Charge a capacitor

You need the power module on its 5 V side, one 10 kΩ resistor, one 100 µF electrolytic capacitor, a jumper wire and the multimeter. For the second half, a red LED, a 4.7 kΩ and a 220 Ω resistor as well.

The one part with a way round

Everything so far could be pushed in either way and nothing would happen except a dark LED. An electrolytic capacitor is the exception. It has a plus leg and a minus leg, and the wrong way round it is damaged.

Read the value and the voltage printed on the can. The voltage is a ceiling and is never to be exceeded: small electrolytics are usually rated from about 16 V upwards, far above the 4.8 V of the rail, but the number is printed on yours and is the one that counts. The two in the kit are 10 µF and 100 µF.

What it does

A capacitor is two metal surfaces separated by an insulator. Put a voltage across them and charge piles up on one and drains from the other, and the capacitor then holds that voltage after the supply goes. It holds it in proportion: the more capacitance, the more charge for the same voltage, and so the longer it takes to fill through a given resistor.

Through a resistor the filling is not steady. At the start the capacitor is empty, the whole rail is across the resistor and the current is at its largest. As the capacitor fills, the voltage across the resistor falls by the same amount, so the current falls, so the filling slows. The voltage across the capacitor therefore rises fast and then more and more slowly toward the rail, and never quite gets there.

Build it

The plus rail feeds a 10 kΩ resistor. The other end of the resistor goes to the capacitor's long leg, and the capacitor's short leg goes to the minus rail. A jumper wire across the capacitor's two legs empties it, and the meter reads across it.

Put the jumper in first. The meter reads 0.00 V. Start your stopwatch at the moment you pull the jumper out, and read the meter at one, two and three seconds. Put the jumper back in and it starts again.

At 4.8 V a 100 µF capacitor holds about a millijoule, so touching the jumper across it is harmless to you and to the part. Do not leave the jumper in: while it is in, the half milliamp of the rail runs through the resistor and the jumper for nothing.

The time constant

The time constant is the resistor times the capacitor: 10 kΩ times 100 µF is one second. It is the time for the capacitor to reach 63 percent of the rail, and what every other number follows from. At two time constants it is 86 percent, at three 95 percent, and by five it is within one percent, which is as full as a meter can show.

Which pairings are worth building

Most of the pairings in the box are too fast or too slow to follow by hand. The 10 kΩ with 100 µF is the first thing to try, and 1 MΩ with 10 µF is slower, ten seconds, and leads to a surprise.

The two ceramic capacitors in the box, 22 pF and 100 nF, are far too small to see in this circuit. With 10 kΩ, 100 nF is a time constant of one millisecond and 22 pF is a fraction of a microsecond. They are for different jobs, in circuits that run quickly.

The meter is part of the circuit

Change the 10 kΩ for the 1 MΩ and the 100 µF for the 10 µF, and measure again. The time constant should be ten seconds, and the reading should reach 4.8 V. It does not.

A voltmeter has to draw a little current to work. On most digital meters its DC-volts input is about 10 MΩ, which is the same as a 10 MΩ resistor across the capacitor. With the 1 MΩ charging resistor that is a divider: the capacitor stops at about 4.4 V, about nine percent under the rail, and gets there a little sooner. With the 10 kΩ it was a thousandth of the circuit and you never saw it. Meters differ and some have a different input resistance on some ranges, so treat 10 MΩ as typical.

The second experiment: a fade

Charge the capacitor, take the supply away, and let it empty through an LED. The LED lights as the capacitor gives up its charge and fades as its voltage falls toward the LED's own.

To build it, leave the 100 µF in place. Remove the 10 kΩ and the jumper. Put a 220 Ω between the plus rail and the strip of the capacitor's long leg, with its rail end on a jumper wire you can pull out: that is the charging wire. Add the LED, long leg to the capacitor's strip, and a 4.7 kΩ from its short leg to the minus rail. While the charging wire is in, the LED glows dimly. Pull it out and watch the LED fade.

The time the fade lasts is the resistor in the LED's path times the capacitor, so the 4.7 kΩ and the 100 µF give roughly a second of visible light. The 220 Ω is only there to charge the capacitor, and is out of the circuit once the charging wire is pulled. A bigger resistor in the LED's path makes a longer and dimmer glow, and a smaller one a brighter and shorter one.

Measure

Set the meter to DC volts, red lead on the capacitor's long leg, black on the short leg.

• Jumper in: 0.00 V.
• At 1 second, jumper out: about 3.0 V, which is 63 percent of 4.8 V. This is one time constant. If yours is 2.5 or 3.5 V, your capacitor is a fifth under or over its marked value, which is normal.
• At 2 seconds: about 4.15 V. At 3 seconds: about 4.55 V. At 5 seconds: about 4.8 V.
• Across the 10 kΩ, at 1 second: about 1.8 V, the rail less the capacitor's 3.0 V. Divide by 10 kΩ for about 0.18 mA, which is the current into the capacitor at that moment. At 5 seconds it reads about 0.0 V and no current flows.
• Pull the rail wire out when full: the reading falls only slowly. The meter's own 10 MΩ is what is emptying it, one time constant of about a thousand seconds, and the capacitor itself leaks a little. A capacitor holds its charge.

On the 3.3 V side the capacitor fills to 3.3 V and the time constant is the same: the 63 percent mark is then 2.1 V, at one second. For the fade, read the capacitor's voltage as the LED dims: it falls to about 2 V, the LED's own, and then falls very slowly, because below that the LED has stopped drawing.

Where the limit is

The only limit is the one on the can: a capacitor wants a voltage under its rating and the plus leg toward the plus. Every circuit that smooths a supply, times a pulse or blocks a steady voltage uses the same arithmetic, the resistor times the capacitor, that you just measured. The kit's last circuit is about light and colour: three LEDs in one package.