This is the notes for electricity and magnetism.
DIRECT CURRENT CIRCUIT
The branch of Physics which deals with charges
either at rest or in motion is called electricity. There
are two branches of electricity :
Electrostatics : The branch of Physics which deals
with the study of different phenomenon of electric
charge at rest(Static electricity). 'Electrostatics' refers
to situation when electric charges are stationary, or
moving very slowly, such that there are no magnetic
forces between them, and no electromagnetic
radiation. The static electricity uses in pollution
control machine, in machine painting, xerography
etc.
Current electricity : The branch of electricity that
deals with a charge in motion is called current
electricity. The electricity which is produced because
of the movement of electrons is known as the
current electricity. It develops only on the material
which has free electrons. The current electricity is
used for performing the mechanical works like for
moving the fan, running the machine, etc. The
magnetic field associates because of current
electricity.
For an electric current to pass to a conductor, there
must be some potential differences across the length
of conductor.
Electric current
The amount of charge flowing through a conductor in one second is known
as electric current. It can also be defined as the rate of flow of charge
through a conductor . Although the current has both magnitude and
direction, it is not a vector quantity. It does not obey the vector addition
rules. Hence current is a scalar quantity.
Therefore, 𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄 𝒄𝒖𝒓𝒓𝒆𝒏𝒕 𝑰 = 𝑨𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝒄𝒉𝒂𝒓𝒈𝒆 𝑸 / 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏(𝒕)
Unit of I:
We have, 𝑰 = 𝑸
So, it unit in S.I system is C/sec which is also known as Ampere. And,
𝟏𝒎𝑨 = 𝟏𝟎−𝟑𝑨
𝟏μ𝑨 = 𝟏𝟎−𝟔𝑨
𝟏𝒏𝑨 = 𝟏𝟎−𝟗𝑨
Therefore, the current flowing in a conductor is said to be
one ampere if one coulomb of charge flows across any cross
section of a conductor in one second.
From quantization of charge,
𝒒 = 𝒏𝒆
𝑵 =
𝒒 / 𝒆
For, q = 1 C , and 𝒆 = 𝟏. 𝟔 ∗ 𝟏𝟎^−𝟏𝟗𝑪
Then, 𝑵 = 𝟏𝑪
𝟏.𝟔∗𝟏𝟎^−𝟏𝟗𝑪
= 𝟔. 𝟐𝟓 ∗ 𝟏𝟎^𝟏𝟖
Therefore, 1 A electric current constitutes of 𝟔. 𝟐𝟓 ∗ 𝟏𝟎^𝟏𝟖
electrons crossing a given cross section in 1 second.
Some facts about current
• The flow of charge can be compared with the mechanism of flow of
water in a pipe of varying diameter. As the water flows from high
pressure to low pressure, charged particles also flow from high
potential to low potential. Whatever the diameter of pipe, the rate
of volume of water is same throughout each cross section.
• The magnitude of current at any cross section of a conductor is
same.
• The conductor is not charged when current flows through it.
Number of electrons that enter into the conductor is equal to the
number of electrons that leave from the conductor, while current
flows.
• ‘Electric Current’ is used for both of phenomenon and a physical
quantity.
• Current is a scalar quantity.
Types of current
There are three types of current. They are :
Direct current: An electric current in which both magnitude and direction of
current always remain constant with time is known as direct
current(D.C).
The source of D.C. is cell or battery.
Varying current : An electric current in which magnitude changes with time but
direction remains constant is known as varying current.
The source of varying current is D.C. generator.
Alternating current : An electric current in which magnitude and direction both change
alternatively and periodically with time is known as alternating
current.
The source of alternating current is a AC generator.
Electric circuit
A closed conducting path through which electric
charges can flow easily is known as electric
circuit. Basically, an electric circuit consists of a
switch, cell, resistance etc. which are known as
circuit components.
Some of the circuit components and their
symbols are given below:
Condition of current flow
For continuous flow of current through a
conductor, there must be some potential
difference between the ends of the conductor.
When a conducting wire is connected across a
battery constant potential difference is
developed across it. This results into continuous
flow of current through a conductor.
Potential difference
The potential difference between any two points in an
electric circuit is defined as the amount of work done
required on moving a unit positive test charge from one
point to another point.
Therefore, 𝑷𝒐𝒕𝒆𝒏𝒕𝒊𝒂𝒍 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = 𝑨𝒎𝒐𝒖𝒏𝒕 𝒐𝒇 𝒘𝒐𝒓𝒌𝒅𝒐𝒏𝒆 (W) / C𝒉𝒂𝒓𝒈𝒆 𝒎𝒐𝒗𝒆𝒅(𝑸)
It is denoted by V and given by;
𝑽 =
𝑾/𝑸
Its SI unit is J/C which is also known as Volt.
Mechanism of metallic conduction
However, if the conductor is connected across the battery a
constant potential difference is established across the
conductor and free electrons start to move towards the end
of the conductor connected to anode(positive terminal) of
battery. These electrons reach to the anode and neutralize
positive Ion. For each neutralization of positive ion in anode,
an electron leaves the cathode of battery and reaches to the
conductor. As a result the total number of electrons in the
conductor remain same but battery goes on losing charges.
Direction of Electric Current
There are two directions of current
1. Direction of conventional current
It is the direction along which positive would move if they were
allowed to move freely figure below shows the direction of
conventional current.
2. Direction of electron current
The actual direction along which electrons move in an electron circuit
is known as direction of electron current. The electrons move from
cathode or battery to conductor and then to the anode of battery.
Figure below shows direction of electron current.
• Drift velocity
When a potential difference is maintained between the ends
of the conductor, free electrons move from the region of low
potential to the reason of high potential. On the way they
collide with the atoms of the conductor and lose some of the
energy.
Since, the electrons are subjected to an external electric
field, they are accelerated again till the next collision. In this
way, electrons gain energy by acceleration and lose energy
during collision. As a result they start to move with a small
average velocity known as Drift velocity.
Hence small average velocity acquired by the free electron
moving inside a conductor subjected to an external electric
field is known as Drift velocity.
𝑰 = 𝒒/𝒕
……………… (i)
Let N be the number of free electrons in the conductor, then from
quantization of charge,
𝒒 = 𝑵𝒆 ……………(ii)
From (i) and (ii) we get,
𝑰 = 𝑵𝒆/𝒕
……………(iii)
Where e is the charge of an electron.
Suppose n be the number of free electrons per unit volume(V), i.e.,
𝒏 =
𝑵/ 𝑽
. It is also called electron density.
Now, 𝑵 = 𝒏𝑽
Also, volume of conductor 𝑽 = 𝑨. 𝒍
So, 𝑵 = 𝒏𝑨𝒍 …………….(iv)
Now using (iv) and (iii), we get,
𝑰 = 𝒏𝑨𝒍𝒆/ 𝒕
= 𝒏𝑨(𝒍/ 𝒕)𝒆
𝑰 = 𝒏𝑨Vd𝒆 ……………(v)
Where, Vd is called the drift velocity of an electron in the conductor.
Here, Vd =
𝒍/ 𝒕
, Since the electron travels 𝒍 distance(crosses the
conductor) at time 𝒕.
Relation between current and drift velocity
Let us consider small section of conducting wire such as copper wire having
length ‘l’ and cross sectional area A. Let ‘n’ be the number of electrons per unit
volume of conductor and ‘e’ be the charge of each electron
Then
Total volume of conductor (V) = 𝑨 ∗ 𝒍
Total number of electrons in conductor (N) = 𝒏𝑽 = 𝒏𝑨𝒍
Total charge in conductor(Q) = 𝒆𝑵 = 𝒆𝒏𝑨𝒍
Let us suppose the conductor is connected with a battery such that charges drift
throughout the conductor. If ‘t’ be the time during which charge ‘Q’ drifts
throughout the conductor then the current of conductor is given by:
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑰 =
𝑪𝒉𝒂𝒓𝒈𝒆 (𝑸) / 𝒕𝒊𝒎𝒆(𝒕 )
Therefore,𝑰 = 𝒆𝒏𝑨𝒍 / 𝒕
So, 𝑰 = 𝒆𝒏𝑨𝑽𝒅 where, 𝑽𝒅 =
𝒍
𝒕
is drift velocity of free electrons.
This is the required relation between current and drift velocity.
Current density (J)
The current density of a conductor is defined as the current
carried by the conductor per unit area of cross section.
It is denoted by (J)
𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝒅𝒆𝒏𝒔𝒊𝒕𝒚 𝑱 = 𝑪𝒖𝒓𝒓𝒆𝒏𝒕 (𝑰) / 𝑨𝒓𝒆𝒂(𝑨)
Therefore, 𝑱 = 𝑽𝒅𝒆𝒏𝑨/ 𝑨
𝑱 = 𝑽𝒅𝒆𝒏
This is the required expression for current density.
Ohm's law
It states that “at constant temperature the current passing
through a conductor is directly proportional to the potential
difference across the conductor.”
So, 𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑰 𝜶 𝑷. 𝒅(𝑽)
Conversely,
𝑷. 𝒅 𝑽 𝜶 𝑪𝒖𝒓𝒓𝒆𝒏𝒕 𝑰
Therefore, 𝑽 = 𝑰𝑹
Where R is the proportionality constant known as resistance
of conductor.
Hence 𝑽 = 𝑰𝑹 which is Ohm's law.
Hope this will help you a lot.
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