# Inductors

concept

Inductors are similar to capacitors (in fact in AC circuits you'll learn they're almost like negative capacitors). The equations involving inductors are therefore very similar to the ones involving capacitors and we won't spend as long covering them as we did before.

fact

An inductor stores energy in a magnetic field it produces in response to a current running through it.

fact

Just like a capacitors are measured in Farads and resistors are measured in Ohms the inductors are measured in a unit called Henries.

fact

The circuit symbol for an inductor is:
Or

fact

An inductor is typically formed by wrapping wire in loops around some kind of cylindrical core (which would be some kind of metal or even air).

fact

The amount of energy stored in an inductor is given by the equation:
\(W = \frac{1}{2}LI^2\)
Where \(W\) is the energy in joules, \(L\) is the inductance in henries and \(I\) is the current through the inductor in amps.

The current through an inductor cannot change instantaneously, when power is applied to an inductor the current will slowly build up to its final value. Likewise when power is interrupted the current cannot immediately stop, attempting to disconnect an inductor from a powered circuit is likely to cause sparks.

fact

The inductance of an inductor is controlled by the number of turns of wire, the length of the turned section of wire, the diameter of the core and the material the core is made out of.
The formula for an inductor's inductance is given by:
\(L = \frac{N^2 \times A \times \mu}{l}\)
Where \(L\) is inductance in Henries, \(N\) is the number of turns, \(A\) is the cross sectional area of the core, \(\mu\) is something called the core's "magnetic permeability" which you would look up in a table and \(l\) is the length of the inductor's coils.

fact

When the current through an inductor attempts to change the inductor will produce a voltage across its terminals in response to that change.
The voltage across an inductor is given by:
\(V = L \frac{\delta i}{\delta t}\)

This means that if the current through an inductor isn't changing there's no voltage across it. If the current is increasing then the voltage will become positive. If the current is decreasing then the voltage will become negative.
The faster the current changes the larger the voltage produced.

practice problems