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Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams
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In an AC circuit with an inductor, the voltage across an inductor "leads" the current because of the Lenz' law.
Learning Objective

Explain why the voltage across an inductor "leads" the current in an AC circuit with an inductor
Key Points
 With an inductor in an AC circuit, the voltage leads the current by onefourth of a cycle, or by a 90º phase angle.
 The rms current I_{rms} through an inductor L is given by a version of Ohm's law:
$I_{rms} = \frac{V_{rms}}{X_L}$ . X_{L} is called the inductive reactance, given as$X_L = 2\pi \nu L$ .  Phasors are vectors rotating in counterclockwise direction. A phasor for an inductor shows that the voltage lead the current by a 90º phase.
Terms

phasor
A representation of a complex number in terms of a complex exponential.

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.
Full Text
Suppose an inductor is connected directly to an AC voltage source, as shown in . It is reasonable to assume negligible resistance because in practice we can make the resistance of an inductor so small that it has a negligible effect on the circuit. The graph shows voltage and current as functions of time. (b) starts with voltage at a maximum. Note that the current starts at zero, then rises to its peak after the voltage driving it (as seen in the preceding section when DC voltage was switched on).
AC Voltage Source in Series with an Inductor
(a) An AC voltage source in series with an inductor having negligible resistance. (b) Graph of current and voltage across the inductor as functions of time.
When the voltage becomes negative at point a, the current begins to decrease; it becomes zero at point b, where voltage is its most negative. The current then becomes negative, again following the voltage. The voltage becomes positive at point c where it begins to make the current less negative. At point d, the current goes through zero just as the voltage reaches its positive peak to start another cycle. Hence, when a sinusoidal voltage is applied to an inductor, the voltage leads the current by onefourth of a cycle, or by a 90º phase angle.
Current lags behind voltage, since inductors oppose change in current. Changing current induces an emf . This is considered an effective resistance of the inductor to AC. The rms current I_{rms} through an inductor L is given by a version of Ohm's law:
Phasor Representation
The voltage across an inductor "leads" the current because of the Lenz's law. Therefore, the phasor representing the current and voltage would be given as in . Again, the phasors are vectors rotating in counterclockwise direction at a frequency
Phasor Diagram
Phasor diagram for an AC circuit with an inductor.
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Key Term Reference
 AC
 Appears in these related concepts: Driven Oscillations and Resonance, Power, and Impedance
 DC
 Appears in these related concepts: Resistors and Capacitors in Series, Phasors, and Resistors in AC Circuits
 Hertz
 Appears in these related concepts: Time, Frequency of Sound Waves, and Characteristics of Sound
 Law
 Appears in these related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 atom
 Appears in these related concepts: Overview of Atomic Structure, Description of the Hydrogen Atom, and Stable Isotopes
 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
 frequency
 Appears in these related concepts: Guidelines for Plotting Frequency Distributions, Properties of Waves and Light, and Sound
 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
 reactance
 Appears in this related concept: Cathode Ray Tube, TV and Computer Monitors, and the Oscilloscope
 resistance
 Appears in these related concepts: Resistors in Parallel, Resisitors in Series, and Introduction to Blood Flow, Pressure, and Resistance
 rms current
 Appears in these related concepts: Resonance in RLC Circuits, Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams, and RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram
 rms voltage
 sinusoidal
 Appears in these related concepts: Sinusoidal Nature of Simple Harmonic Motion, Root Mean Square Values, and Introduction to The Sampling Theorem
 vector
 Appears in these related concepts: Multiplying Vectors by a Scalar, Series and Sigma Notation, and Translations
 voltage
 Appears in these related concepts: The Nernst Equation, Electric Potential Due to a Point Charge, and Principles of Electricity
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Source: Boundless. “Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams.” Boundless Physics Boundless, 08 Aug. 2016. Retrieved 24 Feb. 2017 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/inductorsinaccircuitsinductivereactiveandphasordiagrams5856285/