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LC Energy Exchange

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Recipe #39 — lc energy exchange

After learning capacitors and inductors separately, combine them. An LC circuit can trade stored energy back and forth between an electric field and a magnetic field.

LC ENERGY EXCHANGE — CAPACITOR AND INDUCTOR TOGETHER CL current 1. C CHARGEDelectric energy maxcurrent = 0 2. L CURRENTmagnetic energy maxC voltage = 0 3. C REVERSEDelectric energy maxopposite polarity 4. L CURRENTmagnetic energy maxopposite direction
Start with C charged: the capacitor drives current through L. As capacitor voltage falls, inductor current rises. When C reaches zero volts, current in L is maximum and continues charging C with the opposite polarity. The process then reverses.
EC = ½CV²     EL = ½LI²

Two different energy stores

The capacitor stores energy in an electric field. The inductor stores energy in a magnetic field. An ideal LC circuit can exchange energy between those fields repeatedly.

Another way to think of it

It resembles a pendulum trading gravitational potential energy for motion and back again. The capacitor is analogous to the energy at the ends of the swing; the inductor current is analogous to maximum motion through the center.

A real circuit eventually stops ringing

Wire resistance, core loss, capacitor ESR, radiation, and the connected load remove energy each cycle. Without an amplifier adding energy, the oscillation decays.

Try these yourself

Where is energy stored when capacitor voltage is maximum and current is zero?
At that instant the capacitor holds the energy as an electric field.
Where is energy stored when inductor current is maximum?
The inductor magnetic field contains the stored energy when current is maximum.
Why does a real LC oscillation decay?
Resistance and other losses convert some stored electrical/magnetic energy into heat or radiation each cycle.