Key Takeaways
- Inductance measures how strongly a conductor opposes changes in current flow
- The henry (H) is the SI unit of inductance - 1H produces 1V when current changes at 1A/s
- Energy stored in an inductor is proportional to L and the square of the current
- Inductive reactance increases with frequency: XL = 2 pi f L
- Series inductors add directly; parallel inductors use the reciprocal formula (like resistors)
What Is Inductance? Understanding the Fundamentals
Inductance is a fundamental property of electrical circuits that describes how a conductor opposes changes in electric current flowing through it. When current flows through a wire, it creates a magnetic field around the conductor. If that current changes, the magnetic field changes, which in turn induces a voltage that opposes the original change. This phenomenon, known as electromagnetic induction, was discovered by Michael Faraday in 1831 and forms the basis of countless electrical devices from transformers to electric motors.
An inductor is simply a component designed to exhibit significant inductance, typically consisting of a coil of wire. The coil geometry concentrates the magnetic field and dramatically increases the inductance compared to a straight wire. Understanding inductance is essential for designing power supplies, filters, radio frequency circuits, and any application involving alternating current or transient electrical signals.
The Fundamental Inductance Equations
The defining equation for inductance relates the induced electromotive force (EMF) to the rate of change of current:
V = L x (dI/dt)
From this relationship, we can derive the equation for calculating inductance when we know the voltage, current change, and time interval:
L = V x dt / dI
This equation tells us that one henry of inductance produces one volt of EMF when the current changes at a rate of one ampere per second. In practical circuits, most inductors have values measured in millihenries (mH) or microhenries (uH) because one henry represents a very large inductance.
How to Calculate Inductance (Step-by-Step)
Identify Your Variables
Gather the induced voltage (V), current change (dI), and time interval (dt). For example: 20V induced voltage, 3A current change, 0.01 seconds time interval.
Apply the Inductance Formula
Use L = V x dt / dI. Substituting our values: L = 20 x 0.01 / 3 = 0.0667 H = 66.7 mH.
Convert to Appropriate Units
Express the result in the most convenient unit: henries (H), millihenries (mH), microhenries (uH), or nanohenries (nH) depending on the magnitude.
Verify Your Result
Cross-check by calculating the induced voltage using your result: V = 0.0667 x (3/0.01) = 20V. This confirms our inductance calculation is correct.
Units of Inductance
The SI unit of inductance is the henry (H), named after Joseph Henry who independently discovered electromagnetic induction around the same time as Faraday. Here are the common units and their conversions:
| Unit | Symbol | Equivalent | Typical Applications |
|---|---|---|---|
| Henry | H | 1 H | Large power inductors, chokes |
| Millihenry | mH | 10^-3 H | Audio circuits, power supplies |
| Microhenry | uH | 10^-6 H | RF circuits, switching regulators |
| Nanohenry | nH | 10^-9 H | High-frequency circuits, PCB traces |
Energy Stored in an Inductor
Inductors store energy in their magnetic field, similar to how capacitors store energy in their electric field. The energy stored in an inductor is proportional to its inductance and the square of the current flowing through it:
E = 0.5 x L x I^2
Example: Energy Storage Calculation
Problem: A 100 mH inductor carries a current of 5 amperes. How much energy is stored?
L = 100 mH = 0.1 H
I = 5 A
E = 0.5 x 0.1 x 5^2 = 0.5 x 0.1 x 25
E = 1.25 J (joules)
This energy storage capability makes inductors essential in power electronics. When the current through an inductor is interrupted, the collapsing magnetic field generates a voltage spike as the inductor attempts to maintain current flow. This property is used in boost converters to step up voltage and can cause damage to switches if not properly managed with flyback diodes or snubber circuits.
Inductive Reactance
In AC circuits, inductors oppose the flow of alternating current through a property called inductive reactance. Unlike resistance, which dissipates energy as heat, reactance stores and returns energy to the circuit. Inductive reactance increases with frequency:
XL = 2 x pi x f x L
At DC (frequency = 0), an ideal inductor has zero reactance and behaves like a short circuit after initial transients settle. At very high frequencies, the reactance becomes very large, and the inductor acts nearly like an open circuit. This frequency-dependent behavior makes inductors useful for filtering specific frequencies in audio equipment, radio receivers, and power supplies.
Example: Inductive Reactance Calculation
Problem: What is the inductive reactance of a 47 uH inductor at 10 MHz?
L = 47 uH = 47 x 10^-6 H
f = 10 MHz = 10 x 10^6 Hz
XL = 2 x pi x 10 x 10^6 x 47 x 10^-6
XL = 2,953 ohms
Inductors in Series and Parallel
Like resistors, inductors can be combined in series and parallel configurations. The formulas are analogous to those for resistors:
Series Connection
When inductors are connected in series and have no magnetic coupling between them, the total inductance is simply the sum of individual inductances:
L_total = L1 + L2 + L3 + ...
Parallel Connection
For inductors in parallel with no magnetic coupling:
1/L_total = 1/L1 + 1/L2 + 1/L3 + ...
For two inductors in parallel, this simplifies to L_total = (L1 x L2)/(L1 + L2). Note that if inductors have magnetic coupling (mutual inductance), these formulas must be modified to account for the coupling factor.
RL Time Constant
When an inductor is connected in series with a resistor, the combination exhibits exponential charging and discharging behavior similar to an RC circuit. The time constant tau determines how quickly the current reaches its final value:
tau = L / R
After one time constant, the current reaches approximately 63.2% of its final value. After five time constants, the circuit is considered to be at steady state, with current at over 99% of its final value. This behavior is crucial for understanding switching transients and designing proper dead times in power electronics.
Pro Tip: The 5-Tau Rule
In practical circuit design, always allow for 5 time constants for an RL circuit to reach steady state. If your inductor is 100mH and series resistance is 10 ohms, tau = 0.01s, so allow 50ms for the circuit to stabilize after power-up or switching events.
Quality Factor (Q)
Real inductors have some resistance in their wire windings. The quality factor Q measures how close an inductor comes to ideal behavior:
Q = XL / R = (2 x pi x f x L) / R
Higher Q values indicate lower losses and sharper resonance in tuned circuits. Audio inductors typically have Q values of 10-50, while RF inductors may achieve Q values of 100-300. Air-core inductors generally have higher Q than ferrite-core inductors at high frequencies due to core losses.
Common Mistakes to Avoid
Avoid These Common Errors
- Ignoring saturation current: Operating above the saturation rating causes dramatic inductance drop and potential damage
- Forgetting unit conversion: Always verify that all values are in consistent units (H, not mH or uH) before calculating
- Neglecting mutual inductance: When inductors are close together, magnetic coupling affects total inductance
- Using above self-resonant frequency: Inductors behave like capacitors above their SRF
- Ignoring DC resistance: Real inductors have wire resistance that causes power loss
Practical Applications of Inductors
Inductors are used throughout electronics and electrical engineering:
- Power Supplies: Buck, boost, and buck-boost converters use inductors for energy storage and voltage conversion. The inductor smooths the pulsating current from switching elements.
- Filters: Low-pass, high-pass, and band-pass filters use inductors with capacitors to select or reject specific frequency ranges. EMI filters use common-mode chokes to suppress electromagnetic interference.
- Transformers: Coupled inductors transfer energy between circuits while providing electrical isolation and voltage transformation.
- Motors and Generators: Electric motors use inductors (windings) to create rotating magnetic fields. Generators use the same principle in reverse.
- RF Circuits: Radio transmitters and receivers use inductors in tuned circuits, oscillators, and matching networks.
- Sensors: Inductive proximity sensors detect metallic objects by measuring changes in inductance. LVDTs measure linear displacement.
Pro Tip: Core Material Selection
For frequencies below 100 kHz, use iron powder or laminated steel cores for maximum inductance. For 100 kHz to 10 MHz, ferrite cores offer the best balance. Above 10 MHz, air-core inductors avoid core losses entirely and provide the best Q factor.
Frequently Asked Questions
Inductance is a property of an electrical conductor that opposes changes in current flow by storing energy in a magnetic field. It is measured in henries (H), named after physicist Joseph Henry. One henry is defined as the inductance that produces one volt of electromotive force when the current changes at a rate of one ampere per second. Most practical inductors have values in millihenries (mH) or microhenries (uH).
Inductance (L) is a physical property of a component measured in henries, determined by its construction (number of turns, core material, geometry). Inductive reactance (XL) is the opposition to AC current flow measured in ohms, calculated as XL = 2 pi f L. While inductance remains constant, reactance depends on both the inductance value and the frequency of the applied signal - at DC (0 Hz), reactance is zero; it increases linearly with frequency.
The energy stored in an inductor is calculated using the formula E = 0.5 x L x I squared, where E is energy in joules, L is inductance in henries, and I is the current in amperes. For example, a 100mH inductor carrying 2A stores 0.5 x 0.1 x 4 = 0.2 joules. This energy is stored in the magnetic field surrounding the inductor and is released when the current decreases.
The inductance of a coil depends on several factors: the number of turns (inductance increases with the square of turns), the core material permeability (ferromagnetic materials like iron dramatically increase inductance), the cross-sectional area of the coil (larger area = more inductance), and the length of the coil (shorter coils have higher inductance). Using a ferrite or iron core can increase inductance by factors of 100 to 10,000 compared to an air core.
According to Lenz's law, the induced EMF in an inductor always opposes the change that created it. When current increases, the expanding magnetic field induces a voltage that opposes the increase (like pushing back against the change). When current decreases, the collapsing field induces a voltage that tries to maintain the current. This self-induced EMF is fundamental to how inductors work and is why they act as "current stabilizers" in circuits.
The RL time constant (tau = L/R) describes how quickly current reaches its final value in an RL circuit. After one time constant, current reaches 63.2% of its final value; after five time constants, it reaches 99.3%. This is crucial for understanding switching transients in power electronics, designing proper timing in relay circuits, and ensuring stability in feedback control systems. A larger inductance or smaller resistance means slower response.
For inductors in series without magnetic coupling: L_total = L1 + L2 + L3. For inductors in parallel: 1/L_total = 1/L1 + 1/L2 + 1/L3, or for two inductors: L_total = (L1 x L2)/(L1 + L2). Important: if there is magnetic coupling between inductors, mutual inductance must be considered, which can either add to or subtract from the total inductance depending on the relative winding directions (aiding or opposing).
Inductor saturation occurs when the magnetic core reaches its maximum flux density and cannot accept more magnetic energy. This causes inductance to drop dramatically (often to 10-20% of rated value), leading to current spikes in power circuits and potential damage. To avoid saturation: (1) Select inductors with saturation current ratings 20-30% above your maximum operating current, (2) Consider temperature effects since saturation current decreases at higher temperatures, (3) Use air-gapped or powder cores for high-current applications as they saturate more gradually.
Related Calculators
- Ohm's Law Calculator - Calculate voltage, current, and resistance
- Capacitance Calculator - Calculate capacitance, charge, and stored energy
- Power Calculator - Calculate electrical power
- Frequency Converter - Convert between frequency units