electricity

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 Electricity  There are two types of phenomenon related to charges i. Static electricity or electrostatics and ii. Current electricity. Electrostatics:  Static electricity  is the study of the charges which are at rest and their effects and current electricity  is the study of charges which are in motion.  Charge is the fundamental property of matter that exhibits electrostatic repulsion or attraction.  Matter is generally made up of atoms, in atom there exist electrons which revolves around the nucleus, and inside the nucleus there are protons and neutrons. Protons and electrons are elementary charged particles.  Unit for charge is Co ulombs. We represen t it with letter C .   Protons has a mass of 1.6 x 10 -27  kg a nd a charge of + 1.6 x 10 -19 C  Electron has a mass of 9.1 x10 -31 kg and a charge of - 1.6 x 10 -19 C  Usually when a body gains electrons, it becomes negatively charged. When it loses electrons it becomes positively charged.  Whenever two bodies are charged by rubbing, one gets positively charged and the other, negatively charged. The net charge on the two bodies, however, remains zero- the same as that before rubbing. In other words charge is conserved. It can neither be created nor destroyed. Charging a body: Charging means gaining or losing of electrons. We can charge a body in different ways in such a way that it will host a positive charge or a negative charge. The nature of charge and polarity will depend on the process of charging.  Charging by friction:  When you rub one material to another, they are charged by friction. Material losing electron is positively charged and material gaining electron is negatively charged. Amount of gained and lost electron is equal to each other. Eg: Rubbing a glass rod with a silk cloth.

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  • Electricity There are two types of phenomenon related to charges i. Static electricity or electrostatics and ii. Current electricity.

    Electrostatics:

    Static electricity is the study of the charges which are at rest and their effects and current electricity is the study of charges which are in motion.

    Charge is the fundamental property of matter that exhibits electrostatic repulsion or attraction. Matter is generally made up of atoms, in atom there exist electrons which revolves around the nucleus, and inside the nucleus there are protons and neutrons. Protons and electrons are elementary charged particles. Unit for charge is Coulombs. We represent it with letter C. Protons has a mass of 1.6 x 10-27 kg and a charge of + 1.6 x 10-19 C Electron has a mass of 9.1 x10-31kg and a charge of - 1.6 x 10-19 C Usually when a body gains electrons, it becomes negatively charged. When it loses electrons it becomes positively charged. Whenever two bodies are charged by rubbing, one gets positively charged and the other, negatively charged. The net charge on the two bodies, however, remains zero- the same as that before rubbing. In other words charge is conserved. It can neither be created nor destroyed.

    Charging a body: Charging means gaining or losing of electrons. We can charge a body in different ways in such a way that it will host a positive charge or a negative charge. The nature of charge and polarity will depend on the process of charging. Charging by friction: When you rub one material to another, they are charged by friction. Material losing electron is positively charged and material gaining electron is negatively charged. Amount of gained and lost electron is equal to each other.

    Eg: Rubbing a glass rod with a silk cloth.

  • Charging by Contact: There are equal numbers of electrons and protons in a neutral matter. If something changes this balance we can say it is charged. Eg: Charging of a sphere by ebonite rod.

    Charging by induction:Induction charging is a method used to charge an object without actually touching the object to any other charged object.

    Charging by conduction Charging by conduction involves the contact of a charged object to a neutral object. The difference between charging by conduction and contact is that, in the first case, the material must be a conductor whereas the later need not be.

    Eg: The charging of a neutral sphere by another charged sphere by conduction of charge.

  • Properties of charge: If the sizes of charged bodies are very small as compared to the distances between them, we treat them as point charges. All the charge content of the body is assumed to be concentrated at one point in space. Additivity of charges: If a system contains two point charges 1 2q and q , the total charge of the system is obtained simply by adding algebraically 1 2q and q . i.e., charges add up like real numbers or they are scalars like the mass of a body. But the difference is mass always exists in positive scale whereas charge can be negative too. If a system contains n charges 1 2 3, , ... nq q q q then the total charge of the system is

    1 2 3 ..... nQ q q q q Charge is conserved: Within an isolated system consisting of many charged bodies, due to interactions among the bodies, charges may get redistributed but it is found that the total charge of the isolated system is always conserved. Conservation of charge has been established experimentally. It is not possible to create or destroy net charge carried by any isolated system although the charge carrying particles may be created or destroyed in a process.Sometimes nature creates charged particles: a neutron turns into a proton and an electron. The proton

  • and electron thus created have equal and opposite charges and the total charge is zero before and after the creation. Quantization of charge: All free charges are integral multiples of a basic unit of charge denoted by e.Thus charge qon a body is always given by Q = ne where nis any integer, positive or negative. This basic unit of charge is the charge that an electron or proton carries. By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as e and that on a proton as +e. The value of this basic unit is 1.6 x 10-19 C Solved Problems:

    Q1. Find how many electrons are present in ONE coulomb of charge. Solution: One electron contains - 1.6 x 10-19 C charge. Let n electrons carries one coulomb of charge. 1ne C

    19

    1 11.6 10

    C Cne

    186.6 10n electrons

    Coulombs law The force of attraction or repulsion between two charges is given by Coulombs law.

    Coulombs law state that the force of attraction or repulsion between two charges is - Directly proportional to the product of magnitudes of the charges,

    1 2F Q Q - Inversely proportional to the square of the distance between the two charges.

  • 21FR

    By summing the above two conditions 1 22Q QF R By applying a constant K

    1 1 22

    K Q QF NewtonsR

    Where Q1 ,Q2 are the charges; K is proportionality constant; R is the distance between the charges. The constant K is given by

    0

    14 = 9 x 109 Nm2C-2

    where 0 is called as the permittivity of free space . The value of 0 in SI units is 0 = 8.854 1012 C2N1m2

    Solved Problems:

    Q2. Two charges 10 C and 5 C are separated by a distance 2 m. Calculate the electrostatic force between them. Solution: Given Q1 = 10 C and Q2 =5 C Distance R = 2 m. From the formula: 1 22KQ QF R 2(10 5)2KF

    12.5F K

  • Q3. If the distance is doubled between two charges, find the new electrostatic force between them. Solution: Let the force of attraction between the two charges is F1. Let the new distance is R2 = 2R1

    1 22 2

    2

    KQ QFR

    1 2

    2 214

    KQ QFR

    1

    2 4FF

    Forces Between Multiple Charges: Force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual forces are unaffected due to the presence of other charges. This is termed as the principle of superposition. Conductors and Insulators: Current electricity is the study of charges in motion. Based on the motion of charge, the materials are said to be Conductors and Insulators. Conductors

    The substances which conduct electricity easily are called electric conductors. Conductors have large number of free electrons All metal are generally good conductors.

    Insulators

    The substances which do not conduct electricity Wood, rubber, mica insulators do not have free electrons.

  • Electric field: This is the area in which the force of influence of an electric charge is present. Consider a charge Q due to which a test charge q (test charge is always assumed to be positive in nature and unity magnitude) is experiencing a force F when placed at a distance r in the vacuum Then electric field due to charge Q is defined as FEq

    From Coulombs law of electrostatics, the force is expressed as 2KQqF r

    2

    kQEr

    2

    0

    1 4

    QE rr

    Where r is a unit vector Electric field is a vector quantity. The SI unit of electric field is N/C* *Volt/meter also used as unit of electric field Physical Significance of Electric Field:

    Electric field is an elegant way of characterizing the electrical environment of a system of charges. Electric field at a point in the space around a system of charges tells the force on a unit positive test charge experienceif placed at that point. Electric field is a characteristic of the system of charges and is independent of the test charge that is placed at a point to determine the field. The term fieldin physics generally refers to a quantity that is defined at every point in space and may vary from point to point. Electric field is a vector field, since force is a vector quantity.

  • Lines Of Force Of Charge: These are the imaginary lines, which show the path of a unit positive test charge placed in an electric field. When electric field is caused by a positive charge, the test charge will be repelled and moves out of the field. If we draw a line along the path of the test charge, it will be outward from the charge as shown below.

    When electric field is caused by a negative charge, the test charge will be attracted and moves towards the center. If we draw a line along the path of the test charge, it will be towards the center as shown below.

    Hence, we can conclude that i) Field lines start from positive charges and end at negative charges. If there is a single charge, they may start or end at infinity. ii) Two field lines can never cross each other. (If they did, the field at the point of intersection will not have a unique direction, which is absurd.) iii) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks. iv)Electric lines of force do not form any closed loops. This follows from the conservative nature of electric field.

  • Electric Dipole: An electric dipole is a pair of equal and opposite point charges q and q, separated by a distance 2l.By convention, the direction from q to q is said to be the direction of the dipole. The total charge of the electric dipole is obviously zero.This does not mean that the field of the electric dipole is zero.Since the charge q and q are separated by some distance, the electric fields due to them, when added, do not exactly cancel out.

    Dipole moment: The dipole moment of an electric dipole is defined as the product of magnitude of charge q and the distance of separation 2l. This is a vector quantity. ( 2 )p q l p

    Electric Current

  • The rate of flow of charges is defined as electric current.It is denoted by I.If Q is the net charge passing through any cross section of a conductor in a time t, then QIt

    If the net charge is made up of say n electrons, then neI

    t

    Current is a scalar quantity. S.I. unit of current is ampere (A). One ampere: The current passing through a conductor is said to be one ampere if the net flow of charge is one coulomb in second through its cross section.

    Q neIt t

    n- Number of charge carriers,

    e = magnitude of charge of an electron.

    Standard definition of ampere: If two infinite long parallel conductors are separated by onemeter distance in vacuum, then if the force of attraction or repulsion due to flow of current is 2 x 10-7 N then the current flowing through the conductors is said to be 1 ampere. Electric current is measured by Ammeter. This instrument is always used in series with in a circuit. Internal resistance of an ideal ammeter is zero. Solved Problems:

    Q4. A current of 10 A flows through a conductor for two minutes. Calculate the amount of charge. Solution: Given Current (I) = 10 A; Time (t) =2 minutes = 120 seconds. From the formula: QI

    t

  • Q It = 10 x 120 1200Q C

    Electric Potential: Imagine a situation, where a unit charge to be moved from infinity to a point inside an electric field. To perform this action, some work supposed to be done against the force of attraction/repulsion by the field. The amount work done to bring unit positive test charge from infinity to a point in the electric field is defined as the electric potential at that point. Usually, we dont define the absolute potential at a point but potential difference

    between two points in an electric field. It is denoted by V

    WVq

    If oAV and OBV are the potentials at points A and B in an electric field, then Potential difference between A and B is given by

    AB OB OAV V V Units: The units of electric potential are Volts.

    1 volt = 1 Joule/1coulomb Electric potential is measured by Voltmeter. This is always used in shunt.(parallel) The resistance of an ideal voltmeter is infinity.

    Solved Problems

    Q5. A and B are two points in a circuit. When a charge of 3 C passes from A to B, the work done is 18 J. Calculate the potential difference between A and B. Solution: Given W = 18 J and Q = 3 C.

    From the formula: WVQ

    18 63

    V V

  • Potential Energy Due To Single Charge: Consider a point charge Q at the origin. For definiteness, take Q to be positive.Let the potential at any point P with position vector r from the origin is to be determined. For that we must calculate the work done in bringing a unit positive test charge from infinity to the point P.

    For Q > 0, the work done against the repulsive force on the test charge is positive.Since work done is independent of the path, we choose a convenient path along the radial direction from infinity to the point P. The work done is defined as w = F. 'r Here the force can be calculated from the Coulombs law. The total work done is obtained by integrating the above equation between the limits 'r to r r

    By solving the expression for work done and substituting it in WVQ

    , we have the following expression for electric potential. 0

    1( )4

    QV rr

    Electric Circuit: An electric circuit can be defined as the path of charge (usually electrons) from a voltage source or current source. This path is always a closed loop. The different electronic components are represented by various symbols in the electric circuit. Some of them are shown below.

  • Ohms law: According to this law, at constant temperature the current passing through a conductor (i) is proportional to the voltage (V) applied to it. Mathematically V i V iR where R is a constant of the conductor, called as Resistance. Resistance is the property of a material which opposes the flow of electric current. Its S.I units are Ohms.

  • Mathematically VRi

    and 1 Ohm = 11Voltamp

    The reciprocal of resistance is called conductance.The units of conductance are Mho.

    Factors affecting the resistance of a material:

    Resistance is proportional to length of the wire. Resistance is inversely proportional to cross-sectional-area of the wire. Resistance depends on the material the wire is made of. Resistance increases with the temperature of the wire.

    Relation between Resistance, Length & Area of cross section: Usually the resistance of a material depends on its geometrical parameters like its length, area of cross section etc. So for an element, resistance is variable. Hence another parameter called as resistivity is defined. Resistance of a material is directly proportional to its length and inversely proportional to its area of cross section. Hence lR

    a

    lRa

    where is the resistivity of the material

  • For a given material, the resistivity is constant and the resistance will vary based on its geometry. The units of resistivity are Ohm-meter Some of the materials with their resistivity values are given below

    The reciprocal of resistivity gives the conductivity of a material.

    1

    Conductivity has the units Mho/meter Limitations of Ohms Law:

    Ohms law is valid at constant temperature.However, even at constant temperature, some materials do not obey Ohms law, these materials are called as Non-ohmic materials. The other materials which obeys the law are called Ohmic materials. At the variable temperature, this law doesnt obeyed by the materials.

    Resistance of a system of Resistors:

    In an electric circuit, the electronic components can be connected in two ways mainly. i) Series. ii) Parallel. A circuit composed solely of components connected in series is known as a series. i.e., the components are connected in a single path or end to end. In parallel circuits, the components are connected parallel.

  • An example of series and parallel circuits is shown below using resistors.

    System of Resistors: The resistors can be used in either series or parallel combination. Resistors in Series: When resistors are connected in series, the current in the circuit is constant and the potential across the resistors will vary, based on the resistance value. Let three resistors are connected in series as shown below.

  • If a source of voltage V is connected to the circuit, then 1 2 3V V V V From Ohms law

    1 2 3IR IR IR IR 1 2 3( )IR I R R R

    1 2 3( )R R R R Hence when resistors are connected in series, the resultant resistance is the sum of the individual resistance. Resistors in Parallel: Let three resistors are connected in parallel as shown in figure.

    From Kirchoffs current law: 1 2 3I I I I From Ohms law 1 2 3

    V V V VR R R R (Potential is constant in parallel circuit.)

    1 2 3

    1 1 1 1R R R R

  • The same can be extended for n resistors either in series or parallel. Electric Power: The power of a device is defined as the product of its rated voltage and current. i.e., P = V x I Units: Watt, horse power,Watt hour, KWH From Ohms law: V = IR

    2P I R Also, I = V/R 2VP

    R

    Solved Problems

    Q6. A conductor has a resistance of 10 Ohms resistance. If the applied voltage is 50 Volts, find the current passing through it. Solution: Given R = 10 Ohms; V = 50 V From Ohms law: VI

    R = 50

    10= 5A

    Q7. An electric heater rated as 240 V and 6 A. Find its power consumption. Solution: Given P = 240 V and I = 6 A. Power P = V x I = 240 x 6 = 1440 Watt. Heating effects of Current: When current is passing through a conductor, it generates heat. The amount of heat generated due a current I is given by

    2Q I Rt where R is the resistance of the material measured in Ohms. t is the time measured in seconds. It is said that, 1 J heat is generated, provided the current passed is 1A through a conductor of resistance 1Ohm for 1 second time.

  • Practical Applications of Heating Effect of Electric Current The heating effect occurs in the circuits because the electrons collide with atoms as they pass through a conductor. The electrons lose energy. The atoms gain energy and vibrate faster. Faster vibrations mean a higher temperature. Heating effect of electric current has many useful applications. The electric laundry iron, electric toaster, electric oven, electric kettle and electric heater The electric heating is used to produce light from an electrical lamp. The filament retains as much of the heat generated, so that it gets very hot and emits light Fuse is used in electric circuits to protect the appliances by stopping the flow of high electric current.

    Temperature Dependence Of Resistivity: The resistance of a material depends on many factors, one of the most important being the temperature. For many materials, such as conductors, the relationship between T and R is fairly linear over a wide range of temperatures. It can be written: R = Ro [1+ (T To)] where is the temperature coefficient of resistivity of the material. To is the reference temperature (i.e. room temperature) Ro is the resistance at To Usually, for conductors, the resistance decreases with decrease in temperature and for semiconductors, resistance decreases with increase in temperature. Hence conductors have the positive temperature coefficient of resistance and semi-conductors have negative temperature coefficient of resistance.