Inductance is the property of an electrical conductor that opposes a change in current, and its Standard International (SI) unit is the henry (H). When current flows through a wire, it creates a magnetic field; when that current changes, the collapsing or expanding magnetic field induces a voltage that fights the change. In a real circuit, this property dictates how fast a switching regulator can change states, how much AC current a choke will block, and how much energy a relay coil stores before it dumps it back into your drive transistor. Understanding the scale of these units—from massive millihenry filter chokes to parasitic nanohenry PCB traces—is critical for predicting circuit behavior.
The Core Definition: Inductance and the Henry
Named after American scientist Joseph Henry, the henry is the base SI unit for inductance. According to the National Institute of Standards and Technology (NIST), the SI system defines the henry strictly through its relationship to voltage, time, and current.
To visualize this, use the mechanical flywheel analogy: just as a heavy flywheel resists changes in its rotational speed (requiring high torque to spin up and resisting being stopped), an inductor resists changes in electrical current. It takes high voltage to force current to rise quickly through an inductor, and it will generate a high voltage spike to keep current flowing if you suddenly open the circuit.
Because one whole henry is a massive amount of inductance for most modern electronics, we almost always use sub-multiples. Here is the standard SI prefix table for inductance:
| Unit Name | Symbol | Value in Henrys | Typical Application |
|---|---|---|---|
| Henry | H | 1 | Large mains filter chokes, heavy motor windings |
| Millihenry | mH | 10-3 (0.001) | Audio crossovers, common-mode EMI filters |
| Microhenry | µH | 10-6 (0.000001) | Switch-mode power supply (SMPS) inductors |
| Nanohenry | nH | 10-9 | RF matching networks, parasitic PCB trace inductance |
| Picohenry | pH | 10-12 | Via inductance in high-speed digital IC packaging |
Worked Example: Calculating Energy and Reactance
Let's look at a real-world scenario. You are designing a buck converter and select a Würth Elektronik 7443552470 shielded power inductor. The datasheet specifies an inductance of 47 µH and a maximum DC current rating of 4.5 A. We need to know two things: how much energy it stores at peak current, and what its impedance (reactance) is at the converter's 500 kHz switching frequency.
1. Calculating Stored Energy (E)
The formula for energy stored in a magnetic field is E = 0.5 × L × I².
- L = 47 µH = 0.000047 H
- I = 4.5 A
- E = 0.5 × 0.000047 × (4.5)²
- E = 0.5 × 0.000047 × 20.25 = 0.0004758 Joules
2. Calculating Inductive Reactance (XL)
The formula for AC opposition is XL = 2πfL.
- f = 500,000 Hz
- L = 0.000047 H
- XL = 2 × 3.14159 × 500,000 × 0.000047 = 147.65 Ω
If you were to accidentally swap this part for a 47 mH inductor (1000x larger), the reactance at 500 kHz would jump to 147,650 Ω, completely choking the switching node and likely destroying your MOSFET due to massive voltage spikes.
Where You Meet Inductance SI Units in Practice
The SI unit scale directly maps to the frequency domain of your application. As frequency increases, the required inductance value drops to achieve the same reactance.
- Mains and Audio (mH range): In a 50/60 Hz AC line filter, you need high inductance to block noise. A Schaffner RN202-10-0.8 common-mode choke provides 10 mH per winding. At 60 Hz, 10 mH yields only 3.7 Ω of reactance, but at 10 kHz switching noise, it yields 628 Ω, effectively filtering the high-frequency garbage while passing the 60 Hz mains.
- Switch-Mode Power Supplies (µH range): Buck, boost, and flyback converters operate between 100 kHz and 3 MHz. They require inductors in the 1 µH to 100 µH range to smooth the chopped DC into a clean output. A typical Coilcraft XEL3530 series part might be 330 nH (0.33 µH) for a high-frequency, high-current GPU voltage regulator.
- RF and High-Speed Digital (nH range): At 2.4 GHz (WiFi/Bluetooth), even a straight piece of copper wire has significant inductance. A 10 mm PCB trace might have 10 nH of parasitic inductance. At 2.4 GHz, that tiny 10 nH creates 150 Ω of reactance, which can severely degrade signal integrity or detune an antenna matching network if not accounted for.
Common Confusions: Inductance vs. Capacitance and Resistance
Beginners frequently confuse inductance with capacitance or resistance. While all three oppose electrical flow in some way, their mechanisms and SI units are entirely different. According to foundational texts on All About Circuits, keeping the physical fields straight is the key to mastering AC theory.
| Property | SI Unit | What it Opposes | Energy Storage Field | DC Behavior |
|---|---|---|---|---|
| Resistance | Ohm (Ω) | Steady current flow (DC & AC) | None (dissipates as heat) | Blocks/limits current |
| Capacitance | Farad (F) | Changes in voltage | Electric field | Blocks DC entirely (open circuit) |
| Inductance | Henry (H) | Changes in current | Magnetic field | Passes DC freely (short circuit) |
The most dangerous confusion occurs when treating an inductor like a resistor in a DC circuit. A relay coil might measure only 50 Ω on your multimeter's DC resistance setting. If you connect it to a 12 V supply, Ohm's law says it will draw 240 mA. But when you turn the circuit off, the inductance (which might be 500 mH) tries to keep that 240 mA flowing. Without a flyback diode, it will generate hundreds of volts to force the current across the opening switch contacts, instantly frying your driving transistor.
Frequently Asked Questions About Inductance SI Units
What is the exact SI definition of one henry?
One henry is defined as the inductance that produces exactly one volt of electromotive force (EMF) when the current flowing through it changes at a rate of one ampere per second. In base SI units, it is expressed as kg·m²·s⁻²·A⁻². This definition ties the magnetic properties of a circuit directly to mechanical mass, distance, time, and electrical current.
How do you convert between henrys, millihenrys, and microhenrys?
Conversions follow standard metric prefixes. To convert henrys to millihenrys (mH), multiply by 1,000. To convert henrys to microhenrys (µH), multiply by 1,000,000. Conversely, if you have a 4.7 µH inductor and need the value in henrys for a physics formula, divide by 1,000,000 to get 0.0000047 H (or 4.7 × 10⁻⁶ H). Always convert to base henrys before plugging values into formulas like XL = 2πfL to avoid decimal errors.
Why are inductance SI units usually microhenrys or nanohenrys in modern PCB design?
Modern electronics rely on high-frequency switching to reduce component size. Because inductive reactance (XL) increases with frequency (XL = 2πfL), a much smaller physical inductance is needed to achieve the same filtering or energy storage effect at 1 MHz compared to 60 Hz. Smaller inductance values require fewer turns of wire and smaller magnetic cores, which directly translates to cheaper, lighter, and more compact PCB footprints.
Does the physical size of an inductor change its SI unit value?
Physical size alone does not dictate the henry value; the number of wire turns, the core material (air, ferrite, powdered iron), and the coil geometry determine the inductance. However, physical size does dictate the inductor's current handling capability (saturation current and thermal limits). You can easily find a tiny 0402 surface-mount inductor and a massive through-hole toroidal inductor that both measure exactly 10 µH. The SI unit is identical, but the large toroid can handle 5 amps without the magnetic core saturating, while the tiny SMD part will saturate and lose its inductance at just 100 mA.
