## Capacitors – Part 1

A brief introduction to capacitors: what they are, how they are made, and their basic functionality.

A capacitor is an electric device capable of storing energy in the form of electric charges (electric field).

In the most simple form, a capacitor is made of two conductive plates facing each other and an insulator in between, which is normally called a dielectric. The two plates are then attached to wires, that are used to connect the capacitor in an electric circuit.

The schematic diagram reflects exactly the physical nature of the device:

When a capacitor is connected to a power supply, like a battery, electrons leave the plate that is connected to the positive side of the battery, while the same amount of electrons is pushed into the plate connected to the negative side of the battery. Once the difference of charges at the plates of the capacitor is enough to establish a voltage on the capacitor that is identical to the battery, electrons stop moving around the circuit and an equilibrium is reached.

At this point, if the connection with the battery is severed, the capacitor will retain the amount of charges on its plates: extra charges on the negative plate and defect of charges on the positive plate. If we connect a load to the capacitor, for example a resistor, charges will start moving in the circuit pushed by the voltage at the wires, called electrodes, of the capacitor. So, electrons will leave the negative plate moving toward the load, and an equal amount of electrons will move from the load into the positive plate of the capacitor. The movement of the electrons causes the voltage at the plates of the capacitor to lower until, when an equilibrium of charged is reached, the voltage will be zero and the current will stop flowing through the circuit. At this point all the energy that was stored in the capacitor has been used and the capacitor is said to be discharged.

Both during charge and discharge, the ratio between the amount of charge stored on the capacitor and its voltage remains constant. This can be verified experimentally. We define this constant as the capacitance of the capacitor:

## C = Q / V

Using the above formula, and calculating the work done to move the charges in and out of the capacitor with the help of some calculus, we can determine the energy stored in a capacitor as:

And, finally, the actual capacitance can also be determined by the physical parameters of the capacitor itself. We can see experimentally that the capacitance is directly proportional to the area of the plates of the capacitor, it is inversely proportional to the distance between the plates, and depends on the type of dielectric in between the plates. The type of dielectric is identified in the formula by the Greek letter ε (epsilon). Each type of dielectric has its own value of ε (permittivity), which is the product of the vacuum permittivity and the relative permittivity of the material.

## How Resistors Work

What is a resistor? Why would I want to use it? Where can I find it?

I’m sure you have asked these questions and many others to yourself several times. Here, I hope to give you at least some of the answers. But keep in mind that there is much more behind this and I could keep writing pages and pages on the subject barely scratching the surface of it.

So, why am I doing this? Because, for the most part, the information I will provide here are enough for day to day use of the resistors in simple electronic circuits used to for learning and for early experimentation. If you need to know more, then you are already on the road for becoming a true electric or electronic engineer.

A resistor is an electric device which only reason to exist is to reduce the flow of the current in a circuit. It obtains this effect by dissipating the extra energy of the current into heat. Yes, heat! There was never in the engineering history a device that wasted more energy than a resistor (percent wise). But then you’d ask: why in the world we want to use it? Because, used in the appropriate way, it allows us to do a lot of things that wouldn’t otherwise be possible. Just think at this: there is no electronic circuit in the world that does not use resistors.

Here is how resistors look like:

Back in 1827, a German physicist and mathematician named Georg Ohm, published a paper containing what it was later called Ohm’s law. It was basically a formula that correlated the current that flows in a wire with the voltage applied at its extremities. He found that increasing the voltage, the current also increased of a proportional amount, and he called the proportional constant “resistance”. The formula of the resistance was born (although he did not write it exactly this way):

## V = I x R

A resistor, therefore, is fundamentally a piece of conductor that presents a certain resistance to the flow of the current. When we apply a voltage V at the ends of the conductor, an electric current I will flow, proportional to the amount of voltage by the constant R, the resistance of the conductor. In the SI system, the resistance is measured in Ohms, to honor the discoverer of the law, while the voltage is measured in Volts and the current in Amperes.

Today, resistors are made of different materials. These materials are substantially a mix of a good conductor and an insulator (a material that blocks the flow of current). Adjusting the mix of the two substances, it is possible to create resistors having a wide range of possible resistances, from tens to millions of an ohm.

There are two symbols that are normally used in schematics to represent a resistor. The most common in USA is the one with a zig-zag shape; the other is the one specified by the IEC (International Electrotechnical Commission):

Let’s now talk about how resistors can be connected to each other to accomplish some simple tasks.

The first way to connect together two or more resistors is to put them in series. Two or more resistors are said to be connected in series if the same current I flows through all of them:

The voltage E applied to the whole circuit is split among all the resistors and the sum of all the resistor voltages equals the voltage E:

## E = V1 + V2 + V3

while the total current in the circuit is:

## I = V1/R1 = V2/R2 = V3/R3 = E/Req

Req is the equivalent resistance of the series:

## Req = R1 + R2 + R3

A series of resistors is normally used as a voltage divider like, for example, those that are used to polarize transistors, or other electronic components. Another usage example is to reduce the input voltage coming into a device, to bring it to a value more consistent to what the device needs. An example of that is the input of an amplifier that accepts a voltage no greater than 1V as its input. If the source of the signal that goes into the amplifier has a greater voltage, a couple of resistors in series can do the trick of lowering the voltage to a more adequate value.

Another way to connect resistors is to put them in parallel. Two or more resistors are said to be connected in parallel if the same voltage E is applied to all of them:

The current I that flows from the generator is split among the different resistors and the sum of all the resistor currents equal the current from the generator:

## I = I1 + I2 + I3

The voltage in the circuit can be expressed by the following equation:

## E = R1 * I1 = R2 * I2 = R3 * I3 = Req * I

Req is the equivalent resistance of the parallel:

## 1/Req = 1/R1 + 1/R2 + 1/R3

Resistors in parallel have several uses, but the first two that come to my mind as the most usual are:

1. You need a resistor of a particular value that is not available in the market. To solve the problem, you build the resistor with the value you need by putting in parallel two or more resistors of higher value, such that the Req equals the value of resistance that you need.
2. You can view at all the devises and lamp that you plug in your house receptacles as resistors. All of them are connected in parallel, so each one of them can receive the same voltage regardless of how much current they need.

And, since we were talking about lamps, let’s also talk about power. We have said that the main function of a resistor is to restrict the flow of current by converting the excess power into heat. However, while we do so, we also need to avoid that a resistor becomes too hot, thus damaging its surroundings on the circuit board and maybe even catching on fire.

For this reason, each resistor has a power rating. The power rating the is the max amount of power that the resistor can dissipate without becoming hot enough to cause damage to itself or its surroundings. Normal ratings for resistors that are used in electronic circuit are 1/8, 1/4, 1/2, and 1 W

W is the symbol used in electrical engineering to identify the unit to measure the power, which is called Watt. And yes, that is the same power unit used for mechanics and for thermodynamics, if you were wondering.

The power dissipated by a resistor depends on the voltage applied to the resistor and the current that goes through it:

## P = V * I = R * I2= V2 / R

When designing a circuit, you always have to make sure that you determine the max power that each resistor will dissipate, so you can specify the power rating of the resistors along with their value in Ohms.

Another thing that is worth mentioning is that resistors have also a voltage rating. However, even resistors with very low power rating, like 1/8W, have voltage ratings of at least 200V. Will you ever build an electronic circuit that is powered with such amounts of voltage? Probably not, that’s why you don’t usually have to worry about that. And, in fact, how many times have you heard somebody talking about voltage rating of resistors? Maybe never?

One last thing I would like to talk about is how to identify the value of a resistor. Resistors normally  used in electronic circuits are of two kinds:

• through hole resistors
• SMT resistors (Surface Mount Technology)

The value of the SMT resistors is always written in clear, with numbers and letters, for example 1k2, which means 1.2 kΩ (that is kilo Ohms).

The value of the “through hole” resistors is instead normally identified by a number of color bands painted on the resistor itself. Each color represents a digit in the value of the resistor, or a multiplier, depending on the position. The last colored band represents the tolerance, which tells you how precise is the value of the resistor itself.

Here is a table that shows you the color codes and the meaning of each color in relation with the position on the body of the resistor.

‘Till the next time…