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

Explain why the voltage across an inductor "leads" the current in an AC circuit with an inductor

Determine the rms current through an inductor using Ohm’s law
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

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.

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.
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).
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
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Key Term Reference
 AC
 Appears in this related concepts: Safety Precautions in the Household, Impedance, and Phase Angle and Power Factor
 DC
 Appears in this related concepts: Resistors in AC Circuits, Resistors and Capacitors in Series, and Phasors
 Hertz
 Appears in this related concepts: Time, Frequency of Sound Waves, and Characteristics of Sound
 Law
 Appears in this related concepts: TwoComponent Forces, Physics and Other Fields, and Models, Theories, and Laws
 atom
 Appears in this related concepts: Early Ideas about Atoms, The Law of Multiple Proportions, and Stable Isotopes
 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
 diagram
 Appears in this related concepts: Motion Diagrams, Power, and Bohr Orbits
 frequency
 Appears in this related concepts: Antennae, General Rules for Assigning Electrons to Atomic Orbitals, and Sound
 inductor
 Appears in this related concepts: Induced Charge, RL Circuits, and Inductance
 ohm
 Appears in this related concepts: Poiseuille's Equation and Viscosity, Current and Voltage Measurements in Circuits, and Null Measurements
 phase
 Appears in this 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 this related concepts: Resistors in Parallel, Resisitors in Series, and Ecosystem Dynamics
 rms current
 Appears in this 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 this related concepts: Driven Oscillations and Resonance, Sinusoidal Nature of Simple Harmonic Motion, and Root Mean Square Values
 vector
 Appears in this related concepts: Equations of Lines and Planes, Plant Virus Life Cycles, and Dipole Moments
 voltage
 Appears in this related concepts: Conductors, The Millikan OilDrop Experiment, and Principles of Electricity
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Cite This Source
Source: Boundless. “Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams.” Boundless Physics. Boundless, 02 Jan. 2015. Retrieved 20 May. 2015 from https://www.boundless.com/physics/textbooks/boundlessphysicstextbook/inductionaccircuitsandelectricaltechnologies22/accircuits162/inductorsinaccircuitsinductivereactiveandphasordiagrams5856285/