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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

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

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.

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.
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:
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: Resistors in AC Circuits, Safety Precautions in the Household, and Resistors and Capacitors in Series
 Law
 Appears in these related concepts: Newton and His Laws, Mechanical Work and Electrical Energy, and Models, Theories, and Laws
 Ohm's law
 Appears in these related concepts: Energy Usage, Resistors in Parallel, and Current and Voltage Measurements in Circuits
 atom
 Appears in these related concepts: The Law of Multiple Proportions, Stable Isotopes, and John Dalton and Atomic Theory
 capacitor
 Appears in these related concepts: Impedance, Combinations of Capacitors: Series and Parallel, and ParallelPlate Capacitor
 circuit
 Appears in these related concepts: Forced Vibrations and Resonance, Photon Energies of the EM Spectrum, and Flow Rate and Velocity
 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, The Third Law, and Power
 equation
 Appears in these related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 impedance
 Appears in this related concept: Diffraction
 inductor
 Appears in these related concepts: Energy in a Magnetic Field, RL Circuits, and Inductance
 ohm
 Appears in these related concepts: Poiseuille's Equation and Viscosity, Phase Angle and Power Factor, and Electric Potential Energy and Potential Difference
 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: The Loop Rule, Different Types of Currents, and Introduction and Importance
 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: Taylor Polynomials, Charging a Battery: EMFs in Series and Parallel, and Resisitors in Series
 sinusoidal
 Appears in these related concepts: Driven Oscillations and Resonance, Position, Velocity, and Acceleration as a Function of Time, and Sinusoidal Nature of Simple Harmonic Motion
 voltage
 Appears in these related concepts: Conductors, The Millikan OilDrop Experiment, and The Nernst Equation
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Cite This Source
Source: Boundless. “RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram.” Boundless Physics. Boundless, 01 Jul. 2015. Retrieved 03 Jul. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/rlcseriescircuitatlargeandsmallfrequenciesphasordiagram5826286/