varying quantity.

reactance
The opposition to the change in flow of current in an alternating current circuit, due to inductance and capacitance; the imaginary part of the impedance.
Full Text
Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others. Frequencies at which the response amplitude is a relative maximum are known as the system's resonance frequencies. To study the resonance in an RLC circuit, as illustrated in , we can see how the circuit behaves as a function of the frequency of the driving voltage source.
Combining Ohm's law, I_{rms}=V_{rms}/Z, and the expression for impedance Z from
where I_{rms} and V_{rms} are rms current and voltage, respectively.
The reactances vary with frequency
At some intermediate frequency
The receiver in a radio is an RLC circuit that oscillates best at its
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Key Term Reference
 AC
 Appears in this related concepts: Driven Oscillations and Resonance, Resistors in AC Circuits, and Safety Precautions in the Household
 Law
 Appears in this related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 amplitude
 Appears in this related concepts: Properties of Waves and Light, Reflections, and Sound
 capacitor
 Appears in this related concepts: Resistors and Capacitors in Series, Impedance, and Capacitors with Dielectrics
 circuit
 Appears in this related concepts: Combinations of Capacitors: Series and Parallel, Microwaves, and Maxwell's Equations
 current
 Appears in this related concepts: Reporting LongTerm Liabilities, Magnetic Force Between Two Parallel Conductors, and The Junction Rule
 frequency
 Appears in this related concepts: Guidelines for Plotting Frequency Distributions, Beats, and Frequency of Sound Waves
 inductor
 Appears in this related concepts: Induced Charge, RL Circuits, and Inductance
 natural frequency
 Appears in this related concepts: Forced Vibrations and Resonance and Forced motion
 ohm
 Appears in this related concepts: Poiseuille's Equation and Viscosity, Current and Voltage Measurements in Circuits, and Phase Angle and Power Factor
 oscillate
 Appears in this related concepts: The Speed of a Wave on a String, Polarization By Passing Light Through Polarizers, and Exercises
 phasor
 Appears in this related concepts: Power, Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams, and Phasors
 relative
 Appears in this related concepts: Relative Deprivation Approach, Relative Velocity, and Addition of Velocities
 resistance
 Appears in this related concepts: Resistors in Parallel, Resisitors in Series, and Ecology of Ecosystems
 resonance
 Appears in this related concepts: Bonding in Coordination Compounds: Valence Bond Theory, RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram, and Standing Waves and Resonance
 rms current
 Appears in this related concepts: Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams and Root Mean Square Values
 series
 Appears in this related concepts: Taylor Polynomials, Charging a Battery: EMFs in Series and Parallel, and Finding the General Term
 voltage
 Appears in this related concepts: Conductors, The Millikan OilDrop Experiment, and Principles of Electricity
Sources
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Cite This Source
Source: Boundless. “Resonance in RLC Circuits.” Boundless Physics. Boundless, 02 Jul. 2014. Retrieved 23 Apr. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/resonanceinrlccircuits5863035/