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Inductance: Magnetic Fields and Energy Storage

An inductor is usually a coil of wire, sometimes wound around a magnetic core. When current flows through that coil, it creates a magnetic field. Energy is stored in that field, and that stored energy is the reason inductors resist sudden changes in current.

Inductors are essential in power converters, filters, motors, relays, and electromagnetic sensing.

Learning Objectives

By the end of this lesson, you should be able to:

  • explain the meaning of inductance and the unit henry;
  • use v = L di/dt and E = 1/2 LI^2;
  • describe the startup and shutdown behavior of a simple RL circuit;
  • recognize why flyback protection is mandatory around inductive loads.

The Key Dynamic Relationship

For an ideal inductor:

$$
v_L = L\frac{di_L}{dt}
$$

This means:

  • no current change implies zero ideal inductor voltage;
  • a fast current change requires substantial voltage;
  • larger inductance demands more voltage for the same di/dt.

That is why people say an inductor "opposes change in current." It does not stop current from flowing; it opposes sudden changes in that current.

Inductance and Units

The SI unit is the henry (H). Practical circuits often use:

Unit Symbol Value
millihenry mH 10^-3 H
microhenry uH 10^-6 H
nanohenry nH 10^-9 H

Typical ranges:

  • nH to low uH: RF matching, package and trace inductance;
  • uH to low mH: switch-mode power supplies;
  • mH and above: relays, solenoids, EMI chokes, sensor coils.

Energy Stored in the Magnetic Field

An inductor stores energy according to:

$$
E = \frac{1}{2}LI^2
$$

Worked example

For L = 10 mH carrying 2 A:

$$
E = \frac{1}{2}(10\times10^{-3})(2^2) = 0.02\ \text{J}
$$

That energy must go somewhere when the current path is interrupted.

RL Startup Behavior

V1: Device:Battery_Cell value="12 V"
S1: Switch:SW_SPST value="Close at t = 0"
R1: Device:R value="6"
L1: Device:L value="30 mH" rotate=270

layout direction=LR gap=90
group SOURCE label="Step source" direction=LR {
  V1
  S1
}
group LOAD label="RL path" direction=TB {
  R1
  L1
}

V1.1 --> S1.1
S1.2 --> R1.1
R1.2 --> L1.1
L1.2 --> global:0V
V1.2 --> global:0V

At the instant the switch closes:

  • inductor current is initially unchanged, so if it started at 0 A, it is still 0 A;
  • the inductor initially looks like an open circuit for that first moment;
  • current then ramps upward over time.

For an RL circuit, the time constant is:

$$
\tau = \frac{L}{R}
$$

With L = 30 mH and R = 6 ohm:

$$
\tau = \frac{0.03}{6} = 5\ \text{ms}
$$

After about 5 tau, current is effectively at steady state.

Inductive Kickback

The most important practical inductor behavior appears when you try to turn current off abruptly.

V1: Device:Battery_Cell value="12 V"
Q1: Transistor_BJT:Q_NPN_EBC value="Low-side switch"
L1: Device:L value="Relay coil" rotate=270
D1: Device:D value="Flyback diode"

layout direction=LR gap=90
group DRIVE label="Relay driver" direction=TB {
  V1
  L1
  D1
  Q1
}

V1.1 --> L1.1
L1.2 --> Q1.C
Q1.E --> global:0V
V1.2 --> global:0V
D1.K --> L1.1
D1.A --> Q1.C
Q1.B --> NC

When Q1 turns off, the coil current still wants to flow. The flyback diode gives that current a safe loop. Without the diode, collector voltage rises sharply until another path appears, often by avalanche breakdown or arcing.

Inductors in Power Electronics

Inductors are central to switch-mode conversion because they allow energy to move in controlled packets.

flowchart LR A["Switch ON\ninductor current ramps up\nenergy stored in field"] --> B["Switch OFF\ninductor current keeps flowing\nenergy delivered to load"]

That is the foundation of buck, boost, and flyback converters.

Real Inductors Are Not Ideal

Real components have:

  • winding resistance;
  • core losses;
  • leakage flux;
  • parasitic capacitance;
  • saturation current limits.

If the core saturates, inductance falls sharply and current can rise much faster than expected. That is a common failure mode in poorly designed converters.

Safety Guidance

  • Put a flyback diode across DC relay coils, solenoids, and many motors.
  • Size switching devices for the transient stress, not just steady current.
  • Watch coil temperature and copper losses in continuous-duty systems.
  • Keep current loops physically tight to reduce EMI.

Common Mistakes

  • Saying an inductor "blocks current" instead of "opposes change in current."
  • Ignoring saturation current.
  • Omitting flyback protection on a coil because the nominal supply is only 5 V or 12 V.
  • Forgetting winding resistance when estimating current.
  • Treating trace inductance as negligible in fast switching layouts.

Summary

Inductance is the property that links voltage to rate of current change through v = L di/dt. Inductors store energy in magnetic fields according to E = 1/2 LI^2, shape current ramps in RL circuits, and demand safe discharge paths when switched off. Understanding that behavior is essential for switching, filtering, and protecting real electronic systems.

Further Reading