APPENDIX A RESISTORS A1. What is a resistor? Resistors are probably the most common electrical element in electronic circuits. The passive elements in most circuits consist of resistors and possibly also capacitors and inductors. As the name implies, resistors provide resistance to the flow of electrical current through a circuit. All materials (solids, liquids, and gases) have a varying level of resistivity to the flow of electrical current. At one end of the spectrum, one has superconductors which have essentially zero resistivity (or, equivalently, infinite conductivity); at the other end of the spectrum, one has perfect insulators which have infinite resistivity (or zero conductivity). Metals are good conductors of electricity while plastics and rubbers as well as dried wood are poor conductors of electricity. Water is also a conductor of electricity which means that wet wood is a much better conductor than a dry wood. Carbon is an electrical conductor and is, in fact, commonly used in the manufacture of low-cost standard resistors, as we shall see below. The resistance of a sample of material depends not only on the electrical conductivity of the materal but also on the geometry. For a wire or rod of uniform cross-section, the resistance between the ends of the wire or rod is directly proportional to the length of the wire or rod and inversely proportional to the cross-sectional area of the wire or rod. Thus, for example, for a given cross-sectional area, the resistance of a wire doubles with a doubling of its length; and, similarly, for a given length, the resistance of the wire doubles with a halving of its cross-sectional area. The dependence of resistance R (Ohms or Ω) on length L (m) and cross-sectional area A ( m2) may be written as R = (ρL)/A (1) where the coefficient of proportionality ρ is the so-called resistivity of the material. and has the units of Ω-m (or ohm-m). Thus, one may define resistivity ρ as the resistance of a wire or rod of length L=1m and cross-sectional area A=1m2. The SI unit for ρ is Ω-m. Typical values of ρ are given in Table AA1. 1Material ρ, Ω-m Copper 1.68 x 10-8 Gold 2.44 x 10-8 Iron 1.05 x 10-7 Nichrome 80/20A (composition Cr 19.5%, Si 1.25%, Fe 0.5%, Mn .4%, balance Ni) 1.08 x 10-6 Sea water Fresh water Distilled water 0.2 1000 5 x 105 Sand 1 - 1000 Mica 1011 – 1015 Glass 1010 - 1014 Air ∞ Table AA1. Values of resistivity of different materials at 20°C Notice that Nichrome which is widely used as a heating element has a resistivity about ten times that of iron. Also notice that sea water is much more conductive than fresh water which in turn is much more conductive than distilled water. How do you explain such a big variation in the values of resistivity for different types of water? A2. Fixed and variable resistors Resistors may be classified into two types: Fixed resistors and variable resistors. In fixed resistors, the value of the resistance does not change. Variable resistors are those whose resistance value may be changed through change in the position of a mechanical slider or knob (potentiometer, rheostat or simply pot is an example of such a mechanically adjustable resistor), or by shining light on the resistor (photo-resistor), or by changing temperature (examples of temperature-variable resistors are thermistors and varistors). The standard symbols for the various types of resistors are shown in Fig. AA1. 2Fig. AA1. Symbols of different types or resistor: (a) Fixed resistor, (b) Variable resistor, (c) Potentiometer, and (d) photo-resistor The physical construction of a potentiometer used as a voltage divider or as a rheostat is illustrated in Fig. AA2. Here a wire is wound around a cylindrical core of an insulating plastic material (hence the name wire-wound resistor) and the wire is electrically exposed or bared of its insulation along the length of the resistor over a small section of the circumference of the plastic core. Over this exposed region, a mechanically movable or sliding electrical contact provides a tap point and thus a means of varying resistance. The construction of the potentiometer need not always be of cylindrical geometry. Indeed, it is more commonly toroidal in geometry but the principle of sliding contact is the same. Fig. AA2. Schematic of a wire-wound potentiometer used as (a) a voltage divider, and (b) a rheostat. Resistors in Integrated-circuit (IC) packaging styles called Single-in-Line (SIL) and Dual-in-Line (DIL) are commonly used for certain applications wherein a number of discrete resistors are housed within a single package. A 9-pin 8-resistor SIL packaging in illustrated in Fig. AA4a, with the 3network of 8 resistors shown in Fig. AA4b. Eight of the nine leads represent one end of each resistor, with the ninth lead representing a common connection point of the eight resistors.. One application of such a SIL package would be in driving 8 LEDs, with each resistor connected in series with an LED. A single voltage source applied to the junction point of the resistors is used to drive the diode array, with the other end of each diode connected to ground (Fig. AA4c). Fig. AA4. (a) Schematic of a SIL package of 8 resistors with a common connection point; (b) internal resistors in the SIL package in (a); and (c) SIL package in (a) driving 8 LEDs. Another connection topology of resistors is shown in Fig. AA5 where the housing contains four independent or single resistors. A label “4S” is often imprinted on such a package of four unconnected single resistors. Fig.AA5. Internal resistors of a SIL package consisting of 4 independent resistors. In a DIL package, the leads coming out of the package are connected to terminals on both sides of a channel lying between the two rows of terminal pins. Thus, in a 16-pin DIL resistor, 8 leads come out of each side of the channel (Fig. AA6) 4Fig. AA6. External schematic of a 16-pin DIL resistor B.3. Why the interest in resistors? Resistors play a key role in electronic circuits and other applications. Without them the world of electronics, computers, and home and industrial appliances would come to a halt! Of course, resistors by themselves are of limited use; they are usually combined with capacitors and possibly also inductors in order to achieve the intended functionality of a circuit. Some of the applications of resistors are briefly mentioned below: B.3.1. In electronic circuits,