Inductors

When there is a current in the inductor, a magnetic field is created. Any change in current causes the magnetic field to change, this in turn induces a voltage across the inductor that opposes the original change in current. The polarity of the induced magnetic field opposes the change in current.

A length of wire turned into a coil works as an inductor.

Inductance (L)

A property of electrical conductors. Measured in henries ($H$). When the current through a conductor changes, an electromotive force (emf) is produced. the magnetic field around it changes. $$

For an ideal inductor:

$$v = -L \frac{\text{d}i}{\text{d}t}$$

Here:

• $v$ - voltage difference across the inductor
• $i$ - current through the inductor

Energy stored

Suppose current across an inductor rises from $0$ to $i$ during a time period of $t$ seconds.

$$e = \int_{0}^{t} p\,dt = \int_{0}^{t} vi\,dt = L \int_{0}^{i} i\,di$$ $$E = \frac{1}{2}LI^2$$