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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.
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Key Term Reference
 AC
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 amplitude
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 atom
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 capacitor
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 circuit
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 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, Maxwell's Predictions and Hertz' Confirmation, and Ampere's Law: Magnetic Field Due to a Long Straight Wire
 electromagnetic radiation
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 energy
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 equation
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 frequency
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 inductor
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 kinetic
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 motion
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 period
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 phase
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 phasor
 Appears in this related concepts: Resonance in RLC Circuits, Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams, and Phasors
 potential
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 potential energy
 Appears in this related concepts: The Chain Rule, Escape Speed, and Energy Conservation
 power
 Appears in this related concepts: Sources of Power, Weber's View of Stratification, and Power
 resistance
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 resistor
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 resonance
 Appears in this related concepts: Resonance, 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 Battery, and The Millikan OilDrop Experiment
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Cite This Source
Source: Boundless. “Power.” Boundless Physics. Boundless, 28 May. 2015. Retrieved 28 May. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/power5871645/