# Chapter 7 – Alternating Current

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Today, most of the high-power applications are built to work on alternating current and voltage. Generating and transmitting AC is relatively cost-efficient and results in fewer losses compared to DC (Direct Current). AC motors are popularly used in appliances like fans, refrigerators, washing machines, mixers, etc. Similarly, AC transformers find extensive use in instrumentation circuits, control circuits, communication circuits and power distribution points. Given below is an overview of the essential concepts of alternating current and its usage:

What is Alternating Current?

A current that varies its direction and magnitude with time is called an alternating current. The main electric supply of every home and office arrives as a voltage that alters in the form of a sine wave with respect to time. This voltage is called an alternating (AC) voltage. AC voltage leads to the generation of alternating current in the circuit. Majority of the electrical equipment and devices use AC voltage since the electrical energy supplied by power distribution companies is the same.

#### Alternating Current Vs Direct Current

Unlike the alternating current (AC), the direct current (DC) does not change its direction and magnitude with time. Generally, AC circuits are preferred over DC circuits. This is because it is easy to convert the AC into DC with the help of transformers. The electric motors, generators, and power distribution systems run more efficiently on AC than DC.

#### Generation of Alternating Voltage and Current

The alternating voltage is generated with the help of AC alternators (or generators). The generation of the alternating voltage is carried out in two ways, depending upon the size of the machine. Either a coil is rotated inside a constant magnetic field at a uniform speed, or a magnetic field is rotating around a stationary coil at a uniform speed. In the case of small generators, the former technique is adopted while in the large generators, the latter method is used due to economic reasons. Here is a description of the working of the AC generator:

AC alternators utilize mechanical energy to produce alternating current. These machines are made up of rotors and stators which work based on Faraday’s Law of electromagnetic induction. As the main rotor spins, a magnetic field is created that induces a current and voltage in the stator, which is passed on to the terminals of the AC alternator. The polarity of the voltage across the stator coils reverses when the opposite poles of the rotor (rotating magnet) move by. Hence, the alternating current is generated. AC alternators cause lesser problems compared to the DC generators. AC generators are commonly used at power plants, diesel electrical units, etc.

#### Alternating Current Waveform

In an AC circuit with a resistor, the voltage (or potential difference) between the two terminals has a sinusoidally varying waveform. The AC waveform changes its polarity after every half-cycle, thus alternating between a maximum positive value and a maximum negative value. So, the alternating voltage (v) is represented as:

v = amplitude of the oscillating voltage signal * sin ωt

where vm is the amplitude of the oscillating voltage signal, and ω is its angular frequency.

Similarly, the alternating current (i) generated in the circuit is represented as:

i = im sin ωt

where im is the amplitude of the alternating current.

Here, the resistance is assumed to be constant. Therefore, the current (i) and voltage (v) are in phase with each other. Both the variables reach their maximum, minimum and zero values at the same time. However, this is not true in case of the AC circuits with inductor, capacitor or combination of these elements.

Given below is an overview of some major devices used for the applications of alternating current:

• AC Motors

In contrast to AC alternators, the AC motors convert the electrical energy into mechanical power. AC motors and alternators are similar in terms of construction and parts. However, in AC motors, the alternating current produces a reversing magnetic field across the stator, which in turn drives the rotor. These motors are considered highly efficient due to its capacity to generate constant torque up till rated speeds.

• AC Transformers

Transformers are devices that modify the voltages in the electrical circuits. The ‘step voltage up’ or ‘step down’ the voltage based on the principle of mutual induction. A transformer essentially consists of two coils, namely primary coil and secondary coil. When an AC voltage is applied to the powered (primary) coil, it generates a current which then creates an alternating magnetic flux in the unpowered (secondary) coil. Thus, an AC voltage is induced in the secondary coil whose value depends upon the number of turns of the coil. The induced voltage or emf (vs or εs) in a secondary coil with Ns turns is given by:

vs = -Ns x dφ/dt

where φ is the value of alternating flux.

Similarly, the alternating flux creates a back emf or voltage (vp) in the primary coil given by:

vp = -Np x dφ/dt

where Np is the number of turns of the primary coil.

Hence, the above two formulas give rise to the following relation:

vs/ vp = Ns/ Np

So, if the secondary coil has more turns than the primary coil, it is a step-up transformer. Alternatively, if the number of turns of the primary coil is more than that of the secondary coil, it is called a step-down transformer.

All the equations mentioned above hold accurately true for ideal transformers with no energy loss. However, these formulas also serve as a good approximation for well-designed transformers. A well-constructed transformer exhibits an efficiency of 95% and above.

In general, there are wide applications of alternating current ranging from the production of electricity to transportation and distribution of domestic power supplies.

#### Important Questions

Given below are the examples of the common questions asked in the exams:

1. A 100 Ω resistor is connected to a 50 Hz, 220 V ac supply.
(a) What is the rms value of current in the circuit?
(b) What is the net power consumed over a full cycle?
2. (a) The peak voltage of an ac supply is 300 V. What is the rms voltage?
(b) The rms value of current in an ac circuit is 10 A. What is the peak current?

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time