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How Resistance is important in understanding Electricity?

By on January 14, 2020

Resistance is the hindrance in the flow of electrons and is similar to friction in mechanical movements. It is the property of a substance due to which it opposes (or restricts) the flow of charge or electrons through it. In metals, there is a significant presence of free or loosely-attached electrons in their atoms which attain a drift velocity under the influence of an electric field. Drift velocity depends on the area of the metal’s cross-section and the charge’s mobility. Mobility of charge depends on the property of the material which impacts the flow of charge, and this property is defined through the term’ Resistance.’

Initial Research on Resistance by George Simon Ohm

The wide range of experiments conducted by German Scientist George Simon Ohm (1789-1854) began the understanding of the Resistance. Georg made only a modest living and started his experiments with primitive equipment. He made his metal wire of varying size and length with remarkable consistency, and the invention of the electrochemical cell by Volta helped Simon Ohm to start his research on the flow of current through the wire of various cross-sections and lengths and was able to sow from his experiments   that

  1. There is a simple relationship between resistance, current, and voltage, which is influenced by the temperature.
  2. The flow of current is directly proportional to the area of the cross-section and directly proportional to the length of the wire.

SI Unit of Resistance

The SI unit of resistance is the Ohm, named in honor of Georg Simon Ohm, and is defined that a conductor, if impressed with one volt across its terminal and the current flow is one ampere, then it possesses a resistance of one Ohm.

Laws of Resistance

Based on the experiments conducted by Georg Simon Ohm, he formulated the laws of resistance R offered by a conductor depending on the following factors:

  • It varies directly proportional to its length (say l);
  • It varies inversely as the cross-section (say A) of the conductor;
  • It depends on the nature of the material (mobility of charge); and
  • It also depends on the temperature of the conductor.

Mathematically, it is written as R ∝ l/A or R = ρ*(l /A)  where ρ is constant and called specific resistance or resistivity and depends on the property of the material. The unit of specific resistivity is Ohm-meter, a measurement for all materials to understand the material properties. It may be noted that this factor is not constant and varies with temperature and is written along with the temperature at which it is measured.

Effect of Temperature on Resistance

Temperature is the most critical factor in defining the Resistance (or Conductance) since its value depends on the temperature at which it is measured. Based on the experiments, the following behavior of resistance and temperature is summarised:

  • The resistance of pure metals increases with a rise in temperature;
  • The resistance of alloy increase is relatively small and irregular. For some high-resistance alloys like Eureka (60% Cu and 40% Ni) and manganin, the increase in resistance is negligible over a considerable range of temperatures. Because of this, alloys are used as standard resistance. Some of the alloys used as resistors are as under:

    Material

    Resistivity in ohm-metre at 20ºC (× 10−8) Temperature coefficient at 20ºC (× 10−4)
    German Silver (84% Cu; 12% Ni; 4% Zn) 20.2 2.7
    Constantan or Eureka 49 +0.1 to −0.4
    Manganin (84% Cu; 12% Mn; 4% Ni) 44 – 48 0.15
    Nichrome (60% Cu; 25% Fe; 15% Cr) 108.5 1.5
  • to the resistance of electrolytes, insulators (such as paper, rubber, glass, mica, etc.), and partial conductors such as carbon decrease with temperature rise. Hence, insulators are said to possess a negative temperature coefficient of resistance.

Temperature Coefficient of Resistance

Since the resistance is not constant and varies with temperature, it is vital to understand its behavior with temperature. Let a metallic conductor having a resistance of R0 at 0°C be heated at t°C, and its resistance changes to Rt.  Based on the experiments, it is found that the increase in resistance Δ R = Rt − R0 depends

  1. directly on its initial resistance
  2. directly on the rise in temperature
  3. on the nature of the material of the conductor.

Mathematically, it can be written as Rt − R0 ∝ R × t or Rt − R0 = α R0 t; where α (alpha) is a constant and is known as the temperature coefficient of resistance of the conductor. From this, it can be calculated that-

Rt = R0 (1 + α t)

One should remember that the above equation holds good for both the rise and fall in temperature during the normal range of temperature variation. As the temperature of a conductor is decreased, its resistance is also decreased.

Value of α at Different Temperatures

It is found that the value of ‘α’ is not constant but depends on the initial temperature on which the increment in resistance is based. When the increment is based on the resistance measured at 0°C, then α has the value of α0. At any other initial temperature, say t°C, the value of ‘α’ is ‘αt’, and so on. Because of this, the temperature coefficient is always described at a specific temperature. With simple mathematics, the temperature coefficient at different temperatures can be calculated if we know the temperature coefficient at 00C, as given below:

Note that the temperature coefficient decreases with rising temperature.

One can also calculate the resistance at any temperature when the  coefficient  resistivity is  known at 00C as under:

Variations of Resistivity with Temperature

Not only resistance but specific resistance or resistivity of metallic conductors also increases with the rise in temperature and vice-versa. The resistivities of metals vary linearly with temperature over a significant range of temperatures (the variation becomes non-linear at very high and very low temperatures). Since the relation of resistance and resistivity with temperature is linear, hence the relation is also similar and written as

Rt = R0 (1 + α t)

ρt = ρ0 (1 + α0 t)

Defining materials based on the property of resistance

Based on the material’s properties regarding the resistance, the materials are classified as Conductors and Insulators and play a very important role in electrical systems. However, another group of materials called semi-conductors is used to control the current flow.

Insulators

The material whose resistance is very high in the range of 1010  ohm-meter and more are called insulators. Since the resistance is very high,  a much bigger unit is used, i.e., Mega-ohm = 106 ohm (the prefix ‘mega’ or ‘mego’ meaning a million and, as per convention, always written in the capital letter ‘MΩ’) or kilo-ohm = 103 Ohm (kilo means thousand and written in lower format ‘kΩ’).

The “Megger” instrument for measuring the insulation resistance of electrical devices was introduced by the British firm of Evershed and Vignoles in 1905. The name comes from the fact that the insulating resistance of a properly-designed appliance is in the range of tens and hundreds of MΩ. The crank on one end powers a DC generator connected to a specially-designed meter, and the current flowing is measured to calculate the resistance. The best-known insulators are bakelite, mica, PVC, glass/ceramic, etc., with insulation values as given below:

Material Resistivity (ohm-meter at 20ºC (×10−8)
Amber 5 × 1014
Bakelite 1010
Glass 1010 – 1012
Mica 1015
Rubber 1016
Shellac 1014
Sulphur 1015

Conductors

The material with very low resistance is called Conductors, and smaller units like milli-ohm (mΩ) = 10−3 ohm or micro-ohm (μΩ) = 10−6 ohm is used. The symbol for ohm is Ω.

Studying the resistance of conductors and insulators and their behaviors in varying environmental conditions is important in Electrical Engineering. There is a continued search for developing material with the least possible resistance and insulators with high resistance and minimum effect due to temperature changes.

Conductance and Conductivity

For metals, defining the ease with which the current flows, conductance is commonly used, which is the reciprocal of Resistance. It is denoted with the symbol G.

Mathematically, it is written as G ∝ 1/R, or G ∝ A/l or G =σ (A/l);  where σ is constant and called specific Conductance.

The unit of conductance is Siemens (S). Earlier, this unit was called ‘mho’, pronounced the reverse of ‘ohm.’ The name Siemens for the unit of conductance was adopted by the 14th General Conference on Weights and Measures as an SI-derived unit in 1971. It was named after Ernst Werner von Siemens.  Ernst Werner Siemens was a German electrical engineer, inventor, and industrialist. He was also the founder of the electrical and telecommunications company Siemens, a multinational company in the field of electrical engineering.

It is clear from the above that the conductivity of a material is given as Siemens/meter or S/m. Copper and Aluminium are widely used as conductors for application in Electrical Engineering due to low resistivity with the benefit of cost, density, etc. A comparative table of the conductivity of various metals as compared to Copper is as under

Material IACS (International Annealed Copper Standard)
Ranking Metal % Conductivity*
1 Silver (Pure) 105%
2 Copper 100%
3 Gold (Pure) 70%
4 Aluminum 61%
5 Brass 28%
6 Zinc 27%
7 Nickel 22%
8 Iron (Pure) 17%
9 Tin 15%
10 Phosphor Bronze 15%
11 Steel (Stainless included) 3-15%
12 Lead (Pure) 7%
13 Nickel Aluminum Bronze 7%

* Conductivity ratings are expressed as a relative measurement with reference to copper.

Aluminum and Copper are the best-known conductors widely used for low cost and better conductivity.

Why does the resistance of the conductor increase and the insulator reduce with the rise in temperature

Every material has a conduction and valance band. There exists a forbidden energy gap between the valence and conduction band which varies for different materials and defines the coefficient of resistivity of the material. In the case of conductors, the two bands overlap, and the electrons move easily from the lower energy band to the conduction band, whereas it is very large in the case of insulators and mid-level for semi-conductors

In the case of a conductor, since the valance and conduction band overlap, there are excess electrons in the conduction band of a conductor. With an increase in temperature, more electrons will go to the conduction band from the valance band by absorbing the energy. So, the conduction band becomes crowded and more collision between the electrons and loss of drift velocity, increasing resistivity.

But in the case of an insulator, there is a large energy gap between the two bands. So, with a temperature rise, the electrons will go to the upper band, which is less crowded and moves easily, thus reducing the resistivity.

As stated earlier, the change in the coefficient of resistance due to temperature change finally results in the change of resistance of the metal.

Why Resistance at various temperatures is important in Electrical Engineering?

It is known that with a temperature rise, the resistance of the conductor rises. Now for any reason, the current flowing through the conductor increases, and the heat loss will increase in the square of the increase in current. Suppose the conductor is in an enclosed space and unable to ventilate increased heat or temperature, the temperature will keep rising, making it softer and likely to fracture and fail. Similarly, with a rise in the temperature of insulation material, the resistance will decrease and increase the leakage current and likely insulation failure.

Because of all this, in electrical designs, adequate care has to be taken towards temperature rise, ventilation, forced ventilation, etc., to check the resistance and not permit the temperature to rise beyond its design limit.

What other factors does resistance depend on?

The temperature is the most significant factor influencing the resistivity of metals However, other factors like pressure and tension also affect resistivity to some extent. For most metals except lithium and calcium, an increase in pressure leads to a decrease in resistivity. It is attributed to the changes in the electron energy structure resulting in changing overlaps between various energy bands. However, the resistivity increases with tension due to the obvious reason for an increase in length and decrease in the cross-sectional area.

The property of this change in resistance is generally employed in the measurement and instrumentation of various engineering parameters such as tension, pressure, etc.

How relevant are Resistors in today’s use

Resistors are used in electrical circuits for various functions, but studying how relevant it is to the development of electronic circuits is important.

During the 20th century, resistors were commonly used to regulate the voltage in DC or AC circuits by dropping the undesired voltage across the resistors. This was not an efficient way of controlling the voltage since some useful energy was wasted across the Resistors.  The use of such Resistors was commonly seen in fan regulators, slip ring induction motors, DC series/compound motors, rheostatic braking, etc. But with the introduction of voltage control using semiconductors, it became possible to control the voltage without wasting useful energy. The development of power devices such as Variable voltage variable frequency commonly called VVVF) control of AC induction motors, Switch mode supply for charging mobile, and fan regulators are a few to mention here. The importance of resistors is now limited to a few applications, such as domestic appliances like geysers, heaters, iron, etc. Because of this, the Resistors have lost their sheen in today’s technological world and the application of DC motors. The study of resistance is now limited to developing low-resistance material for conductors and high-resistance material for insulators.

Material with a non-linear resistance behavior

Nonlinear Resistors are those elements whose V − I curves are not straight lines and are called nonlinear elements because their resistances are nonlinear.  Examples of nonlinear elements are filaments of incandescent lamps, where the current is very high due to low resistance as soon the switch is ON but reduces when the resistance rises due to the glowing of the filament and high temperature,  diodes, thermistors and varistors.

A varistor is a special resistor made of carborundum crystals held together by a binder. Varistor has a wide range of applications in electrical circuit protection. Voltage impulse commonly appears on overhead lines due to lightning and switching surges. The same also appeared in low voltage circuits and is likely to damage the circuits if not protected effectively.

It is a voltage-dependent metal-oxide material that has come to the rescue. Its resistance decreases sharply with increasing voltage. The relationship between the current flowing through a varistor and the voltage applied across it is given as under:

i = ken

where i = instantaneous current, e is the instantaneous voltage, and η is a constant whose value depends on the metal oxides used. The value of η for silicon-carbide-based varistors lies between 2 and 6, whereas zinc-oxide-based varistors range from 25 to 50.

The zinc-oxide-based varistors are primarily used for protecting solid-state power supplies from low and medium surge voltage in the supply line. Silicon-carbide varistors protect against high-voltage surges caused by lightning and the discharge of electromagnetic energy stored in the magnetic fields of large coils. A surge arrester provides high resistance in normal application. It should have a low impulse ratio so that when surge incidents are on the surge arrester, it gets bypassed to the ground instead of passing through the apparatus.

Conclusion

From the above, it is clear that the value of resistance is an important value to be measured for all materials and solutions for various applications in the field of engineering. Hence, studying resistance is important for electrical engineers and anyone in any engineering field.

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