Direct Current and Alternating Current
Direct Current
Direct Current (DC) is the electric current whose polarity doesn't change with time. Such a current has a fixed magnitude and a fixed direction (polarity).
Sources of Direct Current are Batteries and DC generators.
The current-time graph of a Direct Current is shown below:
Alternating Current
Alternating Current (AC) is the electric current whose polarity changes with time. Such a current has a variable magnitude and a variable direction (polarity).
Sources of Alternating Current are AC generators and Dynamos. Alternating Current is used in Transformers.
The current-time graph of an Alternating Current is shown below:
Magnetic Effect of Electric Current
When an electric current flows through a conductor, it generates a magnetic field around it. This phenomenon is known as the magnetic effect of electric current and was first observed by Hans Christian Orsted in 1820.
Orsted's experiment demonstrated that a compass needle placed near a current-carrying wire deflects, indicating the presence of a magnetic field.
Magnetic Field Around a Current-Carrying Conductor and Solenoid
The magnetic field around a straight current-carrying conductor can be determined using Ampere's Circuital Law, which states that the line integral of the magnetic field B around any closed path is equal to μ0 times the total current I passing through the enclosed area.
Mathematically,
\[ \rm \oint B \cdot dl = \mu_{o} I \]
For a straight conductor, the magnetic field at a distance r from the wire is:
\[ \rm B = \frac{\mu_{o} I}{2 \pi r} \]
where μ0 is the permeability of free space (\( \rm 4 \pi \times 10^{-7} \) T m/A).
When the conductor is shaped into a coil or solenoid, the magnetic field becomes concentrated inside the coil. For a long solenoid with n turns per unit length carrying a current I, the magnetic field inside the solenoid is:
\[ \rm B = \mu_{o} n I \]
Magnetic Flux
Magnetic flux is the total magnetic field passing through a given area.
Mathematically,
\[ \rm \phi = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos ( \theta ) \]
where B is the magnetic field strength, A is the area through which the field lines pass, and \( \rm ( \theta ) \) is the angle between the field lines and the perpendicular to the surface.
Motor Effect
It is the phenomenon where a current-carrying conductor placed within a magnetic field experiences a force.
Mathematically,
\[ \rm F = I ( \vec{dl} \times \vec{B} ) = B I L \sin ( \theta ) \]
This force is described by Fleming's Left-Hand Rule, which states that if we position our left hand such that the thumb, forefinger, and middle finger are mutually perpendicular, the thumb indicates the direction of the force (motion), the forefinger indicates the magnetic field, and the middle finger indicates the current.
Electromagnetic Induction
Electromagnetic Induction is a current produced because of voltage production (electromotive force) due to a changing magnetic field.
Faraday's Law of Electromagnetic Induction
- First law: It states that whenever there is a change in magnetic flux associated with a coil, EMF is induced in that coil.
- Second law: It states that the magnitude of EMF induced in the coil is directly proportional to the rate of change of magnetic flux associated with that coil.
Mathematically, it can be expressed as
\[ \rm E = - \frac{d \phi}{dt} \]
where E is the induced EMF and \( \rm \frac{d \phi}{dt} \) is the rate of change of magnetic flux.
Dynamo and AC Generator
A dynamo is a device that converts mechanical energy into electrical energy using the principle of electromagnetic induction.
An AC generator operates on the same principle but specifically produces alternating current (AC).
In both devices, rotating a coil within a magnetic field induces an electric current in the coil.
Large Scale Sources of Electricity
Large-scale sources of electricity include power plants that utilize various forms of energy such as fossil fuels, nuclear reactions, and renewable sources like hydro, wind, and solar energy.
These plants often use turbines and generators to convert mechanical energy into electrical energy.
Alternating Current Generator
An alternating current generator, or AC generator, produces alternating current by rotating a coil within a magnetic field.
The rotation causes the direction of the induced current to reverse periodically, resulting in AC.
Transformer: Construction, Working Principle, and Types
A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.
It consists of primary and secondary coils wound around a magnetic core.
The working principle is based on Faraday's Law of Induction, where an alternating current in the primary coil generates a changing magnetic field, which induces a current in the secondary coil.
Types of Transformers
Step-Up Transformer
A step-up transformer increases the voltage from the primary coil to the secondary coil.
This type of transformer has more turns of wire on the secondary coil than on the primary coil.
Step-down Transformer
A step-down transformer decreases the voltage from the primary coil to the secondary coil.
This type of transformer has fewer turns of wire on the secondary coil than on the primary coil.
The relationship between the primary and secondary voltages and the number of turns in the coils is given by:
\[ \rm \frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}} \]
where: \( \rm V_{S} \) is the secondary voltage, \( \rm V_{P} \) is the primary voltage, \( \rm N_{S} \) is the number of turns in the secondary coil, \( \rm N_{P} \) is the number of turns in the primary coil.