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How Resistance is important in understanding Electricity?

By on January 14, 2020

Resistance is the hindrance in the flow of electron 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 cross-section of the metal and the mobility of charge. Mobility of charge depends on the property of material which impacts the flow of charge, and this property is defined through the term called ‘Resistance’.

Initial Research on Resistance by Ohm

The wide range of experiments conducted by German Scientist George Simon Ohm (1789-1854) made the beginning of the understanding of the Resistance.  Georg made only a modest living and began his experiments with primitive equipment, He made his metal wire of varying size and length with remarkable consistency and the invention of electrochemical cell by Volta helped Simon Ohm to start his research on the flow of current through wire of various cross-section and length 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 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 the honour 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 than it possesses a resistance of one ohm.

For insulators whose resistances are 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 current flowing is measured to calculate to resistance. The best-known insulators are bakelite, mica, PVC, glass/ceramic, etc. with insulation values as given below

Material Resistivity in ohm-metre at 20ºC

(× 10−8)

Amber 5 × 1014
Bakelite 1010
Glass 1010 – 1012
Mica 1015
Rubber 1016
Shellac 1014
Sulphur 1015

 

For conductors whose resistance is very low and smaller units like milli-ohm (mΩ) = 10−3 ohm or micro-ohm (μΩ) = 10−6 ohm are used. The symbol for ohm is Ω.

Study of resistance of conductors and insulators is important in Electrical Engineering for the desired purpose.

Laws of Resistance

Based on the experiments conducted by Georg Simon Ohm, he formulated the laws of resistance R offered by a conductor depends 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 and is relevant indices to understand the material properties. It may be noted that this factor is not constant and varies with temperature.

Conductance and Conductivity

For metals and defining the ease with which the current flows, Conudctuance is considered important indices which is 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’, and pronounced 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 multi-national company in the field of electrical engineering.

It is clear from the above that the conductivity of a material is given as Siemens/metre or S/m. Copper and Aluminium are widely used 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 Aluminium 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. Aluminium and Copper best-known conductor widely used.

Effect of Temperature on Resistance

Temperature is the most important factor to define the Resistance (or Conductance) since its value depends on the temperature at which it is measured. Based on the experiments, following behaviour of resistance with temperature is summarised:

  • the resistance of pure metals increases with a rise in temperature;
  • the resistance of alloys, the 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 temperature. 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 rise in temperature. Hence, insulators are said to possess a negative temperature-coefficient of resistance.

Why resistance of conductor increases and of insulator reduces with the rise in temperature

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

In case of a conductor, since the valance band and conduction band overlap with each other, so 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 valance band by absorbing the energy. So, the conduction band becomes crowded and more collision between the electrons and loss of drift velocity, resulting in an increase in resistivity.

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

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

Temperature Coefficient of Resistance

Since the resistance is not constant and varies with temperature hence it is important to understand its behaviour with temperature. Let a metallic conductor having a resistance of R0 at 0°C be heated of 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)

It should be remembered that the above equation holds good for both the rise as well as 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. In view of this, the temperature coefficient is always described at a specific temperature. With simple mathematics, the temperature of coefficient at different temperature can be calculated, if we know the temperature coefficient at 00C, as given below

It may be seen that the temperature coefficient decreases with rising temperature.

One can also calculate the resistance at another temperature if the resistance is known at different temperature with coefficient resistivity known at 00C as under

Variations of Resistivity with Temperature

Not only resistance but specific resistance or resistivity of metallic conductors also increases with rise in temperature and vice-versa. The resistivities of metals vary linearly with temperature over a significant range of temperature (the variation becoming non-linear both at very high and at 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)

Why Resistance at various temperature is important in Electrical Engineering?

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

In view of all this, in electrical designs, adequate care has to be taken towards temperature rise, ventilation, forced ventilation, etc.

Does resistance depends on other factors

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

How relevant are Resistors in today’s use

During the 20th century, resistors were commonly used to regulate the voltage in DC or AC circuit but dropping the undesired voltage across the resistors. This was an efficient means of controlling the voltage since part of the useful energy is wasted across the Resistors.  Use of such Resistors was commonly seen in fan regulators, slip ring induction motor, DC series/compound motor, rheostatic braking, etc. But with the introduction of voltage control using semi-conductors, it became possible to control the voltage without wasting loss of power. The importance of resistors is now limited to a few applications such as domestic appliance like geyser, heater, iron etc. In view of this, the Resistors have lost its sheen in today’s technological world. 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 behaviour

Nonlinear Resistors are those elements whose V − I curves are not straight lines are called nonlinear elements because their resistances are nonlinear resistances.  Examples of nonlinear elements are filaments of incandescent lamps (where resistance increases sharply and reducing the flow of current), diodes, thermistors and varistors.

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

It is a voltage-dependent metal-oxide material that has come to 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 have a value ranging 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 provide protection against high-voltage surges caused by lightning and by the discharge of electromagnetic energy stored in the magnetic fields of large coils. A surge arrester provides high resistance in the normal application and should have a low impulse ratio, so that when surge incidents on the surge arrester, it got bypassed to the ground instead of passing through the apparatus.

 

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