Inductor Stored Energy⚠ unverified
Electrical / Power Electronics · Energy stored in an inductor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| L | L | H | 0.001 | Inductance |
| I | I | A | 2.0 | Current |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| energy | E | J | Stored energy |
The science & history
Understanding the Parameters
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Inductance $L$ — sets how much flux (and energy) is linked per amp. Larger $L$ stores more energy at a given current but also slows current ramp ($v = L\,di/dt$), which is why converter design trades inductance against switching frequency and ripple.
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Current $I$ — energy scales with $I^2$. Peak inductor current (DC load plus ripple) is what determines peak stored energy and the stress on the freewheel path when the switch opens.
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$E$ — joules of field energy available to transfer to the load (or to a snubber/clamp if the path is interrupted).
Same formula as the basic Inductor Energy card; this page frames the PE design use of that energy.
Derivation (Approaching a Proof)
Instantaneous power into an inductor is $p = v i$. With $v = L\,di/dt$ for a linear inductor,
$$E = \int_0^{t} p\,dt = \int_0^{I} L\,i\,di = \frac{1}{2} L I^2,$$
assuming $L$ constant and current rising from zero to $I$. The $\tfrac12$ appears because voltage and current build together, so the average power is half the end-of-ramp product. Equivalently, in field terms the energy density is $u = B^2/(2\mu)$ integrated over the magnetic volume — the dual of the capacitor's $\tfrac12 C V^2$ (see Capacitor Energy).
Design implication
In a switching cycle the inductor is a temporary energy reservoir: charge from the input while the switch is on, discharge into the output while it is off. Sizing $L$ so that $\Delta E$ matches the energy the load needs each period is the PE counterpart of choosing $C$ for a reservoir capacitor.
History
Self-inductance and magnetic energy were formalised in the 19th century (Henry, Faraday). Switch-mode power conversion from the 1960s–70s made $\tfrac12 L I^2$ a routine design quantity — the energy per cycle that must be handled by the switch, diode, and magnetics.
Related Concepts: Inductor Energy, Capacitor Energy, Buck Converter Duty Cycle, Boost Converter Duty Cycle, Buck Inductor Ripple
Notes: Registry calculator inductor-energy (Electrical / Power Electronics; unverified). Linear
(constant-$L$) model; saturable cores need $\int i\,d\lambda$ over flux linkage. Same physics as
basic-inductor-energy / Inductor Energy.