Basics
Current flowing through a wire creates a magnetic field around that wire. Winding the wire into a coil makes the fields from many turns reinforce one another. That concentrated magnetic field gives the coil inductance.
An inductor opposes a change in current
A resistor opposes current itself. An inductor mainly opposes a change in current. The faster current is forced to change, the larger the voltage developed across the inductor.
For a beginner, this finite-change form is often easier to use than calculus. It says that voltage depends on inductance and on how much the current changes during a given time.
V = 0.010 × (1 / 0.01) = 1 V
DC behavior
An ideal inductor eventually behaves like a short circuit to steady DC because the current has stopped changing. A real inductor still has the resistance of its wire, so there is always some voltage drop and heat when DC current flows.
AC behavior
With alternating current, the current is continually changing. The inductor's opposition to sinusoidal AC is called inductive reactance:
- XL is reactance in ohms.
- f is frequency in hertz.
- L is inductance in henries.
XL ≈ 62.8 Ω
Reactance rises as frequency rises. This is the basic reason an inductor can pass DC while impeding high-frequency noise.
Energy storage
Energy stored in an inductor increases with inductance and with the square of current. When current is interrupted, that magnetic energy must go somewhere. The collapsing field can produce a large voltage spike.
RL time constant
A resistor and inductor in series do not allow current to jump instantly to its final value. The time constant is:
After one time constant, current in an ideal series RL circuit driven from a DC source has reached about 63% of its final value. After about five time constants it is very close to the final value.
Series and parallel inductors
For uncoupled inductors in series, inductances add:
For uncoupled inductors in parallel:
DCR and heating
The wire winding has resistance, usually listed as DCR. DC copper loss is:
Higher current causes more heating. At AC and switching frequencies, skin effect, proximity effect, and core losses can add more heat beyond the simple DCR calculation.
Core saturation
Magnetic core materials can only support so much magnetic flux. As current rises, a ferrite or iron-based core may approach saturation. Inductance then falls, so current can begin rising much faster than expected.
Flyback voltage
When a switch opens the current path through a relay coil or solenoid, the coil tries to keep current flowing in the same direction. Without a safe path, its voltage may rise high enough to arc a switch or damage a transistor.
DC relay coils are often protected with a diode placed across the coil in the reverse-biased direction during normal operation. Other applications may use zener clamps, TVS devices, RC snubbers, or active clamps when faster release is required.