Conductors and insulators

Why do some materials conduct electricity, while others don’t? Some materials are populated by good and careful atoms which don’t lose their electrons easily (and probably feel ashamed if they do). Hence the itinerant population is low. The few free electrons that exist tend to sit miserably in one place, having given up hope of ever finding a home. These are insulators, typically air, rubber or the fibreglass backing of a circuit board. In other materials atoms are positively feckless. There are many free electrons and should some charged material come near they move accordingly. How do they know? They feel the voltage. These are conductors. Most metals are conductors. We use copper a great deal, gold where corrosion could be a problem, and sometimes aluminium or other metals for housing equipment.

Resistance

Some materials fall into a kind of grey area between being conductors and insulators. We can use these to make resistors. It’s as if the material was a kind of mud; if we make the mud thicker electrons move less easily. The resistance of a given piece of a material depends on ‘how thick the mud is’ (the ‘resistivity’ of the material) and its geometry. Making it thinner increases, and doubling or tripling length doubles or triples, its resistance.

Ohm’s Law

The unit for resistance is the ohm, or, and the symbol in equations is R. Now we come to the most important equation in electronics:

(2.1a)

with V in volts, I in amps, R in ohms. This is Ohm’s Law. We will use it so much that it bears being rewritten in its two other forms:

(2.1b)

and:

(2.1c)

These are used so frequently that you need to know them by heart.

Ohm’s Law tells us that placing a steady voltage across a material causes a proportional steady current to flow.

Even insulators and conductors have resistance. Insulators have very high resistance; tens or hundreds of MΩ or more, so that for the normal voltages that we use an unmeasurably small current flows. If the voltage is raised to sufficiently high levels, usually at least a kV, a condition called ‘breakdown’ occurs; electrons are blasted free from atoms within the structure of the material, and its essential nature is changed. You will know if this happens; there is a nasty burning smell, and things stop working. It is a condition which we try to avoid.

Conductors are the opposite; their resistance is very low, small fractions of an ohm typically. The commonest conductor that we use is copper. We cannot normally measure the voltage across a piece of copper wire, unless it is long. We can find out, from catalogues and so on, the resistance per metre of any given type of wire; this depends on the wire, but figures of around 0.1 Ω/m are typical. Occasionally we need to find this out and calculate the total resistance of a length of cable when our wires are very long, in a large system. The wire will also have a maximum current rating, which is what we can pass through it before the amount of heat generated in it becomes dangerous to its structure. The insulating material around it may melt, causing it to short to things that it shouldn’t, or the conductor itself. We only need know that we should stay comfortably within the maximum rated current for a conductor. In essence, anything can be destroyed with too much voltage/current.

To summarize, we have three distinct classes of material; conductors, insulators and resistors. Conductors connect our circuit up and have very low resistance. We assume that the voltage is the same at both ends of them unless they are very long or current is very high. They are just vessels to carry current. Insulators are the separating material between different points in a circuit that need to be kept apart and have very high resistance. Resistors are electrical components having a known resistance. We can predict the current through them for any given voltage, or vice versa, using the all-powerful Ohm’s Law, V = IR.

Circuits, diagrams and common expressions

A circuit is exactly what its name suggests; a loop around which electric current can flow. The loop is generally made up of conductors (bits of wire or otherwise), circuit elements or components (which we start to meet soon) and one or more sources of electrical energy – current or voltage.

Circuit diagrams, sometimes called schematic diagrams, are symbolic representations of the way that the components of a circuit are interconnected. They are the starting point for most designs, and invaluable aid in servicing or faultfinding equipment that already exists. Each element of the circuit, from a battery or a tiny resistor to a complex microprocessor chip, is represented by a symbol, with each connection to it represented by a line joining to it. Interconnections between elements are shown by lines drawn between components. In reality, these could be any form of conductor; a wire soldered directly to a leg of the component (not recommended for a microprocessor!), a copper track on a PCB, or a test lead with a crocodile clip at either end of it.

Sometimes a circuit diagram doesn’t show all of the circuit, and you can’t see all of the loop around which the current will flow. (For example, see Figure 2.2 later.) The inference here is that things start to happen when something else is connected to it, completing the circuit – in this case a DC voltage (as you will see).

‘Block diagrams’ are a special type of circuit diagram worthy of explanation. You generally find them with fairly complex electronic circuits which are either too large to see on one drawing, or more understandable by being broken into smaller parts. Each ‘circuit block’ is drawn as a box or some commonly understood symbol, with lines connecting the blocks. The lines represent ‘signals’ (in reality any means by which the individual circuits can communicate), generally one or more conductors carrying voltage or current. It is the job of the person drawing the block diagram to make it less vague than this definition!

Two more very common terms – ‘short circuit’ and ‘Open circuit’. A short circuit is what happens when you connect two points with a conductor. An open circuit between two points means that they are not connected at all (an insulator is between them).

Resistors

We buy resistors as discrete electrical components. They come in values ranging from fractions of an ohm to tens of megohms, and are found everywhere in electronic circuits. We will see values between about 10 Ω and 1 M Ω most commonly in our circuits; values outside that do occur, but less commonly. They are identified by a series of coloured bands, each band signifying a number, or sometimes they just have the value written on. The colour code system is described in Appendix 2. The circuit symbol for a resistor is shown in Figure 2.1.

When we combine more than one resistor together in a circuit we can calculate an equivalent resistance for them, and treat them as a single component. There are two ways of doing this.

Three resistors in series are shown in Figure 2.2. When we have this situation, we just add the values of the resistors to get their equivalent. We can do this for any number of resistors:

(2.2)

Are electrons psychic?

There are two ways in which electrons seem to know about what others are doing and be caused to move. One effect is due to EMF and the other to MMF. A full analysis requires excursions into the subjects of electrostatics and magnetics, but luckily we can get a good picture of these effects without all that. Both forces exist and have an application in electronics whether the charges are in the same conductor or two separate ones.

Capacitance and capacitors

When two conductors are separated by an insulator there is voltage between them if they have different amounts of charge. Changing that voltage requires charge to be moved, which requires energy. We can buy components specially made to have an appreciable amount of capacitance and use the effect in our circuits. Capacitors (‘caps’) consist of a pair of conductive plates separated by a special insulator called a ‘dielectric’, which magnifies the effect. When caps have no voltage across them we say that they are ‘discharged’ or, conversely, when they do that they are ‘charged’.

The capacitance between the plates gets greater when:

The unit of capacitance is the farad, or F, and the symbol used in equations is C. A farad is a lot of capacitance. A capacitor of one farad would have a potential of one volt across it when it had a charge of one volt on it:

(2.4)

where Q is charge in coulombs, C is capacitance in farads and V is voltage in volts. This is more useful if we write it in terms of current, using Eqn (1.1):

(2.5)

This tells us that the rate of change of voltage across a capacitor is proportional to the current through it.

Capacitance exists everywhere, but is so small normally, say between two wires running side by side for a few feet, that we wouldn’t bother much about it. (For cables containing more one conductor, separated by an insulator (‘multicore cables’) we can find out a value of ‘typical capacitance between cores per metre’, which we might take into account, if running signals through long cables, in the same way that we talked about for ‘resistance/metre’ earlier.)

Capacitors range in value from a few pF to 100 000 μF and more, with physical sizes getting larger with value. Figure 2.4 shows the circuit symbol for a capacitor.

Capacitors come in a variety of types, with different characteristics. The most important of these are listed below:

There are other specifications which can come into play, but these are the most important. The value of a capacitor is usually written in numbers, in pF or in μF if no unit is specified. Unfortunately it is not always clear which, but it is usually possible to guess from the physical size, once you become familiar with them.

Self-inductance and inductors

Magnetic fields, when they move through a conductor, cause a voltage which can make electrons move. And electric current (or movement of electrons) causes a magnetic field. This adds up to an interaction of magnetic field, voltage and current, the net effect of which is this: if current flows in a wire there is a certain tendency for it to want to continue to do so, and not to change. (Sometimes we say this another way; when the current through an inductor changes, the inductor sets up a ‘back EMF’ which opposes the change in current.)

This effect is known as self-inductance (or just inductance). Like capacitance, it is not noticeable under normal circumstances. It can be made much stronger, however, if the wire is wound into a coil shape; the more turns the better. Inductance is also much increased by winding the coil on a core of some special material said to have a high ‘permeability’; that is, it has the effect of concentrating the magnetic field. Such a device is called an inductor. Figure 2.5 is the circuit symbol.

The voltage across and current through an inductor are related as follows:

(2.8)

where L is the inductance in its standard unit, the henry(H).

This says that the voltage across an inductor is proportional to the rate of change of current through it. We can see that this is not unlike Eqn (2.5), for a capacitor. And, indeed, capacitors and inductors are in many ways the converse of each other. One resists change in voltage, the other change in current. As we look at these components again in the following chapters, we will see that in each circumstance they do opposite things to each other.

Inductors are available with values from about 0.01 μH to 100 mH and more. Like capacitors, they get physically larger with value. As large value inductors consist of very many turns of wire on a heavy iron former, they also tend to get very heavy, one reason why they are not as popular as capacitors. They also tend to have a significant amount of resistance, which can be a disadvantage. The main specifications for an inductor are:

Despite their problems, they are quite common in some applications, and sometimes nothing else will do.

Mutual-inductance and transformers

Magnetic fields also cause electrons in unconnected conductors to influence each other. This effect is called mutual inductance. To make the effect strong, coils of wire are wound together on a core (which again has the effect of concentrating the magnetic field). This is a transformer. The symbol is shown in Figure 2.6.

The coil of a transformer into which you put current is called the ‘primary’. The coil(s) from which you take current are the ‘secondary(s)’. The ‘turns ratio’ of a transformer is the ratio of the number of turns on the primary to those on the secondary. When we apply AC voltage to the primary, we get AC from the secondary. And, conveniently:

(2.11)

where T_p and T_s are the number of turns on primary and secondary, respectively, and V_p and V_s the voltages.

Transformers are very useful in certain situations, the most common being the passing of a signal from one part of a circuit to another while keeping the two electrically isolated. Virtually all equipment connected to the AC mains supply is done so via a transformer. For safety reasons this is a special type, designed to have good electrical isolation. We never use anything but a proper mains transformer for this! Transformers are also very useful in many other circuits, and many other special types exist.