Inductor Energy
Energy stored in a coil, and the voltage spike when that current is interrupted.
Held in the magnetic field around the coil. Energy goes as the square of current, so doubling the current stores four times as much.
An inductor resists a change in current, so interrupting 2 A in 1 µs generates this spike. It is why a relay or motor coil needs a flyback diode across it.
The mirror of a capacitor: a capacitor stores energy in an electric field and resists a change in voltage, while an inductor stores it in a magnetic field and resists a change in current. That is why switching an inductor off abruptly is what damages transistors, and shorting a charged capacitor is what damages everything else.
An inductor stores E = ½LI² in its magnetic field, so 10 mH carrying 2 A holds 20 mJ. Interrupting that current in 1 µs generates a back-EMF of L × di/dt — about 20 kV, which is why coils need flyback diodes.
The mirror image of a capacitor
The two energy-storing components are exact duals. A capacitor stores energy in an electric field between plates and resists a change in voltage. An inductor stores it in a magnetic field around a coil and resists a change in current. Their energy formulas mirror each other too: ½CV² against ½LI².
That duality has a practical consequence worth remembering. Shorting a charged capacitor is dangerous because it wants to keep its voltage and will deliver enormous current to do so. Open-circuiting an energised inductor is dangerous for the opposite reason: it wants to keep its current and will generate enormous voltage to do so.
Where the voltage spike comes from
An inductor's defining equation is V = L × di/dt — the voltage across it is proportional to how fast the current is changing. Switching a coil off tries to take the current to zero almost instantly, which makes di/dt enormous, which makes the induced voltage enormous with it.
A relay coil carrying 100 mA and switched off in a microsecond can easily produce several hundred volts. That spike appears across whatever did the switching, which is how a 40 V transistor gets destroyed in a 12 V circuit.
Energy in joules with L in henries and I in amps. The back-EMF figure assumes the current falls linearly to zero in the given time — a real switch and the surrounding circuit make it less abrupt.
Worked example: 10 mH at 2 A
Energy first, then what happens when you interrupt it:
- 1 Square the current. 2² = 4. As with capacitors, energy goes as the square, so current is the dominant term.
- 2 Multiply by the inductance. 10 mH × 4 = 0.04.
- 3 Halve it. 0.04 ÷ 2 = 0.02 J, or 20 mJ stored in the magnetic field.
- 4 Estimate the switching rate. Interrupting 2 A in 1 µs gives di/dt = 2,000,000 A/s.
- 5 Apply V = L × di/dt. 0.01 H × 2,000,000 = 20,000 V — an impossible figure in practice, which is the point.
- 6 Understand what really happens. The voltage rises until something breaks down or conducts. A flyback diode gives that energy a safe path instead.
Stored energy at common values
E = ½LI². Doubling the current quadruples the energy; doubling the inductance only doubles it.
| Inductance | Current | Energy |
|---|---|---|
| 1 mH | 1 A | 0.5 mJ |
| 10 mH | 1 A | 5 mJ |
| 10 mH | 2 A | 20 mJ |
| 100 mH | 0.5 A | 12.5 mJ |
| 1 H | 0.1 A | 5 mJ |
| 100 µH | 10 A | 5 mJ |
Giving the energy somewhere to go
The standard fix is a flyback diode reverse-biased across the coil. While the coil is energised the diode does nothing; the moment the switch opens, the collapsing field forward-biases it and the current circulates harmlessly through the loop until the energy dissipates as heat. One cheap diode prevents the spike entirely.
The trade-off is that a plain diode makes the current decay slowly, which for a relay means slower release. Adding a resistor or a zener in series with the diode lets the voltage rise to a controlled level — clamping at, say, 50 V instead of 500 V — and dumps the energy much faster. Relay datasheets often specify this when release time matters.
Two related notes. Inductors also saturate: past a certain current the core cannot magnetise further, inductance collapses, and current rises sharply — so a coil rated at 2 A may store far less than ½LI² suggests if you push it to 5 A. And this same stored energy is the operating principle of boost converters and ignition coils, which deliberately energise an inductor and then interrupt it to generate a higher voltage. The spike is a bug in a relay circuit and the entire feature in a boost converter.