BAKU ENGINEERING UNIVERSITY
ENGINEERING FACULTY
DEPARTMENT OF PHYSICS
Specialty: Electrical engineering
Dual Degree Program
Academic year and term: 2022-2023, Spring term
Subject: Physics 2
The student’s first name and surname: Ali Safarli
The student’s e-mail address: eseferli4@std.beu.edu.az
Individual Activity Work
Current And Resistance
The teacher: Prof. Dr. Vali Huseynov, Corresponding member of the
Azerbaijan National Academy of Sciences
BAKU-2023
Current and Current density
In the modern world electric currents abound and involve many professions. Medical technology
biologists, physiologists, and engineers are interested in the nerve currents that drive muscles,
specifically how such currents might be restored following spinal cord injury. Numerous
electrical systems, including power systems, lightning protection systems, information storage
systems, and music systems, are of interest to electrical engineers. Because the passage of
charged particles from our sun has the potential to destroy power transmission systems on Earth
as well as telecommunication equipment in orbit, space experts closely monitor and analyze this
flow. Meteorologists are concerned with lightning and the less dramatic gradual passage of
charge through the atmosphere. Space engineers watch and examine the passage of charged
particles from our Sun since it has the potential to destroy telecommunications equipment in
space as well as power transmission systems on Earth. Aside from scholarly research, practically
every element of daily life today relies on information carried by electric currents, from stock
trading to ATM transfers, and from video entertainment to social networking. In this individual
activity we discuss the basic physics of electric currents and why they can be established in some
materials but not in others.
Although a stream of moving charges makes up an electric current, not all moving charges are
included in an electric current. There must be a net flow of charge across the surface for there to
be an electric current to flow through it. Two illustrations help to make our point.
1. In an isolated length of copper wire, the free electrons (conduction electrons) are moving at
random speeds of around 106 m/s. Conduction electrons run through such a wire in both
directions if you pass a hypothetical plane across it at a rate of several billions of times per
second, yet there is no net charge transfer and no current flowing down the wire as a result. But
if you attach the wire's ends to a battery, you'll slightly bias the flow in that direction, which will
result in a net transfer of charge and an electric current flowing through the wire.
2. Water flowing through a garden hose symbolizes the directed flow of positive charge (protons
in water molecules) at a rate of millions of coulombs per second. However, there is no net charge
transfer since there is a parallel flow of negative charge (the electrons in the water molecules) of
the same quantity traveling in the same direction.
As seen in the next picture a, any isolated
conducting loop, regardless of whether it carries an
excess charge, is all at the same potential. There can
be no electric field within it or along its surface.
Even though conduction electrons are accessible,
there is no net electric force acting on them, hence
there is no current.
If we place a battery into the loop, as shown in the
next picture b, the conducting loop is no longer at a
single potential. Electric fields act within the loop's
material, putting pressures on conduction electrons,
forcing them to migrate and thereby producing a
current. After a relatively short period, the electron
flow has reached a constant value, and the current
has reached a steady state (it does not change with
time).
The next picture depicts a conductor segment
that is part of a conducting loop in which
current has been created. If at time dt, charge
dq flows through a hypothetical plane (such as
aa′), the current i via that plane is defined as:
𝑖𝑖 =
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
We can find the charge that passes through the plane in a �me interval extending from 0 to t by
integra�on:
𝑡𝑡
𝑞𝑞 = ∫ 𝑑𝑑𝑑𝑑 = ∫0 𝑖𝑖 𝑑𝑑𝑑𝑑 , in which the current i may vary with �me.
Under steady-state circumstances, the current is the same for planes aa′, bb′, and cc′, as well as
any planes that travel entirely through the conductor, regardless of position or orientation. This is
because charge is preserved. An electron must pass through plane aa- for every electron that goes
through plane cc′ under the steady-state circumstances indicated here. Similarly, if there is a
constant flow of water through a garden hose, a drop of water must leave the nozzle for every
drop that enters the hose at the other end. The quantity of water in the hose is preserved.
The SI unit for current is the coulomb per second, which is also a SI base unit:
1 ampere = 1 A = 1 coulomb per second = 1 C/s
The next picture depicts a conductor with current
i0 breaking into two branches at a junction.
Because charge is conserved, the magnitudes of
the currents in the branches must sum to provide
the amplitude of the current in the original
conductor, implying that.
i₀ = i₁ + i₂
Bending or reorienting the wires in space, as
shown in the next picture, has no effect on the
validity of previous equation Current arrows
only depict a direction (or feeling) of flow along
a conductor, not a spatial direction.
A current arrow is drawn in the direction in which positive charge carriers would move, even if
the actual charge carriers are negative and move in the opposite direction.
Current density
We are sometimes interested in the current i in a certain conductor. At times, we use a more
limited approach and investigate the flow of charge across a cross section of a conductor at a
specific place. We may use the current density to characterize this flow, which has the same
direction as the velocity of the flowing charges if they are positive and the opposite way if they
are negative. The magnitude J of each cross-section element is equal to the current per unit area
across that element. The amount of current flowing through the element may be written as where
is the element's area vector perpendicular to the element. The total current through the surface is
then calculated.
𝑖𝑖 = ∫ 𝐽𝐽⃗ ∗ 𝑑𝑑𝐴𝐴⃗
If the current is uniform across the surface and parallel to dA then J is also uniform and parallel
to then
𝑖𝑖 = 𝐽𝐽 ∗ 𝐴𝐴 , 𝐽𝐽 =
𝑖𝑖
𝐴𝐴
When an electric field E is established in a conductor, the charge carriers (assumed positive)
acquire a drift speed vd in the direction of the velocity is related to the current density by
𝐽𝐽⃗ = (ne)𝑣𝑣⃗d
where ne is the carrier charge density.
Resistant and Resistivity
When we apply the same potential difference between the ends of geometrically similar copper
and glass rods, we get significantly different currents. The electrical resistance of the conductor
that enters here is a property. We may calculate the resistance between any two places on a
conductor by applying a potential difference V between them and measuring the resulting current
i. The resistance R is then calculated.
𝑅𝑅 =
𝑉𝑉
𝑖𝑖
The volt per ampere is the SI unit for resistance derived from there. This combination happens so
frequently that it has its own name, the ohm (symbol Ω).
1 ohm = 1 Ω = 1 volt per amper = 1 V/A
A conductor whose function in a circuit is to provide a specified resistance is called a resistor.
We frequently want to take a broad view and deal with materials rather than specific things, as
we have done in previous contexts. In this case, we do so by focusing on the electric field at a
spot in a resistive material rather than the potential difference V across a specific resistor. We
deal with the current density at the place in issue rather than the current i via the resistor. Instead
of dealing with an object's resistance R, we deal with the material's resistivity r:
𝜌𝜌 =
𝐸𝐸
𝐽𝐽
If we combine the SI units of E and J, we get, for
the unit of r, the ohmmeter (Ω *m):
𝑉𝑉 ⁄𝑚𝑚
𝑉𝑉
𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢(𝐸𝐸)
=
=
𝑚𝑚 = Ω ∗ m
𝐴𝐴
𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢(𝐽𝐽)
𝐴𝐴⁄𝑚𝑚2
We can write previous equation in vector form as:
𝐸𝐸�⃑ = 𝜌𝜌 ∗ 𝐽𝐽⃗
We often speak of the conductivity s of a material.
This is simply the reciprocal of its resistivity, so:
σ =
1
𝜌𝜌
The SI unit of conductivity is the reciprocal
ohmmeter (Ω ∗ 𝑚𝑚)−1 . The unit’s name mhos per
meter is sometimes used (mho is ohm backwards).
The definition of s allows us to write previous
Equation the alternative form:
𝐽𝐽⃗ = 𝜎𝜎𝐸𝐸�⃗
However, V/i is the resistance R, which allows us
to recast Equation of resistance as:
𝑅𝑅 = 𝜌𝜌
𝐿𝐿
𝐴𝐴
Change of ρ with Temperature The resistivity ρ for most materials changes with temperature.
For many materials, including metals, the relation between ρ and temperature T is approximated
by the equation:
𝜌𝜌 − 𝜌𝜌₀ = 𝜌𝜌₀𝑎𝑎(𝑇𝑇 − 𝑇𝑇₀)
Here T₀ is a reference temperature, ρ₀ is the resistivity at T₀, and α is the temperature coefficient
of resistivity for the material.
Ohm's Law is a fundamental principle in electrical engineering and physics that relates the
voltage, current, and resistance in an electrical circuit. It provides a mathematical relationship
between these three parameters and is named after the German physicist Georg Simon Ohm, who
first formulated the law.
In its simplest form, Ohm's Law states that the current flowing through a conductor is directly
proportional to the voltage applied across it and inversely proportional to the resistance of the
conductor. Mathematically, it can be expressed as:
Where:
𝑉𝑉 = 𝐼𝐼 ∗ 𝑅𝑅
V represents the voltage across the conductor, I represents the current flowing through the
conductor, and R represents the resistance of the conductor.
According to Ohm's Law, if the voltage applied to a conductor is increased while the resistance
remains constant, the current flowing through the conductor will also increase. Conversely, if the
voltage is decreased, the current will decrease proportionally.
The law can also be rearranged to calculate other parameters. For example, if the current and
resistance are known, the voltage can be calculated using the equation:
𝑉𝑉 = 𝐼𝐼 / 𝑅𝑅
Similarly, if the voltage and current are known, the resistance can be calculated using the
equation:
𝑅𝑅 = 𝑉𝑉 / 𝐼𝐼
It is important to note that Ohm's Law holds true for linear, passive elements such as resistors. It
does not apply to non-linear elements like diodes or transistors. Additionally, it assumes that the
temperature and other environmental factors remain constant.
Ohm's Law serves as a foundational principle for many advanced topics in electrical engineering,
including circuit analysis, power calculations, and circuit design. It forms the basis for numerous
calculations and concepts used in practical applications such as power distribution, electronic
devices, and telecommunications.
Resistivity of a Metal By assuming that the conduction electrons in a metal are free to move like
the molecules of a gas, it is possible to derive an expression for the resistivity of a metal:
𝜌𝜌 =
𝑚𝑚
𝑒𝑒 2 𝑛𝑛τ
Here n is the number of free electrons per unit volume and t is the mean time between the
collisions of an electron with the atoms of the metal. We can explain why metals obey Ohm’s
law by pointing out that τ is essentially independent of the magnitude E of any electric field
applied to a metal.
The picture below depicts a circuit consisting of a battery B linked to an unnamed conducting
device through wires with minimal resistance. A resistor, a storage battery (a rechargeable
battery), a motor, or another electrical device might be used. The battery maintains a potential
difference of magnitude V across its own terminals and hence (due to the cables) across the
terminals of the unknown device, with a bigger potential at terminal a than terminal b.
Because there is an external conducting channel between the battery's two terminals and the
potential differences created by the battery are preserved, In the circuit, a constant current i flows
from terminal a to terminal b.
The charge dq that flows between the terminals in the time period dt equals i dt. This charge dq
passes via a magnitude V reduction in potential, and so its electric potential energy reduces in
magnitude by the amount.
dU = dq V = i dt V
The principle of conservation of energy tells us that the decrease in electric potential energy from
a to b is accompanied by a transfer of energy to some other form. The power P associated with
that transfer is the rate of transfer dU/dt, which is given as:
P = iV
For a resistor or some other device with resistance R, we can write to obtain, for the rate of
electrical energy dissipation due to a resistance, either:
𝑃𝑃 = 𝑖𝑖 2 𝑅𝑅 (resistive dissipation), 𝑃𝑃 =
𝑉𝑉 2
𝑅𝑅
(resistive dissipation)
Semiconductors and superconductors are two distinct classes of materials that
exhibit unique electrical properties and play essential roles in various fields of
science and technology. Here's an overview of semiconductors and
superconductors:
Semiconductors are materials that have electrical conductivity between that of
conductors (such as metals) and insulators (such as non-metals). They possess a
band gap, which is an energy range that exists between the valence band (lower
energy) and the conduction band (higher energy) in their electronic band structure.
At low temperatures or when no external energy is provided, semiconductors act as
insulators since the electrons are predominantly in the valence band, and the
energy gap prevents them from transitioning to the conduction band. However, by
applying an external energy source, such as heat or an electric field, electrons can
be excited to the conduction band, allowing for current flow.
Semiconductors find extensive applications in electronic devices, such as
transistors, diodes, and integrated circuits. The controlled manipulation of their
electrical conductivity through processes like doping (introducing impurities)
enables the creation of semiconductor devices that form the backbone of modern
electronics.
Superconductors are materials that exhibit zero electrical resistance when cooled
below a critical temperature. This phenomenon, known as superconductivity,
allows electric current to flow through a superconductor without any energy loss
due to resistance.
Superconductors also display another remarkable property called the Meissner
effect. When a superconductor is subjected to a magnetic field, it expels the
magnetic field lines from its interior, creating a state of perfect diamagnetism.
Superconductivity was initially observed at extremely low temperatures, close to
absolute zero (-273.15°C or -459.67°F). However, advancements in
superconducting materials have led to the discovery of high-temperature
superconductors that exhibit superconducting properties at relatively higher
temperatures (though still requiring cryogenic cooling).
Superconductors have numerous applications, including magnetic resonance
imaging (MRI) machines, particle accelerators, magnetic levitation (Maglev)
trains, and superconducting quantum interference devices (SQUIDs) used for
highly sensitive magnetic field measurements.
Although superconductivity is a fascinating phenomenon, its practical applications
are limited by the need for low temperatures and the cost associated with cryogenic
cooling. However, ongoing research and developments aim to discover new
materials and mechanisms to achieve higher critical temperatures, making
superconductors more accessible and applicable.