Capacitors, Inductors and Conversion
Inductors and Their Stored Magnetic Energy
See why inductor current changes at a limited rate.
You are applying “Inductors and Their Stored Magnetic Energy” to a real system and need the concept, assumptions and verification boundary to stay clear.
Build intuition for v = L di/dt, calculate ideal current ramps and magnetic-field energy, then include winding resistance, reset paths, current ratings and switching safety.
- Select or check first
- Voltage controls the current slope. For an approximately constant inductance, the voltage across the inductor sets di/dt. Current is the accumulated result of voltage over time, not a value selected independently by the coil.
- Controlling assumption
- Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
- Top risk
- Never interrupt inductive current without a rated path. A mechanical switch, transistor or connector that opens an energized coil can see a damaging arc or overvoltage.
- Proof
- Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Start with the basics Optional foundation before “Inductors and Their Stored Magnetic Energy”
Electrical-engineering basics
Electrical behaviour becomes easier to reason about when every voltage has a reference and every current has a complete return path.
- Voltage
- Voltage is potential difference between two points. A voltage statement is incomplete unless both points or its reference are known.
- Current
- Current is charge flow through a path. It does not disappear after a component; in a complete circuit it returns to the source.
- Resistance and impedance
- Resistance opposes steady current. Impedance extends that idea to changing signals and can depend on frequency through capacitance and inductance.
- Power and heat
- Electrical power is the rate of energy transfer. Some becomes useful output and some becomes heat that must stay within component and enclosure limits.
- Rating versus operating point
- A rating is a limit or qualified condition, not a target. The operating point must remain inside all relevant voltage, current, power, temperature and timing limits.
How to use this article: Draw the source, load, reference and return path before calculating. Treat exposed or stored electrical energy as hazardous until isolation is proved.
On this page
An inductor stores energy in a magnetic field established by current. Its defining terminal relationship says that voltage is required to change that current. This does not make current absolutely continuous under every imaginable event; it means an instantaneous finite current step in an ideal finite inductance would require unbounded voltage. Real circuits instead develop whatever voltage their parasitics, switches, insulation and clamps allow.
Current builds energy in the magnetic field
Diagram description
An illustrative closed magnetic path and air gap show the field-energy concept. The gold path is not a claim that flux is perfectly confined or uniform.
Energy of a linear inductor
E_L = ½ L I²
The familiar form applies when L is constant over the current excursion. In a nonlinear magnetic component, energy and recoverable energy require the actual flux-linkage or inductance-versus-current relationship; substituting one nominal L can be misleading near saturation.
- E_L
- stored magnetic-field energy, J
- L
- inductance in the stated linear model, H
- I
- instantaneous winding current, A
A 1.0 mH ideal inductor at 2.0 A stores ½ × 0.001 × 2² = 0.002 J, or 2 mJ. Doubling current to 4 A would quadruple that ideal energy to 8 mJ.
Energy can return to the circuit when current falls. That is useful in converters, relays and ignition systems, but dangerous if the current path is opened without control. The inductor's voltage reverses polarity as needed to keep current flowing in its established direction. A diode, snubber, transient suppressor, active clamp or intentional receiving rail must provide a designed destination for the energy.
Applied voltage and time determine the ideal current change
Diagram description
A qualitative piecewise-constant voltage waveform and triangular current response illustrate an initially zero-current inductor. Real winding resistance bends a long-duration response toward a finite DC current.
Inductor terminal law and finite interval
v_L = L·di/dt; ΔI = (1/L)∫v_L dt; for constant v: ΔI = v_L·Δt/L
Choose a reference current direction and passive voltage polarity consistently. A positive v_L produces increasing referenced current. For a fixed voltage pulse, more inductance or less time produces a smaller current change.
- v_L
- instantaneous voltage across the inductor under the passive sign convention, V
- i
- referenced winding current, A
- ΔI
- current change over an interval, A
- Δt
- pulse duration, s
Applying 12 V across an ideal 2.0 mH inductor gives di/dt = 6000 A/s. During 100 μs the current changes by 0.60 A. Applying −6 V for 200 μs produces −0.60 A, returning it to the starting value in the ideal example.
| Observation | Ideal interpretation | Real checks |
|---|---|---|
| Straight rising ramp | Nearly constant positive voltage and L | DCR drop and supply droop may slowly reduce slope |
| Straight falling ramp | Nearly constant reverse voltage | Clamp voltage and diode drop set reset time |
| Slope becomes steeper at high current | Effective incremental L is falling | Possible saturation; compare with data-sheet curves |
| Current approaches a steady value | Net inductor voltage approaches zero | Winding and circuit resistance limit DC current |
| Ringing after switching | Energy exchanges with capacitance | Parasitics, clamp behavior and probe loop may contribute |
A real inductor has resistance, capacitance and magnetic limits
First-order RL step response
i(t) = (V/R_total)(1 − e^(−t/τ)); τ = L/R_total
This model applies to a linear inductor driven by a DC step through a total series resistance. At long time, di/dt approaches zero, so ideal inductive voltage approaches zero and resistance sets current. It does not include core saturation or frequency-dependent loss.
- R_total
- winding plus external series resistance, Ω
- τ
- RL time constant, s
A 10 mH coil in a 20 Ω total path has τ = 0.5 ms. On 10 V, the modeled final current is 0.5 A and reaches about 63% of that after one time constant.
| Specification | What it describes | Why it matters |
|---|---|---|
| Inductance and tolerance | Small-signal or stated-condition L | Sets nominal ripple and energy model |
| L versus DC bias | Inductance change with current | Shows soft or abrupt approach to saturation |
| I_sat | Current at a manufacturer-defined L reduction | Definition may be 10%, 20%, 30% or another criterion |
| I_rms / temperature-rise current | Current producing a stated heating condition | Relates mainly to winding and core loss |
| DCR | DC winding resistance | Creates voltage drop and I²R heat |
| Core loss data | Frequency- and waveform-dependent magnetic loss | Can dominate at high switching frequency |
| SRF / parasitic capacitance | Frequency where simple inductive behavior changes | Limits high-frequency usefulness |
Why a flyback diode makes a relay release more slowly
A diode directly across a DC coil usually clamps the reverse voltage to a small magnitude, so |di/dt| = |v|/L is small and current decays slowly. A higher-voltage TVS or active clamp can reset the current faster, but increases voltage stress and electromagnetic emissions. The acceptable method depends on the coil, switch rating, required release time and safety design.
Review voltage, current, power and energy units in Voltage, Current, Power and Energy Are Different. The loop polarity and current-path discipline from Series, Parallel, Open and Short Circuits is essential when tracing an inductor's charge and reset intervals.
One-minute questions
Questions to answer before you apply this lesson
What should I select or check first for Inductors and Their Stored Magnetic Energy?
Voltage controls the current slope. For an approximately constant inductance, the voltage across the inductor sets di/dt. Current is the accumulated result of voltage over time, not a value selected independently by the coil.
Which assumption can change the conclusion?
Circuit state, waveform, source impedance, ratings, temperature and protection topology match the equipment being analysed.
What can go wrong if I copy the example directly?
Never interrupt inductive current without a rated path. A mechanical switch, transistor or connector that opens an energized coil can see a damaging arc or overvoltage.
How do I verify the result in the real system?
Check the exact manufacturer data, units and limits, then verify the result by calculation, measurement or a controlled acceptance test.
Sources and further reading
- Energy in a Magnetic Field — University Physics Volume 2OpenStax, Rice University · 2026-10-13University physics source reviewed for v = L di/dt, instantaneous power and the derivation of U = ½LI² in the linear model.
- Simple AC Circuits — University Physics Volume 2OpenStax, Rice University · 2026-10-13University physics source reviewed for passive voltage polarity and the relationship between inductor voltage and current slope.
- Selecting the Best Inductor for Your DC-DC ConverterCoilcraft · 2026-10-13Manufacturer application note reviewed for inductance, DCR, SRF, saturation-current and RMS temperature-rise definitions; device-specific criteria remain data-sheet dependent.