Place Value, Total Value and Expanded Notation Grade 3

The challenges of working in the new economy recognize: 1.1 Working Today Talent Talented people- What they know, what they learn and what they can achive The source of organisational performance Develop skills and improve What is intellectual capital The combined brain power and shared knowledge of an organization's employees TO orginzations: Intellectual capital resents a strategic asset as human creativity, insight and decision making can be converted into superior performance To individuals: Intellectual capital is a personal asset, one to be nurtured and continually updated Things evolve, make sure we keep updated Intellectual capital: The package on intellect skills and capabilities that set us apart making us valable to potential employers Maintaining your talent: There is no escaping the fact that your career success will require a lot of initiative, self awareness and continuous learning Technology Tech is in our everyday lives Latest developments Smart phone, smart apparel, smart cars, smart homes We struggle to keep up with social media ana staying connected with messaging, full of email and voicemail What happenings as younger workers advance into management Flexibility Work ethic It is critical to build and maintain a high Tech IQ! What is Tech IQ: The ability to use current technologies at work and in your personal life, combined with the commitment to keep yourself updated as technology continues to evolve Intellectual capi5la is a combination of: Commitment x Competency = Intellectual capital How to make the world a better place Globalisation The worldwide interdependence of resources flows, product markets and business competition Under the influence, government leaders worry and about the competitiveness of nations just as corporate leaders worry about business competitiveness Emerging markets will power global growth over the next 20 years. By 2025 overall global consumption is forecast to reach $62 trillion, twice its 2013 level and fully half of this increase will come from the emerging world Consequence: Going to fast in uses resources, inflation, corporate greed It's cheaper to have things made in different countries (wages are low and going down) Shamrock organization 1 leaf - full time employees- standard career paths 2 leaf - “freelancers” 3 leaf - Part times without benefits (first to lose their jobs when employers face economic difficulties) The rising of emerging markets Now account for 60% of all low and medium technology manufacturing worldwide Total value add in high tech manufacturing from a low 26% in the 1970s to 48% at present China strategy to upgrade its industries and move the manufacturing value ching by prioritising 10 sectors Information technology, robotic, aerospace, maritime equipment, modern railway equipment, alternative energy vehicles, power equipment, agriculture equipment, advanced materials, biopharma and medical products Ethics A code of moral principa;s that sets standards for conduct that is “good” and “right” as well as “bad” and “wrong” Enron company huge corruption even in elections same thing happened with The Mechanism 1.2 - Organizations Organizational Purpose An orgnizations is a collection of people working together to achieve a common purpose Unique social phenomenon that enables its members to perform tasks far beyond the reach of individual accomplishment (synergy) The broad purpose of any orginzation is to provide goods or services of value to customers and clients A clear sense of purpose tied to: Quality of products and services Customer satisfaction Social responsibility Can be an important source of organisational strength and performance advantage All organisations are open systems (Systems that interact with its environment for renewal and growth) Organizations as systems All organizations are open systems that interact with their environment Continual process of obtaining resource inputs-people, information, resources and capital- and transforming them into outputs in the form of finished goods and services for customers One simple way to assess the impact of any organisation is to ask the question: How is the world different because it existed Michal Porter - Value Chain Value Creation: Organisations create value when they use resources well to produce good products and take care of their customers One simple way to assess the impact of any organization is to ask the questions: How is the world different because it existed? Triple Bottom Line The 3 Ps of organizational performance Profit - is the decision economically sound? People - Does the decision treat people with respect and dignity? Planet - Is the decision good for the environment? Organizational Performance Productivity: An overall measure of the quantity and quality of work performance with recourse utilisation taken into account Performance effectiveness: An output measure of task or goal accomplishment Performance efficiency: An input measure of the resource costs associated with goal accomplishment. Workplace changes that impact management Focus on valuing human capital Demise of “Command and control” Emphasis on teamwork Pre-eminence of technology New workforce expectations Importance of networking Concern for sustainability 1.3 Managers Importance of human resources and manger People are not ‘costs to be controlled’ High performing organizations treat people as valuable strategic assets Three takeaways 1. Give leaders broad authority 2. Encourage them to think like CEO 3. Challenge strong performers easily with big opportunities Direct support, supervise and help activate the work efforts of others The people who managers help are the ones whose contributions represent the real work of the organisation Levels of management Types of managers Line managers are responsible for work activities that directly affect organization’s output Staff managers use technical expertise to advise and support the efforts of line workers Functional managers are responsible for a single area of activity Quality of work life (QWL) An indicator of the overall quality of human experiences in the workplace QWL Indicators Respect Fair pay Safe working conditions Opportunities to learn and use new skills Room to grow and progress in a career Protection of individuals rights The organization as an upside-down pyramid A manager’s job is to support worker’s efforts The best managers are known for helping and supporting Customers at the top served by worker who are supported by managers 1.4 The management Process Managers achieve high performance for their organizations by best utilizing its humans and material resources Management is the process of planning, organizing, leading and controlling the use of resources to accomplish performance goals All managers are responsible for the four functions The functions are carried on continually Four functions: Planning,organizing, leading and controlling Mintzberg’s 10 Managerial Roles Characteristics of managerial work Long hours Intense pace Fragmented and varied tasks Many communication media Filled with interpersonal relationships Managerial agendas and networks Agenda setting Develops action priorities for accomplishing goals and plans Networking Process of building and maintaining positive relationships with people who can help advance agendas Social Capital Capacity to attract support and help from others Learning The change in a behaviour that results from experience Lifelong learning The process of continuously learning from daily experiences and opportunities Katz’ Essential Managerial Skills

Chapter One: Management Today The challenges of working in the new economy recognize: 1.1 Working Today Talent Talented people- What they know, what they learn and what they can achive The source of organisational performance Develop skills and improve What is intellectual capital The combined brain power and shared knowledge of an organization's employees TO orginzations: Intellectual capital resents a strategic asset as human creativity, insight and decision making can be converted into superior performance To individuals: Intellectual capital is a personal asset, one to be nurtured and continually updated Things evolve, make sure we keep updated Intellectual capital: The package on intellect skills and capabilities that set us apart making us valable to potential employers Maintaining your talent: There is no escaping the fact that your career success will require a lot of initiative, self awareness and continuous learning Technology Tech is in our everyday lives Latest developments Smart phone, smart apparel, smart cars, smart homes We struggle to keep up with social media ana staying connected with messaging, full of email and voicemail What happenings as younger workers advance into management Flexibility Work ethic It is critical to build and maintain a high Tech IQ! What is Tech IQ: The ability to use current technologies at work and in your personal life, combined with the commitment to keep yourself updated as technology continues to evolve Intellectual capi5la is a combination of: Commitment x Competency = Intellectual capital How to make the world a better place Globalisation The worldwide interdependence of resources flows, product markets and business competition Under the influence, government leaders worry and about the competitiveness of nations just as corporate leaders worry about business competitiveness Emerging markets will power global growth over the next 20 years. By 2025 overall global consumption is forecast to reach $62 trillion, twice its 2013 level and fully half of this increase will come from the emerging world Consequence: Going to fast in uses resources, inflation, corporate greed It's cheaper to have things made in different countries (wages are low and going down) Shamrock organization 1 leaf - full time employees- standard career paths 2 leaf - “freelancers” 3 leaf - Part times without benefits (first to lose their jobs when employers face economic difficulties) The rising of emerging markets Now account for 60% of all low and medium technology manufacturing worldwide Total value add in high tech manufacturing from a low 26% in the 1970s to 48% at present China strategy to upgrade its industries and move the manufacturing value ching by prioritising 10 sectors Information technology, robotic, aerospace, maritime equipment, modern railway equipment, alternative energy vehicles, power equipment, agriculture equipment, advanced materials, biopharma and medical products Ethics A code of moral principa;s that sets standards for conduct that is “good” and “right” as well as “bad” and “wrong” Enron company huge corruption even in elections same thing happened with The Mechanism 1.2 - Organizations Organizational Purpose An orgnizations is a collection of people working together to achieve a common purpose Unique social phenomenon that enables its members to perform tasks far beyond the reach of individual accomplishment (synergy) The broad purpose of any orginzation is to provide goods or services of value to customers and clients A clear sense of purpose tied to: Quality of products and services Customer satisfaction Social responsibility Can be an important source of organisational strength and performance advantage All organisations are open systems (Systems that interact with its environment for renewal and growth) Organizations as systems All organizations are open systems that interact with their environment Continual process of obtaining resource inputs-people, information, resources and capital- and transforming them into outputs in the form of finished goods and services for customers One simple way to assess the impact of any organisation is to ask the question: How is the world different because it existed Value Creation: Organisations create value when they use resources well to produce good products and take care of their customers One simple way to assess the impact of any organization is to ask the questions: How is the world different because it existed? The 3 Ps of organizational performance Profit - is the decision economically sound? People - Does the decision treat people with respect and dignity? Planet - Is the decision good for the environment? Productivity: An overall measure of the quantity and quality of work performance with recourse utilisation taken into account Performance effectiveness: An output measure of task or goal accomplishment Performance efficiency: An input measure of the resource costs associated with goal accomplishment. Workplace changes that impact management Focus on valuing human capital Demise of “Command and control” Emphasis on teamwork Pre-eminence of technology New workforce expectations Importance of networking Concern for sustainability 1.3 Managers Importance of human resources and manger People are not ‘costs to be controlled’ High performing organizations treat people as valuable strategic assets Three takeaways 1. Give leaders broad authority 2. Encourage them to think like CEO 3. Challenge strong performers ealy with big opportunities Direct support, supervise and help activate the work efforts of others The people who managers help are the ones whose contributions represent the real work of the organisation Types of managers Line managers are responsible for work activities that directly affect organization’s output Staff managers use technical expertise to advise and support the efforts of line workers Functional managers are responsible for a single area of activity Quality of work life (QWL) An indicator of the overall quality of human experiences in the workplace QWL Indicators Respect Fair pay Safe working conditions Opportunities to learn and use new skills Room to grow and progress in a career Protection of individuals rights The organization as an upside-down pyramid A manager’s job is to support worker’s efforts The best managers are known for helping and supporting Customers at the top served by worker who are supported by managers 1.4 The management Process Managers achieve high performance for their organizations by best utilizing its humans and material resources Management is the process of planning, organizing, leading and controlling the use of resources to accomplish performance goals All managers are responsible for the four functions The functions are carried on continually Characteristics of managerial work Long hours Intense pace Fragmented and varied tasks Many communication media Filled with interpersonal relationships Managerial agendas and networks Agenda setting Develops action priorities for accomplishing goals and plans Networking Process of building and maintaining positive relationships with people who can help advance agendas Social Capital Capacity to attract support and help from others Learning The change in a behaviour that results from experience Lifelong learning The process of continuously learning from daily experiences and opportunities

Orchard / fruit trees Importance of fruit trees • Fruit trees are important for the following uses: They are a source of food, they produce fruits Some are used for making medicines Others provide shade and can also act as wind breakers. Those with beautiful flowers are very decorative. They contain vitamins which means they have nutritional value. Classification of fruit trees • Fruit trees are classified as indigenous and exotic. Indigenous fruit trees • are those that natural grow in a country. • They take longer to grow. • Examples of indigenous fruit trees are: English name Shona Name Snot apple Water berry Red ivory Fig Monkey orange Wild custard apple Mobola fruit Exotic fruit trees • These are trees that were brought from other countries. • They are commercially grown in orchards. • Common exotic fruit trees include: • Exotic fruit trees grow faster than indigenous. Ornamental horticulture • It deals with the growing of decorative plants. • Decorative plants are collectively called ornamental plants. • They include trees, shrubs, flowers and lawn grasses. Importance of ornamental plants They beautify the environment. Flowers often produce a pleasing fragrance. Flowers attract insects like bees that are responsible for pollination. Plants produce oxygen that we need for breathing. • Some are used for making medicines. • Lawn grasses prevent soil erosion. • Plants provide shelter for birds and insects. Classification of ornamental plants • There are four classes of ornamental plants. Trees Shrubs Flowers Lawn Trees: • Ornamental trees are very useful as decorative plants. • This is because most of these trees produce beautiful flowers and some are ever green. • Examples of decorative trees include flamboyant, jacaranda, pines, Cyprus. Shrubs: • A shrub is a woody plant with many branches but smaller than a tree. • Some of them are ornamentals because they produce beautiful flowers. • Others can be cut into decorative shapes. • The golden duranta is good example because it can be cut into nice shapes. • The bougainvillea is another example of a decorative plant because: It can act as a climbing plant. It produces decorative flowers. It can also be cut into any shape using a hedge shear. Flowers: • Flowers have the following functions: They are used for decorations at weddings, hotels and parties. They are used as an expression of love and appreciation such as valentine’s day and get well soon messages. They are useful in bee farming called apiculture as they are a source of nectar used for making honey. Flowers produce a pleasant fragrance used in the production of soaps and scents for perfumes, deodorant and lotions. Lawn: • A lawn is an area of grass that is kept cut short and is usually part of someone's garden or backyard, or part of a park. • Some lawn grasses grown in Zimbabwe are Durban, kikuyu, couch and buffalo lawn. • They prevent soil erosion. • They also provide a comfortable outdoor resting place. Forestry Importance of trees • Trees are important to us and animals. • The Forestry Commission is responsible for taking care of trees in Zimbabwe. • Trees are also important to the environment because: They are a source of fuel in the form of firewood. They are used for making most of the furniture we use. Most medicines come from both exotic and indigenous trees, for example pine trees and gum trees are used for making cough medicines. Trees provide browsing animals like the kudu and giraffe with food. Fruits from both exotic and indigenous fruit trees are a rich source of vitamins Trees give out oxygen which we need for breathing. Trees provide timber that can be used for roofing. • Trees are grouped according to where they come from. • The groups are indigenous and exotic. 1 . Indigenous trees : • These are local trees that have always been grown in their country. Shona name English name Mutohwe Snot apple Mususu Yellow wood Mubvamaropa Blood wood Muuyu Baobab Muonde Fig tree Musasa msasa Characteristics of indigenous trees  take longer to mature  Do not produce straight poles  Grow on their own  Hard wood 2 .Exotic trees : • These are trees that have been brought from another country to be grown in Zimbabwe. Characteristics of exotic trees  They are brought in a country from another country. Grow very fast.  Have soft woods  Usually grow straight  Usually grown in orchards and plantations Common exotic trees in Zimbabwe are: Gum trees Pine trees Wattle Cyprus Date palm Mango Apple pawpaw Causes of plant damage • plant damage is when cultivated crops are kept from normal growth that leads to reduced yields. • plant damage is caused by both living and non living things. • Some of the common causes of crop damage are: (a)Pests • These are living organisms that cause physical damage to crops. • Examples of pests are weevils, army worm, aphids, cutworms and locusts. (b) Diseases • Plant diseases are caused by living organisms called pathogens. • These pathogens infest the plant and take away nutrients. • Fruit rot and bacteria spot are some of the examples of plant diseases. (c) Weeds • these are plant which grow where they are not wanted. • For example if black jack grows in a groundnut field, it is a weed. • Weeds compete for nutrients with cultivated plants. (d) Very high temperatures • High temperatures may cause crops to wither. • High temperatures may also lead to lightning and fires. • This can burn up crops. ( e) Frost • Frost damages crops in winter. • Tomatoes, potatoes, and beans are easily damaged by frost. (f) Drought • drought is when there is no rainfall in a season where it supposed to be raining. • It is one of the most serious forms of crop damage. • Plants wither and die if there is no rainfall. ( g) Animals • Wild animals like baboons often eat maize crops before they mature. • Birds also are a problem to crops like sorghum. Signs of plant damage • There are various signs that show plant damage. • Some can be corrected but some lead to total loss. • Some signs of plant damage include: Lodged plants Flowers and small fruits blown to the ground Dull leaf color Wilted plants Stunted growth

Figure 18-11 represents the amount of energy stored as organic material in each trophic level in an ecosystem. The pyramid shape of the diagram indicates the low percentage of energy transfer from one level to the next. On average, 10 percent of the total energy consumed in one trophic level is incor- porated into the organisms in the next. Why is the percentage of energy transfer so low? One reason is that some of the organisms in a trophic level escape being eaten. They eventually die and become food for decomposers, but the energy contained in their bodies does not pass to a higher trophic level. Even when an organism is eaten, some of the molecules in its body will be in a form that the consumer cannot break down and use. For example, a cougar cannot extract energy from the antlers, hooves, and hair of a deer. Also, the energy used by prey for cellu- lar respiration cannot be used by predators to synthesize new bio- mass. Finally, no transformation or transfer of energy is 100 percent efficient. Every time energy is transformed, such as during the reactions of metabolism, some energy is lost as heat. Limitations of Trophic Levels The low rate of energy transfer between trophic levels explains why ecosystems rarely contain more than a few trophic levels. Because only about 10 percent of the energy available at one trophic level is transferred to the next trophic level, there is not enough energy in the top trophic level to support more levels. Organisms at the lowest trophic level are usually much more abundant than organisms at the highest level. In Africa, for exam- ple, you will see about 1,000 zebras, gazelles, and other herbivores for every lion or leopard you see, and there are far more grasses and shrubs than there are herbivores. Higher trophic levels con- tain less energy, so, they can support fewer individuals.A population is a group of organisms that belong to the same species and live in a particular place at the same time. All of the bass living in a pond during a certain period of time make up a pop- ulation because they are isolated in the pond and do not interact with bass living in other ponds. The boundaries of a population may be imposed by a feature of the environment, such as a lake shore, or they can be arbitrarily chosen to simplify a study of the population. The humans shown in Figure 19-1 are part of the pop- ulation of a city. The properties of populations differ from those of individuals. An individual may be born, it may reproduce, or it may die. A population study focuses on a population as a whole—how many individuals are born, how many die, and so on. Population Size A population’s size is the number of individuals that the population contains. Size is a fundamental and important population property but can be difficult to measure directly. If a population is small and composed of immobile organisms, such as plants, its size can be determined simply by counting individuals. Often, though, individ- uals are too abundant, too widespread, or too mobile to be counted easily, and scientists must estimate the number of individuals in the population. Suppose that a scientist wants to know how many oak trees live in a 10 km2 patch of forest. Instead of searching the entire patch of forest and counting all the oak trees, the scientist could count the trees in a smaller section of the forest, such as a 1 km2 area. The scientist could then use this value to estimate the population of the larger area. SECTION 1 OBJECTIVES ● Describe the main properties that scientists measure when they study populations. ● Compare the three general patterns of population dispersion. ● Identify the measurements used to describe changing populations. ● Compare the three general types of survivorship curves. VOCABULARY population population density dispersion birth rate death rate life expectancy age structure survivorship curve FIGURE 19-1 A population can be widely distributed, as Earth’s human population is, or confined to a small area, as species of fish in a lake are. Copyright © by Holt, Rinehart and Winston. All rights reserved. 382 CHAPTER 19 If the small patch contains 25 oaks, an area 10 times larger would likely contain 10 times as many oak trees. A similar kind of sampling technique might be used to estimate the size of the pop- ulation shown in Figure 19-2. To use this kind of estimate, the sci- entist must assume that the distribution of individuals in the entire population is the same as that in the sampled group. Estimates of population size are based on many such assumptions, so all esti- mates have the potential for error. Population Density Population density measures how crowded a population is. This measurement is always expressed as the number of individuals per unit of area or volume. For example, the population density of humans in the United States is about 30 people per square kilome- ter. Table 19-1 shows the population sizes and densities of humans in several countries in 2003. These estimates are calculated for the total land area. Some areas of a country may be sparsely popu- lated, while other areas are very densely populated. Dispersion A third population property is dispersion (di-SPUHR-zhuhn). Dispersion is the spatial distribution of individuals within the popu- lation. In a clumped distribution, individuals are clustered together. In a uniform distribution, individuals are separated by a fairly con- sistent distance. In a random distribution, each individual’s location is independent of the locations of other individuals in the popula- tion. Figure 19-3 illustrates the three possible patterns of dispersion. Clumped distributions often occur when resources such as food or living space are clumped. Clumped distributions may also occur because of a species’ social behavior, such as when animals gather into herds or flocks. Uniform distributions may result from social behavior in which individuals within the same habitat stay as far away from each other as possible. For example, a bird may locate its nest so as to maximize the distance from the nests of other birds. These migrating wildebeests in East Africa are too numerous and mobile to be counted. Scientists must use sampling methods at several locations to monitor changes in the population size of the animals. FIGURE 19-2 TABLE 19-1 Population Size and Density of Some Countries Population size Population density Country (in millions) (in individuals/km2) China 1,289 135 India 1,069 325 United States 292 30 Russia 146 8 Japan 128 337 Mexico 105 54 Kenya 32 54 Australia 20 3 dispersion from the Latin dis-, meaning “out,” and spargere, meaning “to scatter” Word Roots and Origins Copyright © by Holt, Rinehart and Winston. All rights reserved. POPULATIONS 383 The social interactions of birds called gannets, which are shown in Figure 19-3b, result in a uniform distribution. Each gannet chooses a small nesting area on the coast and defends it from other gannets. In this way, each gannet tries to maximize its distance from all of its neighbors, which causes a uniform distribution of individuals. Few populations are truly randomly dispersed. Rather, they show degrees of clumping or uniformity. The dispersion pattern of a population sometimes depends on the scale at which the popu- lation is observed. The gannets shown in Figure 19-3b are uni- formly distributed on a scale of a few meters. However, if the entire island on which the gannets live is observed, the distribution appears clumped because the birds live only near the shore. POPULATION DYNAMICS All populations are dynamic—they change in size and composition over time. To understand these changes, scientists must know more than the population’s size, density, and dispersion. One important measure is the birth rate, the number of births occur- ring in a period of time. In the United States, for example, there are about 4 million births per year. A second important measure is the death rate, or mortality rate, which is the number of deaths in a

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

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