Inductor

Definition: An inductor is a passive component, usually a coil of wire, that stores energy in a magnetic field when current flows through it.

How It Works

Current through the coil generates a magnetic field around and through the loops of wire, following the right-hand rule
Any change in that current changes the magnetic field, and by Faraday’s law of induction, a changing field induces a voltage that opposes the change
This opposition is called self-inductance, or simply inductance, measured in henries
Inductors resist rapid changes in current while allowing steady, unchanging current to pass through with minimal opposition, essentially the electrical mirror image of a capacitor
Winding wire around a core material, iron, ferrite, or air, changes the inductance: high-permeability cores like iron or ferrite concentrate the magnetic field and dramatically increase inductance for a given coil size
More turns of wire, larger coil area, and a higher-permeability core all increase inductance
In a DC circuit, an inductor briefly opposes current at power-on, then settles into acting like a plain wire (short circuit) at steady state
In an AC circuit, an inductor continuously opposes the constantly changing current, presenting a frequency-dependent reactance that rises as frequency rises
Mutual inductance occurs when two coils are placed close enough that one coil’s changing field induces a voltage in the other, the operating principle behind transformers
Inductors in series add their inductance directly, and inductors in parallel combine reciprocally, mirroring the way resistors combine
Toroidal (ring-shaped) cores confine the magnetic field almost entirely within the core, reducing stray field emission compared to a simple rod or bobbin-wound coil

Illustration

Under the Hood

Induced voltage from a changing current:

V = L × (dI/dt)

L: inductance in henries
dI/dt: rate of change of current over time

Inductive reactance in an AC circuit:

XL = 2πfL

Energy stored in an inductor’s magnetic field:

E = 0.5 × L × I²

Current rise in an RL circuit (charging through a resistor):

I(t) = (Vsupply/R) × (1 - e^(-t×R/L))

Time constant of an RL circuit:

τ = L / R

Worked Problem 1: Induced voltage from a fast current change Given: A 10 mH inductor experiences a current change of 2A over 1 millisecond (0.001s). Step 1: dI/dt = 2 / 0.001 = 2000 A/s Step 2: V = L × (dI/dt) = 0.01 × 2000 Answer: V = 20V is induced across the inductor, illustrating how fast current changes can create large voltage spikes.

Worked Problem 2: Inductive reactance Given: A 100 mH inductor is used in a 60 Hz AC circuit. Step 1: XL = 2πfL = 2 × 3.1416 × 60 × 0.1 Step 2: XL ≈ 37.7Ω Answer: The inductor presents about 37.7Ω of reactance at 60 Hz.

Worked Problem 3: Energy stored Given: A 47 mH inductor carries a steady 3A. Step 1: E = 0.5 × L × I² = 0.5 × 0.047 × 9 Step 2: E = 0.2115 J Answer: The inductor stores about 0.21 joules of energy in its magnetic field.

Worked Problem 4: RL time constant Given: A 200 mH inductor is in series with a 50Ω resistor. Step 1: τ = L / R = 0.2 / 50 Step 2: τ = 0.004 s Answer: The circuit reaches about 63% of final current after 4 milliseconds, and is considered fully settled after roughly 5τ (20 ms).

Worked Problem 5: Inductors in series and parallel Given: Two inductors, 10 mH and 15 mH, need a combined value both in series and in parallel. Step 1: Series: Ltotal = L1 + L2 = 10 + 15 = 25 mH Step 2: Parallel: Ltotal = (L1 × L2) / (L1 + L2) = (10 × 15) / 25 = 6 mH Answer: Series combination gives 25 mH, parallel combination gives 6 mH, following the same pattern as resistors.

Why It Matters

Inductors are essential for filtering, smoothing current ripple in switching power supplies alongside capacitors
They store and release energy efficiently in switch-mode power converters (buck, boost, and flyback converters), which power nearly all modern electronics
Paired with capacitors, they form tuning and filter circuits used in radio receivers, crossover networks, and signal processing
Transformers are built from two or more coupled inductors, making inductance the basis for voltage conversion in AC power systems
Inductive sensors, like proximity sensors and metal detectors, exploit how a nearby conductive object changes a coil’s effective inductance
Wireless charging pads use coupled inductors (coils) to transfer power across an air gap without a physical connector

Common Pitfalls

Interrupting current through an inductor abruptly, such as switching off a relay coil, without a flyback diode or snubber, which produces a dangerous voltage spike as the collapsing field tries to maintain current flow
Assuming an inductor blocks all AC signals, when in fact it only opposes rapidly changing current, low-frequency and DC pass through relatively freely
Ignoring core saturation, driving an iron or ferrite-core inductor beyond its rated current, at which point the core stops effectively concentrating the field and inductance drops sharply
Forgetting that real inductors have parasitic resistance (from the wire itself) and parasitic capacitance (between windings), both of which affect behavior, especially at high frequencies
Mixing up series and parallel inductance formulas with the capacitor formulas, since inductors combine the same way resistors do, the opposite of capacitors
Underestimating an inductor’s physical size and cost relative to a capacitor of comparable filtering effect, often forcing design tradeoffs
Exceeding an inductor’s rated saturation current in a power converter, causing efficiency to collapse and heat to spike unexpectedly under heavy load
Placing inductors too close together on a board without considering unwanted mutual coupling, which can introduce crosstalk between unrelated circuits

Comparison

Property	Capacitor	Inductor
Stores energy in	Electric field	Magnetic field
Opposes changes in	Voltage	Current
Reactance vs frequency	Decreases with frequency	Increases with frequency
DC steady-state behavior	Open circuit	Short circuit (just wire resistance)
Series combination	Reciprocal (like parallel resistors)	Direct sum (like series resistors)
Parallel combination	Direct sum	Reciprocal (like parallel resistors)

Example

A buck converter power supply uses an inductor to smooth out current pulses from a rapidly switching transistor, storing energy briefly during the “on” phase and releasing it during the “off” phase, delivering a steady output current to the load.

History

Michael Faraday and Joseph Henry independently discovered electromagnetic induction around 1831, laying the foundation for both inductors and generators.
The henry, the SI unit of inductance, was named after Joseph Henry, who also discovered self-inductance around the same period.
Early radio “tuning coils” in the late 19th and early 20th centuries were among the first practical applications of inductors, used alongside capacitors to select specific broadcast frequencies.
Ferrite core materials, developed in the mid-20th century, allowed much smaller, lighter inductors for a given inductance than air-core or laminated-iron designs, enabling compact modern power supplies.

FAQ

Why does an inductor resist changes in current instead of blocking current entirely? By Faraday’s law, only a changing magnetic field induces an opposing voltage. A steady current produces a steady, unchanging field, so there’s nothing left to induce a voltage against, and the inductor behaves like a plain low-resistance wire.

What causes the voltage spike when switching off an inductive load? The inductor’s stored magnetic energy resists the sudden current interruption, and since energy must go somewhere, the collapsing field forces a large, brief voltage spike across whatever is trying to stop the current, often high enough to arc across a switch or damage a transistor without protection.

Why do inductors have a core material instead of just being an air-wound coil? A high-permeability core, like iron or ferrite, concentrates the magnetic field far more effectively than air, letting a physically smaller coil achieve much higher inductance, at the cost of potential core saturation at high currents.

Are inductors used less than capacitors in modern electronics? Inductors tend to be larger, heavier, and more expensive than capacitors for comparable energy storage, so designers use capacitors where possible, but inductors remain essential wherever efficient energy transfer or current smoothing is required, such as switching power supplies and transformers.

Why do transformers only work with AC, not DC? A transformer relies on a changing magnetic field in the primary coil to induce voltage in the secondary coil. Steady DC produces a constant, unchanging field, so once the initial current settles, no further voltage is induced in the secondary.

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