Inductors

An inductor can be made physically using a coil of wire, and it stores magnetic flux when a current flows through it. Figure E.2 shows a circuit in which a resistor is in series with the parallel combination of a capacitor and inductor .

The defining equation of an inductor is

where denotes the inductor's stored magnetic flux at time , is the inductance in Henrys (H), and is the current through the inductor coil in Amperes (A), where an Ampere is a Coulomb (of electric charge) per second. Differentiating with respect to time gives

where is the voltage across the inductor in volts. Again, the current is taken to be positive when flowing from plus to minus through the inductor.

Taking the Laplace transform of both sides gives

by the differentiation theorem for Laplace transforms.

Assuming a zero initial current in the inductor at time 0, we have

Thus, the driving-point impedance of the inductor is . Like the capacitor, it can be analyzed in steady state (initial conditions neglected) as a simple resistor with value Ohms.

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Subsections

• • Mechanical Equivalent of an Inductor is a Mass

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.