RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram
Response of an RLC circuit depends on the driving frequency—at large enough frequencies, inductive (capacitive) term dominates.
Learning Objective

Distinguish behavior of RLC series circuits as large and small frequencies
Key Points
 RLC circuits can be described by the (generalized) Ohm's law. As for the phase, when a sinusoidal voltage is applied, the current lags the voltage by a 90º phase in a circuit with an inductor, while the current leads the voltage by 90∘ in a circuit with a capacitor.
 At large enough frequencies
$(\nu \gg \frac{1}{\sqrt{2\pi LC}})$ , the circuit is almost equivalent to an AC circuit with just an inductor. Therefore, the rms current will be Vrms/XL, and the current lags the voltage by almost 90∘.  At small enough frequencies
$(\nu \ll \frac{1}{\sqrt{2\pi LC}})$ , the circuit is almost equivalent to an AC circuit with just a capacitor. Therefore, the rms current will be given as V_{rms}/X_{C,} and the current leads the voltage by almost 90^{∘}.
Terms

resonance
The increase in the amplitude of an oscillation of a system under the influence of a periodic force whose frequency is close to that of the system's natural frequency.

Lenz's law
A law of electromagnetic induction that states that an electromotive force, induced in a conductor, is always in such a direction that the current produced would oppose the change that caused it; this law is a form of the law of conservation of energy.

rms
Root mean square: a statistical measure of the magnitude of a varying quantity.
Full Text
In previous Atoms we learned how an RLC series circuit, as shown in , responds to an AC voltage source. By combining Ohm's law (I_{rms}=V_{rms}/Z; I_{rms} and V_{rms} are rms current and voltage) and the expression for impedance Z, from:
Series RLC Circuit
A series RLC circuit: a resistor, inductor and capacitor (from left).
we arrived at:
From the equation, we studied resonance conditions for the circuit. We also learned the phase relationships among the voltages across resistor, capacitor and inductor: when a sinusoidal voltage is applied, the current lags the voltage by a 90º phase in a circuit with an inductor, while the current leads the voltage by 90^{∘} in a circuit with a capacitor. Now, we will examine the system's response at limits of large and small frequencies.
At Large Frequencies
At large enough frequencies
At Small Frequencies
The impedance Z at small frequencies
Key Term Reference
 AC
 Appears in these related concepts: Driven Oscillations and Resonance, Power, and Impedance
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 Ohm's law
 Appears in these related concepts: Energy Usage, Resistors in Parallel, and Ohm's Law
 atom
 Appears in these related concepts: Overview of Atomic Structure, Description of the Hydrogen Atom, and Stable Isotopes
 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
 diagram
 Appears in these related concepts: Motion Diagrams, Bohr Orbits, and B.4 Chapter 4
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 frequency
 Appears in these related concepts: Properties of Waves and Light, Characteristics of Sound, and Sound
 impedance
 Appears in this related concept: Diffraction
 inductor
 Appears in these related concepts: Energy in a Magnetic Field, Energy Stored in a Magnetic Field, and Inductance
 ohm
 Appears in these related concepts: Poiseuille's Equation and Viscosity, Current and Voltage Measurements in Circuits, and Phase Angle and Power Factor
 phase
 Appears in these related concepts: The Kinetic Molecular Theory of Matter, The Phase of Orbitals, and The Production of Electromagnetic Waves
 phasor
 Appears in these related concepts: Resonance in RLC Circuits, Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams, and Phasors
 resistor
 Appears in these related concepts: Safety Precautions in the Household, The Loop Rule, and Resistors in AC Circuits
 rms current
 Appears in this related concept: Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams
 series
 Appears in these related concepts: Combination Circuits, Resisitors in Series, and The General Term of a Sequence
 sinusoidal
 Appears in these related concepts: Sinusoidal Nature of Simple Harmonic Motion, Root Mean Square Values, and Introduction to The Sampling Theorem
 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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