In this article we will discuss about:- 1. OHM’S Law 2. Mean Free Path (L) 3. Relaxation Time 4. Factors Affecting Resistivity of Metals 5. Low Resistivity Conducting Material 6. High Resistivity Conducting Material 7. Insulating Materials 8. Application of Conductors 9. Types of Conducting Materials.
OHM’S Law (Point Form):
When an electric field is applied to a conductor, the current density developed (J) in the conductor is related to electric field applied (E) as-
J = σE
This relation is a well-known ohm’s law.
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The current density is a general property of the material and does not depend upon the size of the conductor. It is proportional to the electric field E and a constant ne2τ/m, called the conductivity of the material σ-
σ = ne2τ/m
Mobility:
The average drift velocity varies in direct proportion to the electric field, through a proportionality factor eτ/m, called the mobility of the electrons, µe.
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µe = eτ/m
Mobility is defined as the magnitude of the average drift velocity per unit electric field, i.e. µe = vd/E Mobility and conductivity have the relation, σ = neµe.
Unit of µe = m2 volte-1s-1 or m2/Volt – sec.
Effect of Temperature on Conductivity:
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1. Conductor:
We know that,
With increase in temperature there is no appreciable increase in number of electrons as conductor have already large number of electrons in their conduction band. So overall conductivity decreases with increase in temperature.
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2. Semiconductor:
We know that,
Where,
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ni = Intrinsic concentration
Eg0 = Energy gap with 0°K
A0 = is constant that depends on the semiconducting material (9.64 × 1015).
K = is Boltzmann’s constant
Therefore, conductivity of semiconductor increases with the rise in temperature. In other words semiconductors have negative temperature coefficients.
Mean Free Path (L):
It is defined as the average distance travelled by electron before collision takes place.
λ = Vd. τ
Where, τ = average collision time, Vd = drift velocity.
Relaxation Time:
It is defined as the time required at which the drift velocity of electron reduces to 37% of its value after the removal of electric field. For isotropic material the relaxation time and the average collision time are equal.
Factors Affecting Resistivity of Metals:
In pure metals and dilute alloys, the total resistivity is the sum of two terms.
ρ = ρT + ρr …. (i)
The thermal component ρT; which arises from the lattice vibrations, and the residual resistivity ρr, caused by impurities and structural imperfections. The residual resistivity is independent of temperature.
Equation (i) is Matthiessen’s rule. This rule becomes less accurate at high temperature or at high impurity levels.
The electrical resistance of most metals increases with increase of temperature. At temperatures above the so called Debye temperature, the thermal component of resistivity of conductors is approximately linear.
Many conducting materials have vanishing resistivity near absolute zero temperature. This phenomenon is known as superconductivity.
Note:
Debye temperature for Cu is 315 K, while for Al it is 398 K.
Low Resistivity Conducting Material:
Silver has low resistivity than Cu, but it is very costly, which restrict its use for commercial purpose. Aluminium is cheaper than Cu, so it is often used as a Cu substitute in electrical power system. Brass is an alloy of Zinc and Copper. It has high tensile strength but lower conductivity than Copper. Brass is used in rheostats, lamp holders and plug points. It has good corrosion resistance. Bronze is an alloy of Cu, Tin, Al, Ni and Si. It has superior mechanical property and corrosion resistance than brass.
Phosphor-Bronze is used in current carrying springs and brush holders. Silicon Bronze is used in wires and telephone parts. Alloy of Tin, Lead, Cu-Zn are used in solder material. Tungsten is a metal which is used upto 3300°C as heating filament in bulbs, CRTs.
High Resistivity Conducting Material:
Pure carbon is a semi-conductor with negative temperature coefficient of resistivity. It is used in brushes for electrical machine.
Lead has high anti-corrosion properties, because of this it is used for covering of underground and under water cables for power and communication lines.
Platinum is used for contact fabrication in low power rating contactors.
Nickel is used for making electrodes.
Insulating Materials:
1. Ceramics:
These materials are hard, strong and brittle.
They have high temperature stability.
Ceramics are generally in-organic material (absence of carbon).
These are generally crystalline in nature (except amorphous glass).
These are non-metallic oxide, nitrites and carbides.
Examples:
Garnets, BaTiO3, Ferrites, TiO2 (Rutile) (Ti dioxide), Porcelains, Quartz, ZnS, MgO, SiC, CdS etc.
Ceramics can be broadly described as:
(i) Porcelains (εr<12)
(ii) Alumina ceramics (εr<12)
(iii) Steatite (εr <12)
(iv) Titanate (εr > 12)
Porcelain is used in insulation of transmission and distribution of power system. It is used in low and high voltage application.
Steatites are used in high frequency applications.
Alumina ceramics are used for high temperature applications as circuit breakers and resistance cores.
Titanate is used in capacitor dielectrics.
Another Classification of Ceramics:
Ceramics can also be divided into two groups depending whether the permittivity is lesser or greater than 12.
i. er < 12:
Ceramics having permittivity less than 12 are used as insulators, as they have high dielectric strength and low loss tangent.
Example:
Porcelain, Steatite, Alumina Ceramic.
ii. εr > 12:
Ceramics with high permittivity (εr>12) are used in capacitor applications.
Example:
Titanates, Rutile.
2. Transformer Oil:
Transformer cores are dipped in mineral oil known as transformer oil. It acts as an insulator and cooling medium.
Break down voltage of transformer oil decreases with contamination, example: moisture. To absorb moisture, absorbents added are Silica gel and Alumina.
3. Askarels:
They are fire resistance insulating material.
Two types of Askarels:
(a) Chlorinated benzene
(b) Chlorinated biphenyl
Nowadays they are not used in transformer and capacitor because on decomposition they produce toxic and poisonous gases.
Application of Conductors:
i. Electricity transmission and distribution lines,
ii. Electrical contacts viz. relays, brushes, switches etc.,
iii. Resistors and
iv. Heating elements
Gold is the best conductor electricity followed by silver, copper and aluminium. Keeping in view the cost factor, copper and aluminium are the natural choices although silver is used for contacts in aircrafts.
Aluminium conductor reinforced with steel (ACSR) is an improved material for transmission lines.
Oxygen-free-high conductivity (OFHC) copper conductor is very suitable for low temperature applications. It has high purity whose resistivity is 1 × 10-10 ohm m at 4.2K and zero electric field.
Types of Conducting Materials:
I. On the Basis of Quality of Resistivity:
1. Low resistivity (or high conductivity) materials such as Au, Aq, Cu, Al, brass, bronze etc.
2. High resistivity (or low conductivity) materials such as W. Pt, C, Ni, Ta, nichrome, etc.
II. On the Basis of Nature of Materials:
1. Metals such as Cu, steel, Al, Pt, Ir, Pd, Rh etc.
2. Non-metals such as conducting polymer
3. Alloys such as brass, bronze, rose metal, constantan etc.
4. Reinforced composites such as ACSR.
III. On the Basis Applications:
1. Cable purpose materials such as Cu, Al, ACSR, OFHC
2. Filament purpose materials such as W, carbon (graphite)
3. Contact purpose materials such as Au, Pt, Ag, Mo, Ir, W etc.
4. Soldering purpose materials such as Cu, Zn, Sn, Ag, Cd
5. Fusible (or fuse) purpose materials such as Pb, Sn, Ag etc.
6. Sheathing purpose materials such as Pb, p.v.c., Pb-Cd alloy
7. Sealing purpose materials such as Fe with Si, Mn, Mo.
IV. On the Basis Temperature Requirements:
1. High temperature conducting materials such as ACSR
2. Low temperature conducting materials such as OFHC copper
3. Very low (or cryogenic) temperature conducting materials such as Ni-based steel alloy.
V. On the Basis of State of Material:
1. Solid conducting materials such as metals, alloys
2. Liquid conducting materials such as Hg
3. Gaseous conducting materials such as N2 in gas-filled pressure cables.
Copper:
It is High Conductivity and reasonable cost.
It is a crystalline, non-ferrous, non-magnetic (diamagnetic), reddish coloured metal.
It is a ductile metal having a ductility of more than 15%. Because of this property, it can be easily drawn into thin bars and wires. Hence, it is very useful for making cables, strands, and conductors.
Its ultimate tensile strength is high enough (300-350 MPa) which makes it substantially strong to sustain mechanical loads.
Its melting point is sufficiently high (1083°C) so it is use at high temperatures also.
When exposed to atmospheric environment, it forms a protective layer of copper oxide (CuO). Thus, it is highly resistant to corrosion which is require property for bare/open overhead conductors.
It can be easily brazed (a kind of welding) which is a necessary requirement in wiring and other connections.
Aluminium:
Conductivity is lower to that of copper, but it is cheaper than copper.
It is a crystalline, non-ferrous, weak magnetic (paramagnetic) metal of white colour.
It is a lightweight metal having a specific gravity of 2.7 only.
It is a ductile metal because of which it can be easily drawn into thin bars and wires. Therefore, aluminium is very useful for making cables and conductors.
Its ultimate tensile strength is sufficiently high (about 50-70 MPa).
It can be easily soldered which is an essential requirement in wiring. However, due to insulating nature of aluminium oxide layer, the soldered joint may not be so strong
Its electrical contacts face the possibility of loss connections due to its softness.