Andrew Carter

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Inductance, Power and Energy of an Inductor

h2. Power

As Lenz’s Law states, an inductor in a circuit opposes the flow of current through it because the flow induces an electromotive force (emf) that opposes it. In order to keep the current flowing against this induced emf, the work has to be done by the external battery source. The equation below shows the instantaneous power used in forcing the current against this self-induced emf.

V_L_(t) = -L\frac{di}{dt}

An ideal inductor has zero power loss because it has no resistance—only inductance—and therefore no power is dissipated within the coil. And power in a circuit is given as

P =vi= \left [ L\frac{di}{dt} \right ]*i = \frac{1}{2}L\frac{di^{2}}{dt} = \frac{d}{dt}\left [ \frac{1}{2}Li^{2} \right ]


The current flowing through the inductor generates the magnetic field where the energy is actually stored. In a pure inductor, the energy is stored without loss and is returned to the rest of the circuit when the current through the inductor is ramped down and its associated magnetic field collapses. When the current flowing through the inductor is increasing and di/dt becomes greater than zero, the instantaneous power in the circuit must also be greater than zero and vice versa. The equation below is obtained by integrating the power equation where the total magnetic energy being stored in the inductor is always positive.

W_(t) = \frac{1}{2} Li_(t)^{2}

Inductance Concepts

The property of a component that opposes the change of the current flowing through it is known as inductance. Inductance is determined by the behavior of a coil of wire in resisting any change of electric current through the coil. It may also be defined as a property of an electric circuit by which a changing magnetic field creates an electromotive force, or voltage, in the circuit or nearby circuit. It is helpful to have an understanding of magnetic field lines in order to have a better understanding of inductance. The discovery of electromagnetic induction by Faraday is shown below. It uses two coils of wire wound around opposite sides of a ring of soft iron.

A Basic Faraday Circuit

A Basic Faraday Circuit

Self Inductance (L)

Self inductance refers to the property in which the current is changing this effect when the emf is induced in the same circuit. Because its polarity is in the opposite direction of the applied voltage, it is sometimes called back-emf. This is the property of a circuit where a change in current causes a change in voltage in the same circuit. By studying the image of a coil below, it can be seen that the number of turns in the coil will have an effect on the amount of voltage that is induced into the circuit.

Self Inductance Application

Self Inductance Application

Mutual Inductance (M)

The basic operating principal of transformers, motors and relays is the mutual inductance where the emf is induced into an adjacent component situated within the same magnetic field. From the image below, the magnetic field produced by circuit 1 will intersect the wire in circuit 2 and create current flow. The induced current flow in circuit 2 will have its own magnetic field which will interact with the magnetic field of circuit.

Mutual Inductance Setup

Mutual Inductance Setup


Tags: inductor, energy, power, inductance

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