Resistance
When electrons or other charge carriers flow through a conductor, they move through the lattice and pass close to the atoms of the conductor. They may actually collide with them or at least lose energy to them when they come within range of the electrical fields around the atoms or their nuclei. Whatever happens, the electrons lose energy. We say that the conductor offers resistance to the flow of current.
At the same time as the electrons lose energy, the atoms of the conductor gain energy. The effect of gaining energy is usually to make the atoms vibrate slightly about their usual fixed positions in the lattice. The motion of one atom is transferred to other atoms in the lattice, so that all of the atoms are in slight motion. This type of motion is a form of thermal energy, usually known as heat. When a current passes through a conductor, the conductor becomes warm or even very hot. In the case of the filament of an electric lamp, it becomes so hot that it glows with visible light. Some of the electrical energy has been converted to heat and some to light energy.
When a charge carrier begins its journey through a conductor it has potential energy, depending on the electrical potential at the point it starts from. During its passage though the conductor it loses some of this potential energy, which is used to heat the conductor. The loss of energy gives rise to a potential difference (p. 21) between one end of the conductor and the other. The amount of energy lost is proportional to the number of charge carriers passing through the conductor, in other words, to the current. We can say that:
The potential difference between two ends of a conductor of a given material is proportional to the current.
This statement is a version of Ohm’s Law, first stated by Georg Ohm. This law can be put into mathematical form. If a current I is passing through a conductor and there is a p.d. V between its ends, we can calculate R, where:
We find that, for any given conductor, R is constant. R is called the resistance of the conductor. If I is expressed in amps and V in volts, the resistance is in ohms.
For example, a conductor is connected to a battery which has a p.d. of 12 V between its terminals. It is found that a current of 4 A is passing through the conductor. What is its resistance? In this example, V = 12 and I = 4 so:
The resistance is 3 ohms. Instruments for measuring p.d.s and currents are described in Chapter 14.
The ohm is the unit of resistance and its symbol is Ω. It has as multiples, the kilohm (1 kΩ = 1000 Ω) and the megohm (1 MΩ = 1000 kΩ).
The resistance of any given conductor also depends on the nature of the conductor. It depends on the size and shape of the conductor and the material from which it is made. Some conducting materials have a bigger supply of charge carriers than others, which makes it easier for them to conduct a current. Examples of good conductors are copper and aluminium.
Resistors
All conductors except superconductors (see p. 33) offer resistance to electric current. In electronics we use special components, called resistors, to provide a given amount of resistance as required in a circuit. Various types of resistor are available, one widely used type being the metal film resistor shown in the title photograph of this chapter. This consists of a rod of insulating ceramic coated with a metal film. The film forms a spiral track running from one end of the resistor to the other. It makes contact with the terminal wires at each end. The resistance of the resistor depends upon the length and the width of the track, and upon the metal from which it is made.
Resistors can be made to a very high degree of precision, but precision resistors are unnecessary for many electronic circuits. Resistors are manufactured with a quoted degree of precision, known as tolerance. If a resistor has a tolerance of 5%, for example, we know that the actual resistance is within 5% of the nominal value (the value marked on the resistor). For example, if a resistor is marked with a nominal value 33 Ω and its tolerance is indicated as 5%, it means that the actual value of the resistor may be any value within 5% of 33 Ω. Since 5% of 33 is 1.65, the value is between:
If we regard a nominally 33 Ω resistor with 5% tolerance as being close enough for circuit-building, there is no point in making resistors with nominal values in the range 31.35 Ω to 34.65 Ω. The next useful lower value is 30 Ω, for resistors with this nominal value may lie between 28.5 Ω and 31.5 Ω. The range of 30 Ω resistors just touches the range of 33 Ω resistors. Similarly, the next useful value above 33 Ω is 36 Ω, with a range from 34.2 Ω to 37.8 Ω.
To minimize wasteful overlapping of actual resistor values, resistors are made in a series of preferred values, known as the E24 series. In this series, there are twenty-four basic values:
The series continues with twenty-four values ten times the above: 100, 110, 120, 130, 150, … , 910.
And then it continues with twenty-four more values: 1000, 1100, 1200, 1300, 1500 , …, 9100(or 1k, 1.1k, 1.2k, 1.3k, 1.5k, … ,9.1k).
This scheme is repeated decade by decade up to the maximum practicable value, which is usually 10 MΩ.
There is also a set of smaller values: 1.0, 1.1, 1.2, 1.3, 1.5, … , 9.1.
In this way the E24 series comprises resistors with 5% tolerance to completely cover the range 1 Ω to 10 MΩ.
Certain types of resistor are made in a restricted range of values, known as the E12 series. In each decade this comprises alternate values of the E24 series: 10, 12, 15, …, 82. The resistors which are produced as an E12 series have tolerance of 10%, so there is no point in including the other values of the E24 series. The series repeats in each decade as with the E24 series.
For even greater precision, though at greater expense, resistors are made with 2% and 1% tolerance in the E48 and E96 series.
Colour codes
The resistance of a resistor is indicated by a number of coloured bands, the colour code, painted on the resistor. Two main systems are used, the four-band system and the five-band system. The four-band system uses the first three bands to indicate resistance. The colours represent numbers according to the following code:
The first two bands (A and B) indicate the first two digits of the value. The third band (C) indicates a multiplier, specified as a power of 10. For example, if the resistance is 6800 Ω, the first two bands are blue and grey.
To obtain the actual resistance, this value must be multiplied by 100, or 102. The power of 10 required is 2 and red is the colour code for 2, so the three bands are:
blue, grey, red
Another example: if a resistor is marked with yellow, violet, and yellow bands (in that order), the first two bands indicate 47. The yellow third band shows that the multiplier is 104, which is 10000. The value is 47 × 10000 = 470 000 Ω, which is equivalent to 470 kΩ. This system may seem complicated at first but, in the E24 system, there are only twenty-four possible pairs of colours for the two digits (brown/black, brown/brown, brown/red, … , white/brown) and these are soon learnt.
For resistors of less than 10 Ω, we use two sub-multipliers:
For example, if the bands are green, blue, gold, the resistance is:
The five-band colour code is used for the marking of high-precision resistors in the E48 and E96 series, though it is often used for the E12 and E24 series as well.
The first three bands (A, B, C) indicate the first three digits and the multiplier is indicated by the fourth band (D). Band T shows the tolerance.
Example: The value bands on a 0.5% high precision resistor, value 2.49 kΩ, are red, yellow, white and brown.
The colour codes for tolerance (band T in the figures) are listed in the table.
Surface mount components
With the increasing sophistication and complexity of circuits on the one hand and the demand for compact, portable equipment on the other hand, any technique that reduces the physical size of components and therefore that of the circuit board, is welcome. An important development in this direction is surface mount technology, known as SMT for short. This is widely used nowadays in products that need to be small and portable such as pocket telephones and lap-top computers. It is also used for larger equipment in which size reduction gives benefits, for example in personal computers, to reduce the amount of desk space occupied.
Surface mount devices (or SMDs) do not have wire leads. Instead, they are soldered directly to the board on the same side as the component. Since no holes are needed, one exacting step in circuit board production is completely eliminated, with valuable savings in production costs. The other key feature of SMDs is that they are smaller than the equivalent conventional components.
The dimensions of the commonly used 1206 resistors are 3.2 mm × 1.6 mm. Smaller types include 0805 (2.0 mm × 1.25 mm), 0603 (1.6 mm × 0.8 mm, photograph above), and 0402 (1.0 mm × 0.5 mm). All the conventional types of resistor are available as SMT devices, including power resistors and variable resistors. Fixed resistors are available in all the values of the E96 series.
SMT resistors are too small to be marked with the bands of the colour code. Instead they are usually marked with a 3-digit code. The first two digits represent the first two digits of the resistance, in ohms. The third digit represents the multiplier, as a power of 10. Or this can be thought of as the number of zeros following the two value digits.
Examples: The marking ‘822’ indicates 82 × 102, which is 8200 Ω or 8.2 kΩ. Similarly, the marking ‘430’ indicates 43 Ω.
However, most SMDs are sold on reels of tape for use in automatic assembly machines, and the value is marked on the reel, but not on the device itself.
Connected resistances
Two or more resistances may be connected in series or in parallel. When they are connected in series, we find their total resistance by simply adding them together.
Example: If R1, is 47 Ω and R2 is 82 Ω, the resistance of the two in series is 47 + 82 = 129 Ω.
The same rule applies to three or more resistances, all in series.
When two resistances are connected in parallel, we find their total resistance by using this formula:
The formula can be extended by adding 1/R3 and even more terms to cater for three or more resistances in parallel.
If there are only two resistors in parallel, the formula is simplified to:
Example: If R1is 47 Ω and R2 is 82 Ω, the resistance of the two in parallel is:
Note that the resistance of two or more parallel resistances is always less than that of the smallest resistance.
Variable resistors
The resistors described above each have a fixed value. We call them fixed resistors. Quite often a circuit needs a resistor which can be varied in value. A typical example is when we want to be able to control the loudness of the sound coming from a radio set.
Variable resistors have a track made of resistive material (such as carbon) with a springy metal wiper that is in contact with the track and is moved along it to vary resistance. The support for the wiper is not shown in the figure.
The resistance between terminal A and the wiper increases as the wiper is moved to the right. At the same time, the resistance between the wiper and terminal B decreases.
Slider resistors or slider potentiometers, are very similar in appearance to the figure on page 31, except that they are generally enclosed in a case. They are often used as volume controls in audio systems. Five (possibly more) sliders mounted side-by-side allows the response to be adjusted independently for treble, middle and base frequencies. A multiturn potentiometer is similar but the wiper is moved by a threaded rod. It takes many turns of the rod to move the wiper from one end of the track to the other. The result is that the position of the wiper can be very finely adjusted. This feature is useful in circuits that need to be very precisely balanced.
In a rotary potentiometer (right) the track is a 270° sector of a circle and the wiper is mounted on the spindle. The whole is enclosed in a metal or plastic case with three terminal pins, so the track is not visible. These potentiometers, or ‘pots’ as they are often called, have a wide range of uses for controlling electronic circuits. Volume controls, tone controls, brightness controls, and speed controls, may all be effected by a pot.
A smaller version is the preset potentiometer, also known as trimpot, which may be enclosed in a case or may be open. Its rotary wiper has a slot to take a screwdriver. Trimpots, as their name implies, are intended to be adjusted when a circuit is being set up, to trim the resistance to the best value once and for all.
For greater stability, better linearity and longer life, the track of a variable resistor may be made of a metallized ceramic (cermet) instead of a carbon- based material.
Power
As mentioned earlier, charge carriers lose potential when a current flows through a resistance. The energy is transferred to the material of the conductor, making it warm, possibly hot.
In an electric motor, most of the energy is used to make the motor rotate, though a little of it appears as heat. In a TV set, the energy is used to produce light and sound, but some heat is produced too. In fact, heat is nearly always produced and usually represents a waste of energy.
The rate at which electrical energy is being used by a device can be calculated very easily, simply by multiplying the current by the p.d. across the device. The result is the power of the device, the rate at which it is converting energy from one form (electrical energy) into another form (heat, light, sound, motion). The unit of power measurement is the watt, symbol W.
Example: The current through a 6 V torch bulb is found to be 0.5 A. The power of the bulb is P = 6 × 0.5 = 3 W.
This calculation can also be applied to devices which generate current. For example, a solar panel produces a current of 0.8A and the p.d. across its terminals is 12 V. Its power is P = 0.8 × 12 = 9.6 W.
Superconduction
Certain materials, called superconductors, have the ability to conduct electricity without offering any resistance. This phenomenon was first discovered in 1911 by the Dutch physicist, Heike Kemerlingh Onnes.
The physicist used a wire of solid mercury and found that it had no resistance when the temperature was reduced below 4 K (–269°C). He passed current into a ring of mercury wire cooled in a liquid helium bath and found that the current was still circulating one year later. The temperature below which a material becomes superconducting is known as the critical temperature, Tc. Several other substances have since been found to be superconductive, including tungsten, aluminium and lead, but only at critical temperatures of a few kelvin. These are known as Type 1 superconductors. More recently, researchers have investigated Type 2 superconductors. A few of these are pure elements such as technetium and niobium, but most are highly complex compounds. Type 2 superconductors have higher TC, the highest discovered so far being 138 K.
Materials of zero resistance have many practical applications including power lines and high-powered electromagnets. Because there is no resistance, no heat is generated and no energy is wasted. Often the ‘wire’ is a superconductive tape. This consists of a strip of metallic substrate (such as a nickel alloy) coated with a film of Type 2 superconductor, such as yttrium-barium-copper oxide. This has about 100 times the current carrying capacity of copper wire of equal dimensions. As a cable the conductor has channels for cooling it with liquid nitrogen. Such conductors can carry 600 000 A/cm2 at 77 K. 1 kg of superconductor cable can replace over 70 kg of conventional copper cable. They are used for building motors, generators, transformers, and electromagnets, all of which operate with very high efficiency because of their no-resistance windings.
Superconducting magnets are used to levitate vehicles above a metal track so that its movement is practically frictionless. In Japan, a MAGLEV train hovers in the air above its track when its superconducting magnets are energized. The MLX01 test vehicle has achieved a world record speed of 1235 km/h while running on the Yamanashi test line. The ability to generate strong, stable magnetic fields has applications in frictionless bearings. Gyroscopes are used as references for orientation of spacecraft but the problem has always been the size and mass of the gyroscope wheel relative to the payload. By using frictionless bearings, a gyroscope with a small, relatively light, wheel turning at very high speed can achieve the required stability.
The strong magnetic fields produced by superconductor electromagnets have other applications. For instance, they have been used to produce the force required for aircraft catapults and for accelerating roller-coasters. They are also used in magnetic resonance imaging (MRI). In a strong magnetic field, the hydrogen atoms in the water and fat of the body accept energy. They release it at detectable frequencies, allowing the distribution of body tissues to be mapped without surgery.
Another application of superconducting magnets is in the storage of energy. Energy may be stored by building up a high-intensity magnetic field. The energy is released later when current is drawn from the magnet and the field collapses. With the very high field strengths that are attainable with superconducting magnets, it is possible to store large quantities of energy in a relatively small volume. Storage is 100% efficient because there are no heat losses and all the stored energy is recoverable.
A more recent use for superconduction has been found in fault limiters, devices which, for example, switch off the current at a power station when a fault occurs on the distribution lines. The advantage of superconductor fault limiters is that they act extremely rapidly. They take only a few milliseconds to switch currents of thousands of amperes.
At the other end of the scale, a superconducting quantum interference device (SQUID) consists of a superconducting coil which, owing to its zero resistance, is able to produce an appreciable induced current when placed in a very weak magnetic field. SQUIDs have many applications for detecting weak fields or the fields produced by weak currents. For example, a SQUID can detect the electrical field generated by the human heartbeat, and could detect at a distance of 10 km an alternating current amplitude of 1 A flowing in a straight wire. Superconductors are also used in highly sensitive light detectors, for infra-red telecommunications and infra-red astronomy. Sensors based on niobium nitride are able to detect a single photon and operate at 25 GHz.
Internal resistance
Even when a cell is not connected into a circuit, there is an e.m.f. between its terminals. The size of the e.m.f. depends on which two metals are used for the electrodes. The e.m.f. causes a p.d. between the terminals. The size of the p.d. equals the size of the e.m.f. when the cell is unconnected.
In the figure, a cell is causing current (conventional current, see p. 14) to flow round a circuit which consists of a resistor, value R. To complete this circuit, there are ions carrying electric charge through the electrolyte of the cell. Like most conductors, the electrolyte has resistance. Taking this into account, we recognize that the circuit has a second resistance, termed the internal resistance,r, of the cell.
The value of r depends on the composition of the electrolyte, the distance apart of the electrodes (the central rod and the case of the cell) and their area. It may differ from cell to cell.
In the schematic diagram of the circuit, below, everything on the left is the part of the cell. The circles represent its ‘terminals’, where the wires of the circuit connect to it.
The e.m.f. of the cell, that is, the actual electrical force produced by the chemical action of the electrodesand electrolyte is V. Note that the e.m.f. and the resistance of the electrolyte that produces it are shown separately in the diagram.
Suppose that a current I is flowing in the circuit in a clockwise direction. The equation on page 25 tells us that the p.d. across the internal resistance is Ir. So there is a fall of potential as the current flows through the internal resistance. This means that v, the p.d. between the terminals, must be less than V, the e.m.f. When a cell is connected into a circuit, the p.d. between its terminals is always less than its e.m.f. This is called the lost p.d. across the internal resistance.
The lost p.d. is always equal to Ir. If I or r or both are very small, the lost p.d. is small and the p.d. across the terminals is almost equal to the e.m.f. of the cell. If the circuit draws only a few milliamps, p.d. and e.m.f. are almost equal, but the more current flowing around the circuit, the bigger the difference and the lower the p.d. becomes. This explains why we can not use a battery of zinc-carbon cells to power the self-starter motor of a car. The reason is that zinc-carbon cells have a relatively high internal resistance.
If a zinc-carbon cell is used to supply current to a portable radio set, which takes only a few hundred milliamps, the p.d. remains almost as high as the e.m.f. But, if we try to run the starter motor from such a battery, the large internal resistance of the cells prevents the battery from supplying enough current (several amps) to turn the motor. Most of the e.m.f. of the battery is dropped as a p.d. across its internal resistance, with practically no p.d. across the motor. The battery may get hot because the electrons lose most of their potential energy while passing through the electrolyte, but the motor does not turn. The p.d. across the terminals of the cell is insufficient to power the motor. By contrast, the internal resistance of a lead-acid car battery is very low. It can deliver a large current with relatively little drop in p.d. It also explains why we can obtain an unpleasant electric shock from a 6 V car battery but not from a 6 V torch battery.