Theory of Resistance, Resistivity and Resistors

Introduction:

Figure shown below shows the overlap of valence and conduction bands of conductors. In pure metals, like Iron, Copper, Silver or Gold and in metal alloys like Brass or Steel, there is a big degree of overlap in the bands and an abundant supply of free energy levels for charge to move between with easiness. Consequently, such materials conduct electric current readily and a small electric field positioned all along them will outcome in a very high degree of conduction and high values of current. Therefore, interconnecting cables and wires are made up of such metals where they are intended to propose the least possible impediment to the flow of current. They are only employed to provide a path for the current to flow in an electric circuit and to join points altogether electrically where the emf or potential is intended to be similar. Though, practical electric circuits should comprise of conducting elements other than inter-connecting wires or there would be little point to their presence. The real motivation of electric circuit is to transfer energy from its electric form to some other form like mechanical or thermal energy in order to do work. In an electric kettle for illustration the electrical energy drawn from the mains supply is transformed into thermal energy to heat water, whereas in an electric motor it is transformed into mechanical energy to drive a physical load like the drum of a washing machine.

Figure: Energy Bands in Solid Materials

Resistivity:

In electric circuits and in particular electronic circuits, it is usually needed to control the voltages and currents present at different points in the circuit to defined values for given purposes, similar to the biasing of semiconductor devices in a hi-fi amplifier, for illustration. In this situation it is not just a matter of employing wires to make circuits for current to flow in but instead one of limiting the currents and defining the potentials at particular values at particular place in a circuit. In this case materials are employed to make elements that give specific degrees of impediment or resistance to the flow of current via them. Conductors that are not pure metals have a much lower number of free energy levels in their conduction bands and therefore do not conduct current as simply as pure metals. In such materials a much bigger emf or potential drop is needed across them to allow the flow of current and the magnitudes of resultant currents are much lower than in pure metals. Materials such as Cobalt, Carbon and Ferrite compounds and also some metal oxides are popular for this aim.

Conducting materials possess the property of resistivity. The Resistivity is a measure of how strongly a material opposes the flow of electric current via it whenever subjected to the influence of an emf or electric field. A low value of resistivity signifies the material readily permits the movement of charge via it whereas a high value of resistivity signifies a high degree of opposition to the movement of charge. The resistivity, also termed as specific resistance, of a material depends on its specific atomic structure and is given the symbol ρ and has the units of Ohm-metres.

Resistance:

The resistance of a piece of conducting material is basically the combined result of its resistivity established for the piece of material as an entire. This depends on the resistivity of material as a compound or an element and physical dimensions of the piece of material in question and also the way in which, the emf is applied to it.

Figure: A Piece of Resistive material which electrical contacts on both ends

Figure above shows a piece of resistive material containing resistivity ρ, uniform cross-sectional area A and length l. Electrical contacts are made up uniformly over the cross-sectional region at both ends. This permits the uniform flow of charge via the material whenever an electric field is applied all along its length. The total resistance R, of this piece of material as an entire is given as:

R = ρ (l/A) ohms (Ω)

The unit of Resistance is Ohms and employs the Greek letter Omega, Ω, as the symbol of this unit that is named after the German physicist Georg Ohm (1789 - 1854) who first officially explained the property.

Resistors:

The resistors are electrical circuit elements specially manufactured to exploit their properties of resistivity. Resistors usually employed as components in electronic circuits are manufactured employing amorphous Carbon as the material. This is a form of Graphite containing no consistent crystalline structure and offering a resistivity ranging from 1.5 – 4.5 x 10-5 Ωm, with a value of 3.5 x 10-5 Ωm being admired. Resistors are generally cylindrical in shape with electrical connections at both the circular ends to wires that can be soldered into a circuit. This well-known form of resistor is shown in figure below where the common colour bands printed on the component are employed as a numbering system to point out the value of its resistance.

The resistor exhibited can be fabricated in the form of rod or cylinder of conductive carbon granules bound in the resin compound. The more modern technique is to deposit a thin film of carbon into a cylindrical base made up of an insulating material like ceramic or glass. In some situations the deposited layer of Carbon is cut into a spiral shape to permit higher values of resistance to be received. Metal oxides like tin-oxide are sometimes employed as an alternative to Carbon whenever other properties of the resistor like low temperature coefficient are significant.

Resistors are manufactured in series or ranges which have various degrees of refinement of the materials and control of process. This generates resistors having various ranges of accuracy or manufacturing tolerance. The most general ranges of manufacturing tolerance nowadays are ±5%, ±2%, ±1%, whereas the most general series of values are the E12 and E24.

The colour-code printed to the body of the resistor is employed internationally to state the value of a resistor. By using the colour code, the value of resistance that might range over numerous decades can be determined for any individual resistor. The colour code is exhibited printed on the body of a typical resistor in figure shown below. This code comprises of usually of four coloured bands. The three left hand bands point out the value of resistance whereas the fourth band on the right hand side points out the manufacturing tolerance.

Figure: The Resistor Colour Code

Each of the left hand group of three bands symbolizes one decimal digit in the value of resistance. The first and second digits are the numerical important digits whereas the third is the multiplier digit that gives the numerical value of the power of ten that the two significant digits in the value are multiplied by. The decimal numbers related with each colour in the resistor value are provided in Table (a) whereas the value of the tolerance equivalent to the colour of the fourth band is provided in Table (b).

Number   Colour                             Tolerance     Colour

0               Black                            ±1%        Brown

1              Brown                           ±2%        Red

2              Red                              ±5%        Gold

3              Orange                         ±10%       Silver

4              Yellow

5              Green

6              Blue

7              Violet

8              Grey

9              White

From the above value of the resistor in figure is obtained as:

Digit 1    Yellow = 4    Digit 2    Violet = 7    Digit 3 Multiplier   Red = 2
Value is   47 x 102 = 47 x 100 = 4700 Ω = 4.7 kΩ.

Digit 4    Gold      Tolerance = ±5%

The E12 sequence of resistors is so called since it has 12 values of resistance per decade. This signifies that Digits 1 and 2 in the code contain 12 values. The E24 sequence has 24 values per decade. The values in each of such series are given in table shown below.

Table: E12 and E24 Series of Resistors

 E12 series     tol. ±5%, ±10% E24 series    tol. ±5% 10 10 11 12 12 13 15 15 16 18 18 20 22 22 24 27 27 30 33 33 36 39 39 43 47 47 51 56 56 62 68 68 75 82 82 91

Fixed resistors, containing specific values in specific ranges, come in a number of various forms. The form shown in figure above is the most well-known in low-and medium power electronic circuits like those implemented on printed circuit boards. Though, for higher power ratings bigger packages are employed as shown in figure below and the resistors are frequently constructed of resistance wire wound on an insulated former.

In modern low-power electronic circuits, where long-term battery operation and miniaturisation of the size is of significance other forms of packages are accessible like pin-arrays and surface mounted resistors.

There is as well a broad variety of variable resistors whose value can be modified to suit particular circumstances or to attain a particular purpose in electric and electronic circuits. Small low-power trimmers are employed to make in-circuit adjustments to cancel out unnecessary errors like offset voltages in semiconductor devices.

Bigger manually variable resistors, termed as potentiometers, are employed as volume controls, for illustration in radios of hi-fi systems.

The conventional symbols employed for variable and fixed resistors in schematic diagrams of electric circuits are shown in figure below:

Figure: Schematic Symbols for Resistor

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