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
Learning Objective

Compare resonance characteristics of higher and lowerresistance circuits
Key Points
 Resonance condition of an RLC series circuit can be obtained by equating X_{L} and X_{C}, so that the two opposing phasors cancel each other.
 At resonance, the effects of the inductor and capacitor cancel, so that Z=R, and I_{rms} 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

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

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.

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 below, we can see how the circuit behaves as a function of the frequency of the driving voltage source.
RLC Series Circuit
An RLC series circuit with an AC voltage source. f is the frequency of the 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
Current vs. Frequency
A graph of current versus frequency for two RLC series circuits differing only in the amount of resistance. Both have a resonance at f0, but that for the higher resistance is lower and broader. The driving AC voltage source has a fixed amplitude V0.
Key Term Reference
 AC
 Appears in these related concepts: Driven Oscillations and Resonance, Impedance, and Resistors in AC Circuits
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 amplitude
 Appears in these related concepts: Properties of Waves and Light, Period of a Mass on a Spring, and Sound
 capacitor
 Appears in these related concepts: Introduction and Importance, ParallelPlate Capacitor, and ParallelPlate Capacitor
 circuit
 Appears in these related concepts: Combinations of Capacitors: Series and Parallel, Microwaves, and Maxwell's Equations
 current
 Appears in these related concepts: Reporting LongTerm Liabilities, The Battery, and Magnetic Force Between Two Parallel Conductors
 frequency
 Appears in these related concepts: Guidelines for Plotting Frequency Distributions, Frequency of Sound Waves, and Characteristics of Sound
 inductor
 Appears in these related concepts: Energy in a Magnetic Field, Energy Stored in a Magnetic Field, and Inductance
 natural frequency
 Appears in this related concept: Forced Vibrations and Resonance
 ohm
 Appears in these related concepts: Poiseuille's Equation and Viscosity, Current and Voltage Measurements in Circuits, and Phase Angle and Power Factor
 oscillate
 Appears in these related concepts: Problems, The Speed of a Wave on a String, and Polarization By Passing Light Through Polarizers
 phasor
 Appears in these related concepts: Power, Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams, and Phasors
 relative
 Appears in these related concepts: Relative Deprivation Approach, Addition of Velocities, and Relative Velocity
 resistance
 Appears in these related concepts: Resistors in Parallel, Resisitors in Series, and Introduction to Blood Flow, Pressure, and Resistance
 resonance
 Appears in these 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 these related concepts: Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams and Root Mean Square Values
 series
 Appears in these related concepts: Combination Circuits, APA: Series and Lists, and The General Term of a Sequence
 voltage
 Appears in these related concepts: The Nernst Equation, Electric Potential Due to a Point Charge, and Principles of Electricity
Sources
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