An inductor is a circuit component that stores energy in a magnetic field when electric current flows through it. It is often made from a coil of wire, because each loop strengthens the magnetic field produced by the current. Inductors matter because they control how quickly current can change in circuits, which makes them useful in power supplies, radios, filters, motors, and transformers.
Their behavior is strongest when current is changing, not when current is steady.
Inductance is the property that tells how much magnetic flux a circuit produces for a given current. When the current through an inductor changes, the changing magnetic field creates an induced voltage called back-EMF that opposes the change in current. This opposition follows Lenz's law and is described by V = -L dI/dt for an ideal inductor.
The energy stored in the magnetic field is U = 1/2 L I^2, so larger inductance or larger current means more stored magnetic energy.
Key Facts
- Inductance measures how strongly a changing current produces an induced voltage and is measured in henries, H.
- For an ideal inductor, V = -L dI/dt, where the minus sign means the induced voltage opposes the change in current.
- Energy stored in an inductor is U = 1/2 L I^2.
- A long solenoid has approximate inductance L = μN^2A/l, where μ is permeability, N is turns, A is cross-sectional area, and l is length.
- Current through an ideal inductor cannot change instantly because that would require an infinite voltage.
- In DC steady state, an ideal inductor acts like a wire, but during switching it resists changes in current.
Vocabulary
- Inductor
- A circuit component, usually a coil of wire, that stores energy in a magnetic field when current flows.
- Inductance
- The ability of a circuit or device to produce an induced voltage when its current changes.
- Back-EMF
- An induced voltage that opposes the change in current that created it.
- Henry
- The SI unit of inductance, equal to one volt-second per ampere.
- Magnetic flux
- A measure of the magnetic field passing through a surface, often linked through the loops of a coil.
Common Mistakes to Avoid
- Treating an inductor like a resistor is wrong because a resistor opposes current itself, while an inductor opposes changes in current.
- Forgetting the negative sign in V = -L dI/dt is wrong because the induced voltage points in a direction that opposes the change in current.
- Assuming current through an inductor jumps instantly is wrong because an instantaneous current change would require an extremely large voltage.
- Using U = 1/2 L V^2 is wrong because the energy in an inductor depends on current, so the correct formula is U = 1/2 L I^2.
Practice Questions
- 1 A 0.50 H inductor has its current increase from 0 A to 4.0 A in 0.20 s. What is the magnitude of the induced voltage?
- 2 How much energy is stored in a 2.0 H inductor when the current through it is 3.0 A?
- 3 A switch is opened in a circuit containing an inductor and a lamp. Explain why the inductor can briefly keep current flowing after the switch opens.