RTU Paper Solution - Global Institute of Technology, Jaipur · RTU Paper Solution Branch- ELECTRICAL ENGINEERING Subject Name- ELECTRICAL ... Jaipur 302022 (Rajasthan) Solution V

GLOBAL INSTITUTE OF TECHNOLOGY JAIPUR

RTU Paper Solution

Branch- ELECTRICAL ENGINEERING

Subject Name- ELECTRICAL MATERIALS

Paper Code- 5EE3-01

Date of Exam-14/11/2019

Global Institute of Technology, Jaipur ITS-1, IT Park, EPIP, Sitapura Jaipur 302022 (Rajasthan)

Solution V Sem University Examination 2019

Subject- ELECTRICAL MATERIAL SCode-5EE3-01 Semester- V /Year- III







PART-A Ans: 1

The atoms in these materials have permanent magnetic moments, and a phenomenon called

exchange coupling takes place in which the magnetic moments of nearby atoms line up with one

another. This forms domains, small neighborhoods where the magnetic moments are aligned.

Examples of ferromagnetic materials include iron, cobalt, nickel, and an alloy called Alnico.

Fig: 1 “Magnetic domain in ferromagnetic materials

Ans: 2

Diffusion Current is a current in a semiconductor caused by the diffusion of charge carriers

(holes and/or electrons). This is the current which is due to the transport of charges occurring

because of non-uniform concentration of charged particles in a semiconductor. Diffusion current

can be in the same or opposite direction of a drift current.

Ans: 3

When a dielectric is placed in an electric field, electric charges do not flow through the material

as they do in an electrical conductor but only slightly shift from their average equilibrium

positions causing dielectric polarization. Because of dielectric polarization, positive charges are

displaced in the direction of the field and negative charges shift in the direction opposite to the

field.




Ans 4:

Crystalline state of a crystal may be defined as “A condition of matter resulting from an orderly,

cohesive, three dimensional arrangement of its component particles (atoms, ions or molecules) in

space”. Crystalline defects are classified in three types:

(i) Point Defect

(ii) Line Defect

(iii) Surface defect

Ans 5:

Charge carrier density, also known as carrier concentration, denotes the number of charge

carriers in per volume. In solid-state physics, a band gap, also called an energy gap or bandgap, is

an energy range in a solid where no electron states can exist. Semiconductors having band gap

less than 4 eV.

PART-B

Ans 1:






















Ans 2:

Piezoelectricity: Examples and application







Ans 3:

The superconducting state cannot exist in the presence of a magnetic field greater than a critical

value, even at absolute zero. This critical magnetic field is strongly correlated with the critical

temperature for the superconductor, which is in turn correlated with the bandgap. Type II

superconductors show two critical magnetic field values, one at the onset of a mixed

superconducting and normal state and one where superconductivity ceases.

It is the nature of superconductors to exclude magnetic fields (Meissner effect) so long as the

applied field does not exceed their critical magnetic field. This critical magnetic field is tabulated

for 0K and decreases from that magnitude with increasing temperature, reaching zero at the

critical temperature for superconductivity. The critical magnetic field at any temperature below

the critical temperature is given by the relationship

[ (

)

]

Ans 4:

Semiconductors types / classifications

There are two basic groups or classifications that can be used to define the different

semiconductor types:

Intrinsic material: An intrinsic type of semiconductor material made to be very pure chemically.

As a result it possesses a very low conductivity level having very few number of charge carriers,

namely holes and electrons, which it possesses in equal quantities.

Extrinsic material: Extrinsic types of semiconductor are those where a small amount of impurity

has been added to the basic intrinsic material. This 'doping' uses an element from a different

periodic table group and in this way it will either have more or less electrons in the valence band




than the semiconductor itself. This creates either an excess or shortage of electrons. In this way

two types of semiconductor are available: Electrons are negatively charged carriers.

N-type: An N-type semiconductor material has an excess of electrons. In this way, free electrons

are available within the lattices and their overall movement in one direction under the influence

of a potential difference results in an electric current flow. This in an N-type semiconductor, the

charge carriers are electrons.

P-type: In a P-type semiconductor material there is a shortage of electrons, i.e. there are 'holes' in

the crystal lattice. Electrons may move from one empty position to another and in this case it can

be considered that the holes are moving. This can happen under the influence of a potential

difference and the holes can be seen to flow in one direction resulting in an electric current flow.

It is actually harder for holes to move than for free electrons to move and therefore the mobility

of holes is less than that of free electrons. Holes are positively charged carriers.

Material

Chemical

Symb

Group Detail

Germanium Ge IV This type of semiconductor material was used in many early devices from radar

detection diodes to the first transistors.

Silicon S IV Silicon is the most widely used type of semiconductor material. Its major

advantage is that it is easy to fabricate and provides good general electrical and

mechanical properties.

Gallium

arsenide

GaAs III-V Gallium arsenide is the second most widely used type of semiconductor after

silicon. It is widely used in high performance RF devices where its high

electron mobility is utilised. It is also used as substrate for other III-V

semiconductors, e.g. InGaAs and GaInNAs.

Silicon

carbide

SiC IV Silicon carbide finds uses in a number of applications. It is often used in power

devices where its losses are significantly lower and operating temperatures can

be higher than those of silicon based devices.

Gallium

Nitride

GaN III-V This type of semiconductor material is starting to be more widely in microwave

transistors where high temperatures and powers are needed. It is also being used

in some microwave ICs.

Gallium

phosphide

GaP III-V This semiconductor material has found many uses within LED technology. It

was used in many early low to medium brightness LEDs producing a variety of

colours dependent upon the addition of other dopants.

Cadmium

sulphide

CdS II-VI Used in photoresistors and also solar cells.

Lead

sulphide

PbS IV-VI Used as the mineral galena, this semiconductor material was used in the very

early radio detectors known as 'Cat's Whiskers' where a point contact was made

with the tin wire onto the galena to provide rectification of the signals.

Fermi level position in pure semiconductors

At this point, we should comment further on the position of the Fermi level relative to the energy

bands of the semiconductor. We mentioned earlier that the Fermi level lies within the forbidden




gap, which basically results from the need to maintain equal concentrations of electrons and

holes. The following expression is used for the position of the Fermi level in an intrinsic

semiconductor:

[

]

For a typical germanium semiconductor, the first term on the right-hand side of above Eqn. is of

the order of 1 eV, while the second is of the order of a few tens of millielectron volts at 300 K.

Consequently, we see from this equation that the Fermi level should typically lie very close to the

middle of the energy gap in germanium semiconductor.

Ans 5:

The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical

conductor, transverse to an electric current in the conductor and to an applied magnetic field

perpendicular to the current. It was discovered by Edwin Hall in 1879.

The Hall coefficient is defined as the ratio of the induced electric field to the product of the

current density and the applied magnetic field. It is a characteristic of the material from which the

conductor is made, since its value depends on the type, number, and properties of the charge

carriers that constitute the current.

The Hall effect is due to the nature of the current in a conductor. Current consists of the

movement of many small charge carriers, typically electrons, holes, ions or all three. When a

magnetic field is present, these charges experience a force, called the Lorentz force. When such a

magnetic field is absent, the charges follow approximately straight, 'line of sight' paths between

collisions with impurities, phonons, etc. However, when a magnetic field with a perpendicular

component is applied, their paths between collisions are curved, thus moving charges accumulate

on one face of the material. This leaves equal and opposite charges exposed on the other face,

where there is a scarcity of mobile charges. The result is an asymmetric distribution of charge

density across the Hall element, arising from a force that is perpendicular to both the 'line of

sight' path and the applied magnetic field. The separation of charge establishes an electric field

that opposes the migration of further charge, so a steady electric potential is established for as

long as the charge is flowing.




Figure 1.14 Hall Effect

For a simple metal where there is only one type of charge carrier (electrons), the Hall voltage VH

can be derived by using the Lorentz force and seeing that, in the steady-state condition, charges

are not moving in the y-axis direction. Thus, the magnetic force on each electron in the y-axis

direction is cancelled by a y-axis electrical force due to the buildup of charges. The vx term is the

drift velocity of the current which is assumed at this point to be holes by convention. The

vxBzterm is negative in the y-axis direction by the right hand rule.

In steady state, F = 0, so 0 = Ey− vxBz, where Ey is assigned in the direction of the y-axis.

In wires, electrons instead of holes are flowing, so vx → −vx and q → −q. Also Ey= −VH/w.

Substituting these changes gives

The Hall coefficient is defined as

where j is the current density of the carrier electrons, and Eyis the induced electric field. In SI

units, this becomes

The units of RH are usually expressed as m3/C. As a result, the Hall effect is very useful as a

means to measure either the carrier density or the magnetic field.

One very important feature of the Hall effect is that it differentiates between positive charges

moving in one direction and negative charges moving in the opposite. The Hall effect offered the

first real proof that electric currents in metals are carried by moving electrons, not by protons.

The Hall effect also showed that in some substances (especially p-type semiconductors), it is

more appropriate to think of the current as positive "holes" moving rather than negative electrons.




Ans 6.




PART-C

Ans 1:

The magnetic field within an unmagnetized piece of steel is zero. As the magnetizing force (H)

is increased from zero,the flux density (B) within the part will also increase from zero. The

curve from points A to E in Figure illustrates this behavior. In the region of point E, the flux

density increases up to a point and then tends to level off; this conditionis called magnetic

saturation and for a magnetically saturated ferromagnetic material, the relative

permeability (m) is approximately equal to 1.When the magnetizing force is reduced to

zero the flux density does not return to zero. Instead, the flux density returns to a value

shown at point F in Figure. This is the amount of residual magnetism resulting from the applied

magnetizing force (H) that reached the point E in the hysteresis curve. As the magnetizing force

(H) is increased from zero in the opposite direction, the flux density (B) will decrease to zero, as




shown at point G in Figure, and then start to increase to point I. The magnetizing force (H)

represented by the distance OG on the H axis in Figure is called the coercive force. It represents

the strength of the magnetizing force (H) required to reduce the flux density (B) to zero in a

saturated ferromagnetic material. A further increase in the magnetizing force (H) to the point I

results in saturation of the material in a direction opposite to that represented by point E.

Reduction of the magnetizing force (H) to zero from point I will reduce the flux density (B) to

the value represented by point J. Application of a magnetizing force (H) in the original direction

will change the flux density (B) as shown in the portion JK of the hysteresis curve. Increasing

the magnetizing force (H) sufficiently will return the material to saturation as illustrated at

point E.

Ans 2 (a)

Since the resistivity of the insulating material is greater than 107Ωm, only a very small current is

passed by the applied voltage, which is generally considered to be non-conductive. The main

characteristic of insulating material is its insulation and heat resistance. Insulation can be

measured by insulation strength; Heat resistance is the ability of insulating materials under high

temperature without changing dielectric, mechanical and chemical properties.Insulation

characteristics:

（1 ） resistance to chemical attack

（2）gloss, transparent or translucent




（3） mostly good insulators

（4） light weight and solid mass produced

（5） easy processing, cheap

（6） more widely used, the utility, easy coloring, partial resistance to high temperature

Ans 2 (b):




Ans 3(a):

Atomic packing factor (A.P.F): It can be defined as the ratio between the volume of the basic

atoms of the unit cell (which represent the volume of all atoms in one unit cell ) to the volume of

the unit cell itself.

For cubic crystals, A.P. F its depends on the riadus of atoms and characrtiziation of chemical

bondings.

Atomic Packing Factor for Simple Cubic :-

No. of atoms = 1

Volume of one atom =

Volume of unit cell (cubic) = (when, a= 2r)

Filling Factor =

=

Atomic Filling Factor for Body Centered cube (BCC) :-

No. of atoms = 2

Volume of one atom =2*

Volume of unit cell (cubic) =

(when,

)

Filling Factor =

=




Ans 3(b):

The seven unique crystal systems, listed in order of decreasing symmetry, are: 1. Isometric

System, 2. Hexagonal System, 3. Tetragonal System, 4. Rhombohedric (Trigonal) System, 5.

Orthorhombic System, 6. Monoclinic System, 7. Triclinic System.

The Seven Crystal Systems

1. Cubic

The Cubic crystal system is also known as the "isometric" system. The Cubic (Isometric) crystal

system is characterized by its total symmetry. The Cubic system has three crystallographic axes

that are all perpendicular to each other and equal in length. The cubic system has one lattice point

on each of the cube's four corners.

2. Hexagonal

The Hexagonal crystal system is has four crystallographic axes consisting of three equal

horizontal or equatorial (a, b, and d) axes at 120º, and one vertical (c) axis that is perpendicular to

the other three. The (c) axis can be shorter or longer than the horizontal axes.

3. Tetragonal




A Tetragonal crystal is a simple cubic that is stretched along its (c) axis to form a rectangular

prism. The Tetragonal crystal will have a square base and top, but a height that is taller. By

continuing to stretch the "body-centered" cubic one more Bravais lattice of the Tetragonal system

is constructed.

4. Rhombohedral

A Rhombohedron (aka Trigonal) has a three-dimensional shape that is similar to a cube that has

been compressed to one side. Its form is considered prismatic, as all faces are parallel to each

other. The faces that are not square are called "rhombi." A rhombohedral crystal has six faces or

rhombi, 12 edges, and 8 vertices.

5. Orthorhombic

Minerals that form in the Orthorhombic (aka Rhombic) crystal system have three mutually

perpendicular axes, all with different or unequal lengths.




6. Monoclinic

Crystals that form in the Monoclinic System have three unequal axes. The (a) and (c)

crystallographic axes are inclined toward each other at an oblique angle, and the (b) axis is

perpendicular to a and c. The (b) crystallographic axis is called the "ortho" axis.

7. Triclinic

Crystals that form in the Triclinic System have three unequal crystallographic axes, all of which

intersect at oblique angles. Triclinic crystals have a 1-fold symmetry axis with virtually no

symmetry and no mirrored planes.

Crystal imperfections: A perfect crystal, with every atom of the same type in the correct

position, does not exist. There always exist crystalline defects, which can be point defects

occurring at a single lattice point; line defects occurring along a row of atoms; or planar defects

occurring over a two-dimensional surface in the crystal. There can also be three-dimensional

defects such as voids. Crystalline defects are classified in three types:

(i) Point Defect

(ii) Line Defect

(iii) Surface defect




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RTU Paper Solution - Global Institute of Technology, Jaipur · RTU Paper Solution Branch- ELECTRICAL ENGINEERING Subject Name- ELECTRICAL ... Jaipur 302022 (Rajasthan) Solution V