Current Affairs 10th Class

  Life Processes   Life Processes There are some processes for obtaining nutrition, some help in procreating offspring. The processes which maintain body functions and are necessary for survival are called life processes.   Nutrition Nutrition is the process of intake of nutrients by an organism and the utilization of these nutrients. It is a substance that is obtained by an organism from its surrounding and used as a source of energy. Our body needs different types of nutrients in right amount. They are carbohydrates, fats, proteins, vitamins, minerals and roughage.   Mode of Nutrition                                                          Different organisms obtained their food in different ways. Thus the mode of nutrition among organisms is different. The following are the two modes of nutrition among the organisms:  
  • Autotrophic mode of nutrition: In this mode of nutrition, an organism makes its own food with the help of carbon dioxide, water and sunlight. Green plants have this mode of nutrition. Green plants make their own food by the process of photosynthesis in the presence of carbon dioxide, water and sunlight. Autotrophic bacteria also obtain their, food by this mode of nutrition. The organisms that make their own food are called autotrophs. All the green plants are called autotrophs. The green plants contain a green pigment called chlorophyll that traps the sunlight. The green plants are also called producers because they make their own food.
  • Heterotrophic mode of nutrition: In this mode of nutrition, organisms depend on other organisms for their food. All the animals come in this category. Most of the bacteria and fungi have heterotrophic mode of nutrition because they cannot make their own food. Non green plants are also called heterotrophs. The organisms that cannot make their own food are called heterotrophs.
  The following are the types of heterotrophic nutrition:
  • Saprophytic nutrition: In this mode of nutrition, an organism obtains its food from dead and decaying organic matters such as dead animals, plants, rotten bread, etc. They are called saprophytes. For example, fungi and bacteria. These organisms break down the complex organic molecule into simpler substances and absorb them as their food.
  • Parasitic nutrition: In this mode of nutrition, an organism obtains its food from the body of another living organism called host without killing that organism. In this mode of J nutrition, the organism harms the host. For example, disease causing bacteria lives in the body of the humans and causes harm to them.
  • Holozoic nutrition: In this mode of nutrition, an organism takes the complex organic food materials in its body by the process of ingestion, the ingested food is digested and then absorbed into the body cells of the organism. For example, human beings, dog, amoeba, etc.
  Steps of Nutrition The following are the steps of nutrition in animals:
  • Ingestion: It is the process of taking food into more...

  Reproduction, Control and Coordination   All the organisms reproduce to continue their existence on the earth. The production of new organism from the existing organisms of the same species is called reproduction. It is a necessary process to maintain the life on the earth. There are several ways through which animals can produce offspring. The two main methods of reproduction are sexual and asexual.   Sexual Reproduction The production of new organism with the use of their sex gametes is called sexual reproduction. This type of reproduction requires two parents who donate genes to the young one, resulting in offspring with a mix of inherited genes. Humans, animals and many other organisms reproduce by this method. Many flowering plants also reproduce by this method.   Asexual Reproduction The production of new organism without the involvement of sex gametes is called asexual reproduction. In this type of reproduction, only a single parent is required.   Types of Asexual reproduction: Fragmentation In fragmentation, parent breaks different fragments, which eventually forms new individuals. For example, spirogyra.   Regeneration In regeneration, when an animal that is capable of regeneration loses a body part, it can grow a replacement part. If the lost body part contains enough genetic information from the parent, it can regenerate into an entirely new organism. For example, sea stars, flatworms, etc.   Budding In budding, a bulb- like projection or outgrowth arises from the parent body known as bud which detaches and forms a new organism. These buds develop into tiny individuals and when get fully mature.   Vegetative propagation In this type of reproduction, any vegetative part of the plant body like leaf, stem or root develops into a complete new plant. For example, leaf in bryophyllum, stem in rose, bulb in onion, etc.   Spore formation In this mode of reproduction, the organism breaks up into a number of pieces or spores, each of which eventually develops into an organism. Spore formation is a mode of reproduction resembling multiple fission. For example. Ferns, Mosses, Rhizopus, etc.   Sexual Reproduction in Flowering Plants In sexual reproduction, the male cell produced by the male part of the flower and female cell produced by the female part of the flower fuses together. The male and female cells are called gametes. The fusion of male and female gametes is known as fertilization and leads to the formation of single cell, called zygote. The zygote divides repeatedly and gives rise to a new individual.   Structure of a flower: The flower consists of four whorls. The outermost whorl consists of sepals. Then next is petals. Then after that comes stamens and at the centre is the female whorl, called pistil. The pistil can consist of one or many carpels. The carpel has a stalklike style with a sticky tip called the stigma and swollen base called ovary. Inside the ovary, there exists egg like ovules.   All flowers do not have all the four whorls. Flowers having all more...

  Trigonometry and Its Application   The word trigonometry is a Greek word consists of two parts 'trigonon' and 'metron' which means measurements of the sides and angles of a triangle. This was basically developed to find the solutions of the problems related to the triangles in the geometry. Initially we use to measure angles in terms of degree, but now we will use another unit of measurement of angles called radians. The relation between the radian and degree measure is given by:     1 radian\[={{\left( \frac{180}{\pi } \right)}^{o}}\]and \[{{1}^{o}}=\left( \frac{\pi }{180} \right)\] radians or \[{{\pi }^{c}}={{180}^{o}}\]   Trigonametric ratios of allied angles Two angles are called allied angles when their sum or difference is either zero or a multiple of\[90{}^\circ \]. The angles\[-\text{ }\theta ,\,\,90{}^\circ \pm \theta ,\,\,180{}^\circ \pm \theta \], etc are angles allied to the angles \[\theta \]where \[\theta \]is measured in degrees.   more...
  Geometry   In this chapter we will discuss about the similarity of triangles and properties of circles. Two figures having the same shape and not necessarily the same size are called the similar figures. Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are in the same ratio. Circle is defined as the locus of a point which is at a constant distance from a fixed point. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle.   Similar Triangles Two triangles are similar, if their corresponding angles are equal and their corresponding sides are in the same ratio. The ratio of any two corresponding sides in two equiangular triangles is always the same.   Basic Proportionality Theorem It states that if a line is drawn parallel to one side of a triangle to intersect the other two sides in the distinct points, the other two sides are divided in the same ratio. Conversely, If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side of the triangle.   Area of Similar Triangles It states that the ratio of area of two similar triangles is equal to the square of the ratio of their corresponding sides.   Tangent to a Circle A tangent to a circle is a line which intersects the circle at exactly one point. The point where the tangent intersects the circle is known as the point of contact.   Properties of Tangent to a Circle Following are some properties of tangent to a circle:
  • A tangent to a circle is perpendicular to the radius through the point of contact.
  • A line drawn through the end-point of a radius and perpendicular to it is a tangent to the circle.
  • The lengths of the two tangents drawn from an external point to a circle are equal.
  • If two tangents are drawn to a circle from an external point, they subtend equal angles at the centre.
  • If two tangents are drawn to a circle from an external point, then they are equally inclined to the segment, joining the Centre to that point.
From the above points we conclude that in the following figure; \[\angle OPT=\angle OQT={{90}^{o}},\,\,\angle POT=\angle QOT\] \[\angle QTO=\angle OTP\] and \[PT=QT\].  
  • Example:
Two tangents PT and QT are drawn to a circle with center 0 from an external point as shown in the following figure, then: (a)\[\angle QTP=\angle QPO\]      (b) \[\angle QTP=2\angle QPO\] (c)\[\angle QTP=3\angle QPO\]    (d) \[\angle QTP=90{}^\circ \] (e) None of these   Answer (b) Explanation: In the given figure, we have TP = TQ [tangents drawn from an external point are equal in length] \[\Rightarrow \angle TPQ=\angle TQP\] In\[\Delta TPQ\], more...

  Heredity and Evolution   Heredity The transmission of traits from parents to their offspring is called heredity. It is the continuity of features from one generation to another generation.   Rules for the Inheritance of Traits: Menders Contribution The transmission of genetically controlled traits from one generation to another is called inheritance. Mendelian laws of inheritance states about the way certain characteristics are transmitted from one generation to another in an organism. Mendel used pea plants for his experiments. He studied the colour of flowers, their location on the plant, the shape and colour of pea pods, the shape and colour of seeds, and the length of plant stems. Mendel concluded that characteristics are transmitted from one generation to the next in pea plants.   Mendel's Laws of inheritance: Law I: Law of dominance - It states that when two homozygous individuals with one or more sets of contrasting characteristics are crossed, the characteristics which appear in the \[{{F}_{1}}\]hybrids are dominant and those which do not appear in \[{{F}_{1}}\]generation are recessive.   Law II: Law of segregation - It states that when a pair of allele is brought together in a hybrid, the members of the allelic pair remain together without mixing and separate or segregate from each other when the hybrid forms gametes.   Law III: Law of independent assortment - It states that, when a dihybrid organism forms gametes, each allelic pair (or each characteristic), the assortment of alleles of different characteristics during gamete formation is independent of their parental combinations.   Sex determination in human beings A person can have a male sex or a female sex. The process by which the sex of a person is determined is called sex determination. Genetics is involved in the determination of the sex of a person. Sex determination of a child   Evolution Evolution is the series of gradual changes that take place over millions of years. It is the change in the genetic material of a population of organisms from one generation to another. Genes are the basis of evolution that passes from one generation to another and thus produces an organism's inherited traits. The inherited traits vary within organisms.   The mechanisms that determine which variant will become more common or rare in a population are natural selection and genetic drift. Natural selection is a process that causes helpful traits to become more common in a population and harmful traits to become rarer. This happens because individuals with useful traits are more likely to reproduce. This clearly indicates that more individuals in the next generation will inherit these traits. Adaptations occur through a combination of successive, small, random changes in traits over many generations and natural selection of the variants best-suited for their environment. Genetic drift is an independent process that produces random changes in the frequency of traits in a population. Genetic drift results from the disappearance of particular genes as individuals die more...

  Light and Human Eye   Light is an electromagnetic wave which do not require a material medium for their propagation. Light is composed of particles which travel in a straight line at very high speed. Light has a dual nature i.e. waves and particles. Speed of light is different in different mediums. Speed of light in vacuum is \[3\times {{10}^{8}}m/s.\]   Reflection of Light The process of sending back the light rays which fall on the surface of an object, is called reflection of light.     Rules for obtaining images formed by concave mirrors
  • A ray of light which is parallel to the principal axis of a concave mirror, passes through its focus after refection from the mirror.
  • A ray of light passing through the centre of curvature of a concave mirror is reflected back along the same path.
  • A ray of light passing through the focus of a concave mirror becomes parallel to the principal axis after reflection.
  • A ray of light which is incident at the pole of a concave mirror is reflected back making the same angle with the principal axis.
  • \[F=\text{ }R/2\], where R = radius of curvature and F = focal length
\[\theta \] \[\sin \theta \] \[\cos \theta \] \[\tan \theta \] \[\cos \text{ec}\theta \] \[\sec \theta \] \[\cot \theta \]
\[-\theta \] \[{{90}^{o}}-\theta \] \[{{90}^{o}}+\theta \] \[{{180}^{o}}-\theta \] \[{{180}^{o}}+\theta \] \[-\sin \theta \] \[\cos \theta \] \[\cos \theta \] \[\sin \theta \] \[-\sin \theta \] \[\cos \theta \] \[\sin \theta \] \[-\sin \theta \] \[-\cos \theta \] \[-\cos \theta \] \[-\tan \theta \] \[\cot \theta \] \[-\cot \theta \] \[-\tan \theta \] \[\tan \theta \] \[-\cos \text{ec}\theta \] \[\sec \theta \] \[\sec \theta \] \[\cos \text{ec}\theta \] \[-\cos \text{ec}\theta \] \[\sec \theta \] \[\cos \text{ec}\theta \] \[-\cos \text{ec}\theta \] \[-\sec \theta \] \[-\sec \theta \]
  Sequence and Series   A particular order in which related things follow each other. Called sequence. The sequence having specified patterns is called progression. The real sequence is that sequence whose range is a subset of the real numbers. A series is defined as the expression denoting the sum of the terms of the sequence. The sum is obtained after adding the terms of the sequence. If \[{{a}_{1}},\,\,{{a}_{2}}\,\,{{a}_{3}},----,\,\,{{a}_{n}}\,\]is a sequence having n terms, then the sum of the series is given by: \[\sum\limits_{K=1}^{n}{{{a}_{k}}={{a}_{1}}+{{a}_{2}}+{{a}_{3}}+----+{{a}_{n}}}\]   Arithmetic Progression (A.P.) A sequence is said to be in arithmetic progression if the difference between its consecutive terms is a constant. The difference between the consecutive terms of an A.P. is called common difference and nth term of the sequence is called general term. If \[{{a}_{1}},\,\,{{a}_{2}}\,\,{{a}_{3}},----,\,\,{{a}_{n}}\,\]be n terms of the sequence in A.P., then nth term of the sequence is given by \[{{a}_{n}}=a+(n-1)d\], where 'a' is the first term of the sequence, 'd' is the common difference and 'n' is the number of terms in the sequence. For example 10th term of the sequence \[3,\,\,5,\,\,7,\,\,9,---\] is given by: \[{{a}_{10}}=a+9d\]    \[\Rightarrow \]   \[{{a}_{10}}=3+9\times 2=21\]   Sum of n terms of the A.P. If \[{{a}_{1}},\,\,{{a}_{2}}\,\,{{a}_{3}},---,\,\,{{a}_{n}}\,\]be n terms of the sequence in A.P., then the sum of n- terms of the sequence is given by \[{{S}_{n}}=\frac{n}{2}[2a+(n-1)d].\] For example the sum of first 10 terms of the sequence 3, 5, 7, 9, --- is given by: \[{{S}_{10}}=\frac{10}{2}[2\times 3+9\times 2]\Rightarrow {{S}_{10}}=120\] If S is the sum of the first n terms of an AP, then its \[{{n}^{th}}\]term is given by \[{{a}_{n}}={{S}_{n}}-{{S}_{n-1}}\]   Geometric Progression (G.P.) A sequence is said to be in G.P., if the ratio between its consecutive terms is constant. The sequence \[{{a}_{1}},\,\,{{a}_{2}}\,\,{{a}_{3}},---,\,\,{{a}_{n}}\,\]is said to be in G.P. If the ratio of its consecutive terms is a constant, the constant term is called common ratio of the G.P. and is denoted by r. For example any sequence of the form 2, 4, 8, 16, --- is a G.P. Here the common ratio of any two consecutive terms is 2.   If ‘r’ is the common ratio, then the nth term of the sequence is given by \[{{a}_{n}}=a{{r}^{n-1}}\] The sum of n terms of a G.P. is given by \[{{S}_{n}}=\frac{a({{r}^{n}}-1)}{r-1}\], if \[r>1\]and \[{{S}_{n}}=\frac{a(1-{{r}^{n}})}{1-r}\]if \[r<1\] Sum to infinity of a G.P. is given by \[{{S}_{\infty }}=\frac{a}{1-r}\] Harmonic Progression (H.P.) A sequence is said to be in H.P. If the reciprocal of its consecutive terms are in A.P. It has got wide application in the field of geometry and theory of sound. These progressions are generally solved by inverting the terms and using the property of arithmetic progression. Three numbers a, b, c are said to be in H.P. if, \[\frac{1}{a},\,\frac{1}{b}and\frac{1}{c}\]are in A.P.   Some Useful Results (i) Sum of first n natural numbers ie.\[1+2+3+......n=\frac{(n+1)n}{2}\] (ii) Sum of the squares of first n natural numbers ie.\[{{1}^{2}}+{{2}^{2}}+{{3}^{2}}+......{{n}^{2}}=\frac{n(n+1)(2n+1)}{6}\] (iii) Sum of the cubes of first n natural numbers
  • \[{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+......{{n}^{3}}={{\left[ \frac{n(n+1)}{2} \right]}^{2}}\]
  •   Arithmetic Mean If two numbers a more...

      Co-ordinate Geometry   In this chapter we will discuss about the two as well as three dimensional geometry. We will discuss about the position of the points and locate the point in the plane or on the surface. The three mutually perpendicular lines in the plane are called coordinate axes of the plane. The numbers in a plane which represent the position of a point is called coordinates of the point with reference to the coordinate planes. The eight equal regions into which space is divided by three dimensional axes are called octants.   Distance Formula Let us consider the two points\[A({{x}_{1}},\,\,{{y}_{1}})\]and\[B({{x}_{2}},\,\,{{y}_{2}})\] in a two dimensional plane, then the distance between the two points is given by\[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]. If it is a three dimensional plane containing the points\[A({{x}_{1}},{{y}_{1}},{{z}_{1}})\]and\[B({{x}_{2}},{{y}_{2}},{{z}_{2}})\] then the distance between the points is given by: \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}+{{({{z}_{2}}-{{z}_{1}})}^{2}}}\]   Section Formula Let us consider the point \[P(x,\,\,y)\]which divides the line segment joining \[A({{x}_{1}},\,\,{{y}_{1}})\]and \[B({{x}_{2}},\,\,{{y}_{2}})\] in the ratio k : 1 internally, then the coordinates of the point P(x, y) is given by: \[x=\frac{{{x}_{1}}+k{{x}_{2}}}{k+1}\] and \[y=\frac{{{y}_{1}}+k{{y}_{2}}}{k+1}\]   Coordinates of Midpoint The coordinates of the mid-point of a line segment AB with coordinates \[A({{x}_{1}},{{y}_{1}})\]and\[B({{x}_{2}},{{y}_{2}})\]is given by \[\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right)\] Note: (i) If the mid-point of a \[\Delta ABC\] are\[P({{x}_{1}},{{y}_{1}}),\]\[Q({{x}_{2}},{{y}_{2}})\]and \[R({{x}_{3}},{{y}_{3}})\] then its vertices will be \[A(-{{x}_{1}}+{{x}_{2}}+{{x}_{3}},-{{y}_{1}}+{{y}_{2}}+{{y}_{3}}),\]\[B({{x}_{1}}-{{x}_{2}}+{{x}_{3}},\,\,{{y}_{1}}-{{y}_{2}}+{{y}_{3}})\]and \[C({{x}_{1}}+{{x}_{2}}-{{x}_{3}},\,\,{{y}_{1}}+{{y}_{2}}-{{y}_{3}})\] (ii) The fourth vertex of a whose three vertices in order are\[({{x}_{1}},\,\,{{y}_{1}}),\,\,({{x}_{2}},\,\,{{y}_{2}})\] and \[R({{x}_{3}},\,\,{{y}_{3}})\]is \[({{x}_{1}}-{{x}_{2}}+{{x}_{3}},\,\,{{y}_{1}}-{{y}_{2}}+{{y}_{3}})\]   Centroid of a Triangle It is defined as the point of intersection of the medians of the triangle. The coordinates of centroid of a triangle with vertices\[({{x}_{1}},\,\,{{y}_{1}}),\,\,({{x}_{2}},\,\,{{y}_{2}})\]and \[({{x}_{3}}-{{y}_{3}})\]is: \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] Note: In an equilateral triangle orthocentre, centroid, circumcentre, incentre coincide.   Area of a Triangle Let\[A({{x}_{1}},\,\,{{y}_{1}})\], \[B({{x}_{2}},\,\,{{y}_{2}})\]and \[C({{x}_{3}},{{y}_{3}})\]be the vertices of a triangle, then the area of the triangle is given by: \[=\frac{1}{2}\left| {{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}}) \right|=0\]   Conditions for Collinearity Let the given points be\[A({{x}_{1}},\,\,{{y}_{1}}),B({{x}_{2}},\,\,{{y}_{2}})\]and \[C({{x}_{3}},{{y}_{3}})\]is: If A, B and C are collinear then, Area of \[\Delta ABC=0.\] \[=\frac{1}{2}\left| {{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}}) \right|=0\] Also if ABC are collinear, then slope of AB = slope of BC = slope of CA   Locus The curve described by a point which moves under given condition(s) is called its locus. The equation of the locus of a point is satisfied by the coordinates of every point.   Slope of a Line The trigonometrical tangent of the angle that a line makes with the positive direction of the x-axis in anticlockwise direction is called the slope of the line. So, slope of a line \[(m)=\tan \theta ,\]where \[\theta \]is the angle made by the line with positive direction of x-axis. Note: For any two points\[A({{x}_{1}},{{y}_{1}})\]and \[B({{x}_{2}},{{y}_{2}})\], the slope of the line is \[m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]   Equation of a Line General equation of a line is ax + by + c = 0, where a, b and c are constants and x and y are variables. The equation of a line with slope m and making an intercept c on y-axis is y =mx + c.  

      Pair of Linear Equations in two Variables and Quadratic Equation   Linear Equation in Two Variables A linear equation in two variables is an equation which contains a pair of variables which can be graphically represented in xy-plane by using the coordinate system. For example ax + by=c and dx+ ey=f, is a pair of linear equations in two variables. Solutions of the linear equation in two variables are the pair of values of the variables that satisfies the given equation. In other words, we can say that a system of linear equation is nothing but two or more linear equations that are being solved simultaneously. Mostly, the system of equations are used in the business purposes by predicting their future events. They model a real life situation in two system of equations to find the solution and manage their business. We can make an accurate prediction by using system of equations. The solution of the system of equations in two variables is an ordered pair that satisfies each equation.   Graphical Representation of a Pair of Linear Equations in Two Variables If \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]are a pair of linear equations in two variables such that:
    • If\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\], then pair of linear equations is consistent with a unique solution.
    • If\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\], then the pair of linear equations is consistent and dependent and having infinitely many solutions.
    • If\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\], then the pair of linear equations is inconsistent and have no solution.
      Unique Solution If the lines represented by a pair of linear equations are intersecting each other at one point, then the system is said to have unique solution. The point at which the two lines intersect each other is called the solution of the system of equation.   No Solution If the graph of the system of equation is parallel and does not intersect each other at any point, then it is said to have no solution.   Infinitely Many Solutions If the lines represented by the pair of linear equations in two variables coincides each other, then it is said to have infinitely many solution.   Solving the System of Equations There are different algebraic methods for solving the system of linear equations. The three different methods are:
    • Elimination Method
    • Substitution Method
    • Cross Multiplication Method
    • Example:
    Find the relation between m and n for which the system of equations \[4x+6y=7and(m+n)x+(2m-n)y=21\], has unique solution. (a) 2m=3n                     (b) m = 5n       (c)\[2m\ne 3n\]               (d) \[m\ne 5n\]   Answer (d) Explanation: We have, the system of equations \[4x+6y=7\]and \[(m+n)x+(2m-n)y=21\] For a unique solution, the required condition is   \[\frac{4}{m+n}\ne \frac{6}{2m-n}\] \[\Rightarrow 8m-4n\ne 6m+6n\Rightarrow 8m-6m\ne 6n+4n\]\[\Rightarrow 2m\ne 10n\Rightarrow m\ne 5n\]   Quadratic Equation Quadratic equation is a type of polynomial of degree two. The general form of a quadratic equation is\[a{{x}^{2}}+bx+c=0\], where a, b, c are the constants and\[a\ne 0\]. The quadratic equation which contains both second and first powers of the variable is called a more...

      Electricity and Magnetic Effects of Electric Current   Electricity is the identity of modernity. It has really redefined the way of our life. Thus it has an important place in modern society. It is used almost at every place to facilitate modern activities.   Electric Current Electric current is the rate at which charge passes by a point in the circuit. The magnitude of electric current in a conductor is the amount of electric charge passing through a given point of the conductor in one second. The SI unit of current is ampere. A current of 1 ampere means that there is 1 coulomb of charge passing through a cross section of a wire in 1 second.   Electric Circuit Electric circuit is an incessant conducting path that consists of wires, electric bulb and switch between the two terminals of a cell or a battery along which an electric current flows.   Electric Circuit   Electric Potential (V) Electric potential at a point is defined as the work done in moving a unit positive charge from infinity to that point. The S.I unit of electric potential is volt.   Potential Difference Potential difference is defined as the amount of work done in moving a unit charge from one point to the other point. \[V=\frac{W}{Q}\] Where, V is potential difference W is work done Q, is charge moved   Heating Effect of Electric Current Through a high resistance wire when an electric current is passed, it becomes very hot and produces heat. This phenomenon is known as Heating Effect of current. \[H={{I}^{2}}RT\] Where H = heat produced I = current R = resistance of wire t = time, for which current is passed This is known as Joule's law of heating.   Ohm's Law Ohm's law represents the relationship between current and potential difference. According to Ohm's law the current flowing through a conductor between two points is directly proportional to the potential difference and inversely proportional to the resistance between them when the temperature and pressure remains the same. \[V\alpha I\] V=IR So, I=V/R Where, I is the current v is the potential difference R is the resistance.   Electric Power Electric power is the electric work done per unit time. The S.I unit of electric power is watt. \[\text{Power=}\frac{\text{Work}\,\,\text{done}}{\text{Time}\,\,\text{taken}}\] \[P=\frac{W}{t}\] By substituting from\[W=VIT\], we obtain the formula for the power dissipated in an electric circuit, as follows: \[Power\,\,P=VI\] This formula gives the power which is degenerated when a current I moves through a conductor when there is a potential difference V. From Ohm's law, we can write: \[\begin{align}   & Power\,\,P={{I}_{2}}R \\  & and\,\,\,P={{V}_{2}}/R \\ \end{align}\]   Magnetic Field Magnetic field is the space/region around a magnet in which magnetic force is exerted. Electric current produces magnetic field. The SI unit for magnetic field is Tesla. The strength of magnetic field is indicated by the degree of closeness of the field lines. Where the field lines more...


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        Object Position Image Position Nature of Image
    (a) at infinity at the focus F real and point-sized
    (b) between infinity and the center of curvature C