The Classroom

# Coping With Capacitors

Daniel Koch

Issue 4, October 2017

Storing electrical charge, a little like air in a tyre. Capacitors are valuable components, and easy to understand.

Last month, we looked at resistors, arguably the most commonly found component on a circuit board. This month, we continue on to capacitors, which are a versatile component used in dozens of applications around even a moderately complex circuit. Capacitors are so versatile, in fact, that we only have space to talk about using them with direct current, which is by far the most common situation most makers will find or use them in. Their use with alternating current, therefore, will be left for another time. One final note – this article will no doubt look very similar in sequence and content to many textbooks or primers. This is because we are not proverbially reinventing the wheel; rather, we are describing it, and there is usually a lot of similarity when many people describe the same wheel!

# CAPACITANCE

It is said that a person must learn to crawl before they can walk. In the case of electronics, it is more that we need to learn what feet are and how they work before we can use them. So before learning about capacitors, first we will summarise capacitance.

The word capacitance is formed from the root word “capacity”, which we use across our lives to describe the ability to hold, carry, or store. This is no accident, as capacitance is the ability to store an electrical charge. This can occur in any situation where two conductors are separated by an insulator. This means that the power lines out in your street, if you are in an above-ground transmission area, have capacitance between them, separated as they are by the air gap between them.

At the other end of the scale, the windings of an electric motor also have capacitance between them. Even the tracks on a circuit board have a small amount of capacitance between them. In most cases the capacitance is either negligible or irrelevant; however, anyone working in specialised situations such as radio or medical electronics, which are usually highly sensitive, needs to remain aware of this.

To understand capacitance, consider two metal plates separated by an air gap [1]. When the DC power source is applied, electrons flow from the negative side of the supply to the plate they are connected to, causing that plate to have a negative charge.

The electrons at that plate repel the electrons on the other plate, which are drawn to the positive side of the battery. Therefore, current flows for as long as electrons are on the move, from the positive plate to the negative plate of the battery. This is referred to as the “charging current”. Most makers typically encounter this term and its associated maths when calculating timing circuits.

The quantity of charge (Q) in a capacitor is a function of the Capacity (C) of the capacitor, and the applied voltage (V). If the voltage is increased, the charge will also be increased (Q = CV). However, the imbalance of electrons results in a stored charge in the form of a potential difference between the two plates. In theory, the capacitor will remain charged forever. In the real world though, even the best insulator is not perfect, and electrons will slowly leak across the gap, or back through the non-infinite resistance of the open circuit. A modern plastic encapsulated capacitor can store a charge for a very useful time, long enough, in fact, that people working on high voltage circuits need to deliberately discharge capacitors before working on them, to avoid lethal shocks, even after an entire day for some capacitive components.

The value of Capacitance is measured in “farads (F)”, in honour of the work of Michael Faraday. The Farad is a unit describing how much charge a capacitor can store. Those who have read the Classroom article in the previous issue may remember that in DC terms, a capacitor value of 1F will take the equivalent of 1A of current for 1 second to charge, and result in a potential difference of 1V. Of course, these numbers are proportional, so a 1F capacitor charging at a potential difference of 10V at 1A will take one-tenth of a second to charge.

# CAPACITORS

For now you can imagine a capacitor as two metal plates separated by an air gap, and for some capacitors this is true. In fact, old valve radios, and even transistor radios used a capacitor to tune the radio stations that was made from one set of fixed metal plates, and another set of moving metal plates, separated by nothing but air.

A modern practical capacitor has two thin insulating films called a “dielectric”, that have been metallised by coating one side with an Aluminium vapour. One type of capacitor construction places many layers of the film one on top of another, to be then cut into ‘blocks’. Another type rolls the two films together into one long sausage which is then cut into sections of the capacitance required. Either type is connected at the ends, or sides, by the component leads. The whole assemble is then dipped or molded into the component case.

The two construction methods each have pros and cons, but for average users, there is no difference in the effect. Do note however, that some are better for high frequency, others for low leakage, some for higher voltage and others for higher capacitance.

To the casual observer, they have a similar physical layout, being somewhat flat and broad in one plane and quite narrow in another [2]. Capacitor types use a variety of dielectrics, from ceramic, mica (a mineral insulator), and of course, polyester. In most cases they are named after the dielectric they use. It should be noted that these types of capacitors are all non-polarised. That is, they can be connected with negative or positive connections either way around, and will work the same way. Additionally, these types are usually of lower capacitance, typically values under 1µF.

Electrolytic capacitors, which have a distinctive can-shape, use a chemical electrolyte as the dielectric material. The chemical action of the electrolyte forms an oxide layer on one sheet of foil during construction,but not the other. This means that electrolyte capacitor types are polarised capacitors, and they can only be used with the negative electrode more negative than the positive electrode. Electrolytic Capacitors are always marked accordingly, with through-hole types having a stripe down the negative side, and a series of ‘-’s marked down that side. Surface mount types having a black line to one side of the top of the case [3].

Although it is normally loathsome to suggest Wikipedia as further reading, simply because it is open to editing by non-qualified people and issues can take time to identify (anyone who has been through university will remember the golden rule – Wikipedia in a reference list will either cost marks or constitute a fail!), in the case of electrolytic capacitors, there is actually a very informative and in-depth article that can be sourced from there. Check out https://en.wikipedia.org/wiki/Capacitor.

For small physical size, but limited capacity, Tantalum capacitors [4] are an alternative to electrolytic capacitors. They have a very different construction, and are quite effective devices, if kept within their limitations. Tantalum capacitors are expensive compared with electrolyte capacitors, and therefore less common. Tantalums behave in a circuit the same way as electrolytic capacitors – they are polarised and usually of larger values than non-polarised types. Tantalum values are more consistent and more accurate, and are therefore are often used in timing circuits of longer durations.

# USING CAPACITORS

As explained in the previous article on resistors, capacitors also have a variety of markings to show their value of capacitance, and other parameters, depending on type. Additionally, while a 1Ω resistor would be considered small and uncommon, a 1F capacitor would be considered large, a Super Capacitor.

Capacitors in common use range from less than ten milliFarads, still referred to as 10,000µF, down to 1 picoFarad, or 1e-12 Farads [5]! Yes, truly tiny numbers! For this reason, decimal dividers must be used.

For most smaller capacitors, below 1µF, a multiplier system is used that works in the smallest common unit of capacitance, ‘picoFarad (pF)’. The value will generally consist of three numbers, a letter, and a voltage rating in some cases. Some other capacitors only display the three-number value. As with resistors, capacitors are made in a set range of values, such as the e12, e24, e46 series. So, you could purchase a ceramic disc capacitor in 4.7pf, 47pf, 470pf, and so forth, but you are unlikely to find a 44.3pf capacitor.

To read the codes, the first two numbers are the significant figures, while the third is the number of zeros used to give the value in picofarads. Therefore, a 470pf capacitor would have a value stamp reading “471”. This is significant figure “4”, significant figure “7”, with the “1” corresponding to one multiple of ten, or one zero, following. Unfortunately – and very confusingly – some manufacturers use the “0” when there is no multiple; so 47pf can be stamped as “470”. This does exist but is not common; in fact, in 14 years of selling electronic components, I only saw this a handful of times.

A hint: Whether Resistors, Capacitors or Inductors, the exponential function of the calculator is a great tool for beginners. The 471 above would be typed in as 47 [exp] 1 [enter]. Try it! Also for various other notations such as 333, 684, or a common group, 102, 103, 104 etc. For resistors, once you can translate the colours into numbers, you can also enter them straight into the calculator until you learn what each colour code means. Brown, Black, Black, Orange? Go on try it.

Generally, a value of 47pF would be stamped as “47” and all higher values will be three digits. The codes work the same way on ceramic, MKT, greencap, and polyester capacitors [5]. Greencaps are a form of polyester capacitor; however, there are others.

On some capacitors, particularly greencaps, a letter may be found. This is a tolerance designator. All components are manufactured to a tolerance, which means the value can be over or under the rated value by a percentage. The codes are generally the same as for resistors. Additionally, some capacitors have a voltage rating stamped on them. This is usually directly stamped, with no coding or multiple system. Some polyester capacitors, for example, have “100V” on them, which literally means they are rated to 100 volts.

For larger capacitors, usually electrolytic capacitors, the value is directly stamped. In most cases the value is in microFarads (µF). The “u” in this abbreviation is actually the Greek letter “mu”, which has a longer tail on the left side extending down (μ), but many standard printing fonts do not cope with this. So even though 4.7 millifarads is a real value, it will be written as 4700 microfarads, or 4700µF. This has led to the tendency for most users to talk in microFarads instead of milliFarads. So, numbers of ten thousand microFarads are heard commonly, despite this being more mathematically correct when stated as ten milliFarads.

As with resistors, some manufacturers prefer to avoid decimal points, so you may see a value of 3.3µF stamped as 3u3, or even 3µF3 [6].

The second piece of information on an electrolytic capacitor is its voltage rating. Electrolytic capacitors ALWAYS have a voltage rating on them, as well as a stripe to indicate the negative terminal. This is because electrolytic capacitors behave differently unless used at or close to their rated voltage.

A curious property of electrolytics is that they only begin to show a curve in their charging current when operating closer to their design voltage. If used well below this, they may not respond as expected. This has implications in timing applications as discussed ahead. A 10µF 63V electrolytic may give a different timing result than a 10µF 16V example when used on a 12V circuit.

Electrolytic Capacitors also have a temperature rating. Mostly for higher power applications but essential knowledge if you are to repair a circuit such as a power supply, particularly a SMPS. Often such power supplies use a 105° component, and when it fails, it should be replaced with a 105° component. A power supply or amplifier that has used an 85° component to replace the original 105° value, will continue to fail, periodically, until the correct temperature rating is used.

# POWER SUPPLIES AND CAPACITORS

One of the most familiar situations involving capacitors for many makers, will be the small cluster around the power supply on their breadboard’s plug-in supply, or around a board that take a plug pack as a power source. In this situation, capacitors are employed so that their ability to store and then release a charge can be used to filter and stabilise the power rails. In very basic terms, they absorb spikes by charging up as quickly as they can, then slowly releasing this charge into the circuit [7].

There are many other reasons to use capacitors around power circuits; however, without the space to describe inductance, reactance, and resonance, this explanation is best left for later. The important thing to know is that capacitors across a power supply rail can help with stability and the reduction of electronic noise.

# SOME QUICK MATHS

Capacitors can be used alone, or in combination with each other. If so, they can be connected in “series”, or “parallel”. There is nothing tricky about these names, they are what they describe.

When working in series, the total combined capacitance is actually lower than the smallest capacitor in the series [8]. The advantage to this is that the total potential difference that can exist across the combined chain, is the sum the voltage ratings of the individual capacitors. So three 100pF, 100V greencaps in series now yield a capacitance of 33.3pF, but can withstand 300V. The increase in voltage is the main reason for adding capacitors in series.

On the other hand, things are simpler for parallel circuits. The total capacitance is simply the sum of the individual values, while the voltage ratings are unaffected. Of course, the smallest voltage value determines the voltage that can be applied to the network, without causing damage to that capacitor.

# TIMING WITH CAPACITORS

This same property of capacitors can be used to form a timing circuit. With the exception of electrolytic capacitors operating well below their design voltage, capacitors operate to what is known as an exponential, or “Universal Time Curve”. To do this, they are used in series with a resistor, and called an RC network. The values of the capacitor and resistor do not affect the relationship curve; however, they will affect the length of the axes if graphed to scale. This is because of something called a Time Constant (TC). A TC is determined by an agreed standard, and it is defined as the time it takes for a capacitor to charge, via the resistor, to 63% of the voltage being supplied.

The maths for this is fairly simple: TC = R x C, with R in ohms and C in farads. Be careful to convert both the Resistance and capacitance to a whole unit, and not use the decimal multiplied or divided form.

The resulting number is the length of one time constant in seconds. This could also be a decimal with quite a few places, which you would usually convert for practical use, to milliSeconds or even microSeconds.

Once the time constant has been determined, the length of time a given RC network will yield can be determined. If your circuit will trigger at two thirds of the supply voltage, then your time delay is ever so slightly more than 1TC. If it is nothing like what you need, then you have an educated guessing point with which to try other values in the equation. For many makers, not being engineers, guess-and-check will be quite a valid way of working.

If you choose to trigger at around 63% and set your circuit to that value, you can choose a starting value of capacitor and a resistor, either from experience or by performing the maths. e.g. 1MOhm and 1µF have a TC of 1 second. You can begin by changing values in decades to get close to the value you want. Let us say you want a circuit to turn on in 200mS. You can drop the value of either R or C by 10, purely aiming at the next lower decade, and get 100mS. Then double one or the other value to get 200mS (e.g. 200kiloOhms and 1µF, or 2MegaOhms and 0.2µF).

Of course you would need to choose between standard values of 220kΩ, and 180kΩ. In engineering terms, there are other considerations that would determine the values used, where a large resistance may be undesirable, for example; but this will still be a good starting point.

To learn more, see below “Hands-On Activity”. Note: the maths for this involves transposing or rearranging the equation, so it becomes: R = TC/C.

That’s all for now.

# For The Educators

For educators, metalanguage is a central part of learning in any subject. These terms are all subject-specific, and important to students learning the field, as the words all have defined, often-used meanings; understanding of which, is vital for success.

Science is no different, whether being taught at kindergarten level or senior high school. What sets science apart, however, is the sheer volume of metalanguage that may be encountered. This is because of the almost limitless variety of topics that may be used to satisfy some outcomes. The question though, is how to teach it.

An example will, of course, be explained and defined at a point in the lesson; however, research shows that most students need to repeatedly engage with a technical word before its meaning is fully understood. Even if the concept sinks in, spelling may be an issue for some words, affecting fluent written communication.

In primary teaching, this is often overcome with a word wall, mind map, or graffiti wall that students can constantly refer to. These artefacts have the correctly spelled language, possibly with definitions, in a visible place that can be referred to at will. Younger students enjoy these brainstorming activities, and are usually in the same space lesson after lesson for a given topic, even if they change classes for subjects, as some primary schools do.

For high school teachers, the challenge is greater. Older students find such activities childish (although it is amazing how much we love them again at university), and often have no regular classroom for a given topic. In discussion with a high school teacher friend of mine, we adapted some of my primary school ideas for his robotics lessons in science class. This discussion eventually involved the whole science faculty, along with myself – a ring-in primary teacher! The result was a three-tier differentiated activity, which resulted in a cheat sheet that the students were able to access digitally at any time.

For struggling students, words were provided that they had to find definitions for. Some equations were also provided, which the students had to show worked examples of. The next tier was a handful of words and equations, where students were required to define and work examples. They also then had to find the same number of examples themselves. The final tier was a blank sheet with a required number of words and equations that the students had to find, define, and work as examples.

These three tiers were all marked against a rubric, constructed collaboratively by the teacher and students. They offered marks for thinking skills, processes, and creativity as much as for correct results. The resulting cheat sheet is allowed as a resource sheet during assessment which itself, aims to assess skills and processes rather than knowledge. This is proving very popular with the students at the moment; however, the unit of work had not concluded at the time of writing this. I do feel that it may be useful for other teachers who find that students do not absorb metalanguage well during direct instruction.

# Hands On: Demonstrating Capacity

To get a feel for capacitors in general, and RC networks in particular, this simple, hands-on activity uses just a few components and a breadboard to demonstrate how the value of a capacitor affects the time it takes to charge and discharge; and the effects that a resistor can have on this.

For this experiment, we’ll work with electrolytics. They're cheap and have a fantastic range of available values. Many makers will have an assortment of components on their workbench for testing or development, so the capacitors in the following parts list are a guide only. If buying values for a class, decade values are the best as they clearly show the effect of going up or down a decade.

Parts Required:
Electrolytic Capacitors in:
10µF, 47µF, 100µF, 220µF, 330µF, 1000µF
1 x Diffused LED in any colour (low current draw)
1 x 220Ω Resistor (for LED)
Resistors in Various Values (we suggest 10Ωm, 10kΩ, and 1MΩ)
1 x Small Breadboard and Prototyping Jumpers

# EXPERIMENT ONE

Follow the diagram below with just one capacitor. Connect your power supply to your breadboard, probably the 5V supply often used with Arduino and Raspberry Pi experimentation.

Note: Because the power supply may have capacitors also, we are using links to break the power to our test circuit. This ensures a clean application / shut off of power. If we simply turned the power supply on and off, it could skew our results by still ramping power up and down with the internal capacitors.

Following the diagram below, wire up everything but the blue jumper wire. This will be our power-control wire. You could use a switch in-place of the wire. Both options will work fine and produce the same result.

Using the smallest capacitor you have, insert it taking care of polarity shown and connect the blue link. Watching the LED, notice if it turns on instantly or slowly. Then keep watching when you remove the blue-coloured jumper wire. You should notice a nice gradation in the LED, turning on slowly, and off slowly.

Replace the capacitor with the next value up, and reconnect power. Continue until you have worked through all your chosen values. You can record the time the LED stays on, the plot the results on a graph. You should notice a pattern!

The capacitor values will have a predictable and reliable effect on the power to the LED, inline with their capacitance value.

# EXPERIMENT TWO

Follow the diagram below. Add one or more additional capacitors in parallel, and note what effects this has on turn on / turn off time for the LED.

# EXPERIMENT THREE

We'll simply replace one of the links with a resistor. Using the same method as before to apply and remove power, notice how the use of different resistor values between the capacitors and LED change the rate and which it turns on and off.