* LC resonant tank circuits are fascinating. If the ohmic resistance is low then they can oscillate for many cycles.
* Make a simple AM radio based on a large coil and tunable capacitor. (Often called a crystal radio, although you can use a diode to detect the signal.)
* Make different types of filters, depending on where you tap for the output signal. High pass, low pass, bandpass, bandstop. Discover how ohmic resistance influences the rolloff curve.
* Observe capacitor leading, and inductor lagging.
* Make a power supply and try different smoothing capacitors. Observe the amounts of ripple voltage.
* Similarly with coils (used as a choke).
* Explore the time constant through a capacitor and resistor. See how long you can keep an LED lit from a charged capacitor (several thousand uF).
* Explore methods to determine Henry value of an unknown coil.
* Loop wire to make an air-coil coil, and see if you can construct the same Henry value from a smaller metal-core coil.
* Wave a magnet near a coil and observe the waveforms on an oscilloscope. Hook up an LED, and see what direction and speed of motion are required to light it. (Caution: reverse voltage may exceed LED threshold, maybe 5V or more).
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I have several Youtube videos of animated simulations. Many depict capacitor and coil, action and interaction.
My user name is 'patientbrad'.
Capacitor behavior (various waveforms):
www.youtube.com/watch?v=eIWEU4pObJw
Inductor behavior with AC:
https://www.youtube.com/watch?v=Os3jF9UeMoE
Inductor behavior with DC:
https://www.youtube.com/watch?v=LVNxrN4jgvs
Equal time constants, caps and coils:
https://www.youtube.com/watch?v=q2FRCUuE0d0
Cap leads, coil lags:
https://www.youtube.com/watch?v=O2kJQLSNqns
LC tank circuit animation:
https://www.youtube.com/watch?v=cX1-CpzGUHc