Designs of voltage/current controlled resistance

Usually opto devices or FETs. It has been recently demonstrated here that there are other approaches but it depends on what you're trying to achieve.

If it's for school students I'd have them play with one of these and a variable light source in a closed box.

Depends on exactly what you want to achieve.

There are also thermal devices like tungsten-filament lamps, iron-hydrogen barretters and thermistors. These have a relatively slow reponse but are less likely to distort the waveform. They have fallen out of popularity in recent years and may not suit your application because of the power they consume and the difficulty of obtaining the particular type you may need.

They are two-terminal devices, so the heating power has to be fed into the same terminals as the signal. It can sometimes be difficult to prevent interaction between them.

Photoconductive cells have a faster (but slightly strange) response and can be illuminated by LEDs, tungsten lamps or gas-discharge tubes. Their linearity is quite good enough for domestic audio purposes. They are disliked by environmental campaigners because many of them contain cadmium (in insignificant quantities).

Another method is to use a fast-acting CMOS switch in series with a resistor. By controlling the on/off ratio of the switch, the resistor can appear to be a higher value. This is particularly useful for making resistors in different parts of the circuit track accurately together, such as in an audio filter. The disadvantage is the need for a switching frquency which is much higher than the highest frequency signal and the necessity for a filter on the output to remove that switching frequency from the signal.

To control audio volume, you could use an analog multiplier, a DPOT, or an MDAC.

You can use a diode or a jfet as a variable resistor, but you'd have to keep the signal swing low, millivolts, to avoid distortion and then give up s/n.

A tube or a jfet can be used as a variable gain amp, by adjusting the DC operating point, but again the price is distortion.

A PWM based VGA would be fun. Not very practical but fun.

If it's just educational, a simple jfet amp with AC coupling in and out, gain set by DC gate voltage, would be instructive. The distortion would be instructive too, audible even.

I'll help Spice something if you like. I like to help kids learn electronics.

That would be a cool class. Discuss it, Spice it, build it, listen to it.

Read some jfet data sheets too.

To be more specific, have a look at the H11F1 which is an LED coupled with a bidirectional light sensitive FET. This has been around for many decades but is still available. John

Thanks. Interesting device, and LTSpice models exist.

Interesting, but that looks linear to maybe 20 millivolts.

The LM13700 works fine as a multiplier/gain control for audio, but the values given in the datasheet for the resistors driving the linearizing diodes are kind of nonsense, it works better when the diodes are actively driven a la:

Not too many extra parts for a substantial improvement in large-signal distortion.

We are talking about the linearity of the light-sensitive FET