INDUCTANCE

Cuthbert Nyack

It is easier to think of an inductor as consisting of a coil of N turns of wire. If the flux within the coil is F_B then the coil can be described as having an inductance L given by the following expression. F_B has units of Weber, I has units of Ampere and L has units of Henry.

The Inductance of an inductor (like the capacitance of a capacitor ) depends on geometric factors and can be evaluated analytically for some simple cases. For a solenoid of length l, Area A and n turns per unit length, the inductance is:-

For a coaxial cable of length l, inner radius a and outer radius b, the inductance is given by:-

For a length l of 2 wires of radius a separated by a distance d, the inductance is:-

When a current I is flowing through an inductor, the energy stored in the magnetic field of the inductor is given by:-

If a sinusoidal current is flowing through an inductor, then it appears to have an impedance of jwL. The j means that the voltage leads the current by 90º. Because of this, circuits in which the voltage leads the current are often referred to as inductive. Because of the phase relation between current and voltage, no power is dissipated in an ideal inductor.

More generally the impedance can be written as sL where s is the Laplace variable.

Inductors are common in a variety of electronic circuits eg. transformers, rf amplifiers and filters and receivers. Usdesirable inductive effects (parasitic inductance) also occur in circuits particularly at high frequencies.

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