What Is Inductance?
The basic inductive device is a coil of wire, called an inductor or a solenoid. Its functioning is based on the physical fact that an electric current produces a magnetic field around it.
This magnetic field describes a circular pattern around a current-carrying wire; the direction of the field can be specified with a “right-hand rule.” When a wire is coiled up as shown in figure below, it effectively amplifies this magnetic field, because the contributions from the individual loops add together.
The sum of these contributions is especially great in the center, pointing along the central axis of the coil. The resulting field can be further amplified by inserting a material of high magnetic permeability (such as iron) into the coil; this is how an electromagnet is made.
When such a coil is placed in an a.c. circuit, a second physical fact comes into play, namely, that a changing magnetic field in the vicinity of a conducting wire induces an electric current to flow through this wire. If the current through the coil oscillates back and forth, then so does the magnetic field in its center.
Because this magnetic field is continuously changing, it induces another current in the coil. This induced current is proportional to the rate of change of the magnetic field. The direction of the induced current will be such as to oppose the change in the current responsible for producing the magnetic field.
In other words, the inductor exerts an inhibitive effect on a change in current flow. This inhibitive effect results in a delay or phase shift of the alternating current with respect to the alternating voltage. Specifically, an ideal inductor (with no resistance at all) will cause the current to lag behind the voltage by a quarter cycle, or 90 degrees.
This result is difficult to explain intuitively. We will not attempt to detail the specific changes in the current and magnetic field over the course of a cycle. One thing that can readily be seen from the graph, though, is that the current has its maximum at the instant that the magnetic field changes most rapidly.
As the magnetic field increases and decreases during different parts of the cycle, it stores and releases energy. This energy is not being dissipated, only repeatedly exchanged between the magnetic field and the rest of the circuit. This exchange process becomes very important in the context of power transfer. Because the induced current in an inductor is related to the change in the field per unit time, the frequency of the applied alternating current is important.
The higher the frequency, the more rapidly the magnetic field is changing and reversing, and thus the greater the induced current with its impeding effect is. The lower the frequency, the easier it is for the current to pass through the inductor.
A direct current corresponds to the extreme case of zero frequency. When a steady d.c. voltage is applied to an inductor, it essentially behaves like an ordinary piece of wire. After a brief initial period, during which the field is established, the magnetic field remains constant along with the current.
An unchanging magnetic field exerts no further influence on an electric current, so the flow of a steady direct current through a coil of wire is unaffected by the inductive property. Overall, the effect of an inductor on an a.c. circuit is expressed by its reactance, denoted by X (to specify inductive reactance, the subscript L is sometimes added).
The inductive reactance is the product of the angular a.c. frequency7 and the inductance, denoted by L, which depends on the physical shape of the inductor and is measured in units of henrys (H). In equation form, XL = wL
Thus, unlike resistance, the reactance is not solely determined by the intrinsic characteristics of a device. In the context of power systems, however, because the frequency is always the same, reactance is treated as if it were a constant property.
When describing the behavior of electrical devices in the context of circuit analysis, we are generally interested in writing down a mathematical relationship between the current passing through and the voltage drop across the device. For a resistor, this is simply Ohm’s law, V = IR, where the resistance R is the proportionality constant between voltage and current.
It turns out that the inductance L also works as a proportionality constant between current and voltage across an inductor, but in this case the equation involves the rate of change of current, rather than simply the value of current at any given time. Readers familiar with calculus will recognize the notation dI/dt, which represents the time derivative or rate of change of current with respect to time.
Thus, we write V = L dI/dt meaning that the voltage drop V across an inductor is the product of its inductance L and the rate of change of the current I through it. This equation is used in circuit analysis in a manner analogous to Ohm’s law to establish relationships between current and voltage at different points in the circuit, except that it is more cumbersome to manipulate owing to the time derivative.
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