An inductor is essentially just

wire wrapped into loops. However, instead of just acting like a lot of wire, the inductor has special properties. If the inductor is at

zero state and then current is run through it, it will initially not let the current by, acting like an

open circuit. As time goes on, the inductor will act more and more like a

short circuit (that is, just wire), simply letting the current pass through.

Resistors have resistances, and capacitors have capacitances. Inductors have inductance, usually represented by the letter L. The unit for inductance is the henry. Inductance, or more specifically self inductance, is equal to the number of loops that make up the inductor, times the flux of the B field emanating from it, divided by the current passing through.

(phi_{B}) * N
L = -----------
i

L actually is a constant that depends on the properties of the inductor. This isn't intuitive, because the flux and current are both variables. But sure enough, you can look at a typical EE student's lab kit and find a 47 millihenry inductor. How is this possible? Well, the B field's flux depends on the current flowing through it. When current runs through a wire, it generates a B field whose field lines run in a circle around the wire. Since phi_{B} is a function of i, L is indeed a constant.

The relation between voltage and current for an inductor is as follows: the voltage across the inductor is equal to the inductance times the first time derivative of the current:

di
V_{L} = L * ----
dt

di/dt is the rate of change of current. So the voltage across the inductor depends on that rate of change.

The impedance of an inductor is equal to L * S, where S is is equal to j * omega. j is the square root of -1, and omega is the frequency. This impedance is a very useful property. Comparatively, capacitors have an impedance of 1/(S * C), and the impedance of the resistor is just R, completely independent of frequency. Since inductors are more cumbersome to implement than those other two elements, circuit designers try to use inductors infrequently. In addition to that, it is difficult to produce high inductances that are good to use in miniature circuits. For that, the properties of an inductor are simulated in gyrator circuits.