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Power
Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$ .
Here, $\phi$ is called the phase angle.
Learning Objectives

Determine power delivered to an RLC series AC circuit from the current and the voltage

Identify conditions when the source voltage and the current are in phase
Key Points

Phase angle ϕ is the phase difference between the source voltage V and the current I. See the phasor diagram in .

At the resonant frequency or in a purely resistive circuit Z=R, so that cosϕ=1. This implies that ϕ=0º and that voltage and current are in phase.

Average power dissipated in an RLC circuit can be calculated by taking a time average of power, P(t) = I(t)V(t), over a period.
Term

rms
Root mean square: a statistical measure of the magnitude of a varying quantity.
Full Text
If current varies with frequency in an RLC circuit, then the power delivered to it also varies with frequency. However, the average power is not simply current times voltage, as is the case in purely resistive circuits. As seen in previous Atoms, voltage and current are out of phase in an RLC circuit. There is a phase angle ϕ between the source voltage V and the current I, given as
For example, at the resonant frequency
The fact that source voltage and current are out of phase affects the power delivered to the circuit. It can be shown that the average power is
(an equation derived by taking a time average of power, P(t) = I(t)V(t), over a period. I(t) and V(t) are current and voltage at time t). Thus cosϕ is called the power factor, which can range from 0 to 1. Power factors near 1 are desirable when designing an efficient motor, for example. At the resonant frequency, cosϕ=1.
Power delivered to an RLC series AC circuit is dissipated by the resistance alone. The inductor and capacitor have energy input and output, but do not dissipate energy out of the circuit. Rather, they transfer energy back and forth to one another, with the resistor dissipating the exact amount that the voltage source gives the circuit. This assumes no significant electromagnetic radiation from the inductor and capacitor (such as radio waves).
The circuit is analogous to the wheel of a car driven over a corrugated road, as seen in . The regularly spaced bumps in the road are analogous to the voltage source, driving the wheel up and down. The shock absorber is analogous to the resistance damping and limiting the amplitude of the oscillation. Energy within the system goes back and forth between kinetic (analogous to maximum current, and energy stored in an inductor) and potential energy stored in the car spring (analogous to no current, and energy stored in the electric field of a capacitor). The amplitude of the wheels' motion is a maximum if the bumps in the road are hit at the resonant frequency.
Key Term Reference
 AC
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 amplitude
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 atom
 Appears in this related concepts: Early Ideas about Atoms, Stable Isotopes, and John Dalton and Atomic Theory
 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
 damping
 Appears in this related concepts: Forced Vibrations and Resonance, Applications of SecondOrder Differential Equations, and Damped Harmonic Motion
 diagram
 Appears in this related concepts: Motion Diagrams, Bohr Orbits, and Muscles and Joints
 electric field
 Appears in this related concepts: Gauss's Law, Uniform Electric Field, and Maxwell's Predictions and Hertz' Confirmation
 electromagnetic radiation
 Appears in this related concepts: Scattering of Light by the Atmosphere, Gamma Decay, and Planck's Quantum Theory
 energy
 Appears in this related concepts: Energy Transportation, Surface Tension, and Introduction to Work and Energy
 equation
 Appears in this related concepts: A General Approach, Equations and Inequalities, and Equations and Their Solutions
 frequency
 Appears in this related concepts: Antennae, Guidelines for Plotting Frequency Distributions, and Beats
 inductor
 Appears in this related concepts: Induced Charge, RL Circuits, and Inductance
 kinetic
 Appears in this related concepts: Friction: Static, The Kinetic Molecular Theory of Matter, and Sculpture
 motion
 Appears in this related concepts: TwoComponent Forces, Time, and Moving Source
 period
 Appears in this related concepts: Number of Periods, Atomic Size, and Frequency of Sound Waves
 phase
 Appears in this related concepts: Borates: BoronOxygen Compounds, The Phase of Orbitals, and The Production of Electromagnetic Waves
 phasor
 Appears in this related concepts: Resonance in RLC Circuits, Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams, and Phasors
 potential
 Appears in this related concepts: What is Potential Energy?, Conservative and Nonconservative Forces, and Linear Expansion
 potential energy
 Appears in this related concepts: Escape Speed, Defining Graviational Potential Energy, and Types of Energy
 power
 Appears in this related concepts: What is Power?, Sources of Power, and Power
 resistance
 Appears in this related concepts: Resistors in Parallel, Resisitors in Series, and Ecology of Ecosystems
 resistor
 Appears in this related concepts: The Loop Rule, Current and Voltage Measurements in Circuits, and Introduction and Importance
 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
 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
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Cite This Source
Source: Boundless. “Power.” Boundless Physics. Boundless, 02 Jul. 2014. Retrieved 23 Apr. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/power5871645/