MDCAT XII-Physics PDF

CHAPTER NO.11 HEAT AND THERMODYNAMICS CARLORIC THEORY OF HEAT According to “caloric theory” (old concept) heat was considered as weightless fluid and invisible fluid. The caloric theory is old concept about heat. By using this concept, conduction could be defined. This theory...

CHAPTER NO.11 HEAT AND THERMODYNAMICS CARLORIC THEORY OF HEAT According to “caloric theory” (old concept) heat was considered as weightless fluid and invisible fluid. The caloric theory is old concept about heat. By using this concept, conduction could be defined. This theory is not fit for that, heat is produced by friction. This concept of heat fluid was challenged by count Rumford. MODERN CONCEPT OF HEAT It is the form of energy which flow from hot body to cold body due to temperature difference. Its unit is joule. Heat is also defined as the total kinetic energy of molecules. 1 calorie=4.18J and 1J=0.239calories MODE OF TRANSFER OF HEAT 1. CONDUTION Usually occurs in solids. Slowest method. In this method heat is transferred from atoms to atoms due to contact with each other. 2. CONVECTION In this method heat is transferred due to the motion of molecules. It occurs in liquids. 3. RADIATIONS Heat is transferred by electromagnetic waves. Independent of medium Fastest method. WORK AND HEAT Heat is the change in energy of body through random motion. It is less efficient way of transfer of energy. Work is change in energy of body through order motion. It is more efficient way of transfer of energy. Both work and heat are path function because they are depend on path. INTERNAL ENERGY Internal energy is State function. It is sum of Kinetic energy and Potential energy. For real gases, it is sum of all forms of Kinetic energy and Potential energy. For ideal gases, it is sum of translational Kinetic energy of molecules. The internal energy depends upon number of molecules and temperature of substance. TEMPERATURE Temperature is measure of Intensity of heat. It is degree of hotness and coldness of the body. It is average KE of molecules of substance Scales of temperature; 1. Centigrade Scale 100 parts (divisions) LFP=0°C UFP=100°C 1℃ is equal to 1.8℉. Zero Kelvin is equal to -273℃. 𝟓 ℃ = (℉ − 32) ℃ = K − 273 𝟗 2. Fahrenheit Scale 180 parts (divisions) LFP=32°F UFP=212°F 𝟗 𝟗 ℉ = (℃ + 32) ℉ = [ (K-273)] +32 𝟓 𝟓 3. Kelvin Scale Also called absolute scale or non-negative scale 100 parts (divisions) LFP=273K UFP=373K 𝟓 K= ℃ + 273 K =273+ [ (℉ - 32) ] 𝟗 Page 1 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) SOME IMPORTANT VALUES OR POINTS ABOUT SCALES OF TEMPERATURE 1°C=1.8°F 0K=-273°C=-460°F ∆T℉ = 1.8∆T℃ ∆T℃ = ∆TK ℃ = ℉ = −40° K=°F=-574.25° THERMOMETRIC PROPERTIES  Those properties which changed due to change of temperature.  Change in volume at constant pressure.  Change in pressure at constant volume.  Change in resistance of a conductor.  By using these properties, the temperature of substance can be determined. THERMAL EXPANSION  The change in dimension of a substance due to change in temperature.  Linear Expansion: The change in length of substance due to change in temperature.  According to linear expansion, the change in length is directly proportional to original length and change in temperature. ∆𝑳 ∝ 𝑳𝑶 ∆𝑻, ∆𝑳 = 𝜶𝑳𝑶 ∆𝑻  Where ‘𝜶’ is called co-efficient of linear expansion.  The co-efficient of linear expansion is the change in length per original length per degree rise in temperature OR it is the fractional change in length per degree rise in temperature.  The co-efficient of linear expansion depends upon the nature of substances and independent of the temperature.\  -1 The unit of co-efficient of linear expansion is K.  Volumetric Expansion: It occurs in all types of states of matter. It is the change in volume due to change in temperature.  According to volumetric expansion, the change in volume is directly proportional to original volume and change in temperature. ∆𝑽 ∝ 𝑽𝑶 ∆𝑻, ∆𝑽 = 𝜷𝑽𝑶 ∆𝑻 = 𝟑𝜶𝑽𝒐 ∆𝑻  Where ‘𝜷’ is called co-efficient of volumetric expansion.  The co-efficient of volumetric expansion is the change in volume per original volume per degree rise in temperature OR it is fractional change in volume per degree rise in temperature.  The co-efficient of volumetric expansion depends upon the nature of substance and independent of the temperature.  -1 The unit of co-efficient of volumetric expansion is K. BIMETALLIC STRIP  Bimetallic strip consists of two dissimilar metals having same length but different co-efficient of linear expansion.  Bimetallic strip works on thermal equilibrium.  Bimetallic strip can be used as bimetallic thermostat and bimetallic thermometer.  Bimetallic thermostat is used to control the temperature at desired value.  Bimetallic thermostat controls the temperature by making and breaking the circuit.  Bimetallic thermometer is used to measure the temperature. THERMAL EQUILIBRIUM  When two bodies have same temperature then these are say to be in thermal equilibrium.  Conditions: Same temperature, No heat flow and Same Average KE. KINETIC MOLECULAR THEORY The gas consist of enormous molecules and molecules are made up of group of atoms or atoms only. The molecules of gases are continuously in motion, they collide with each other and collide with the walls of container. The molecules of gas exerts no force on each other except during collision. The pressure of gas is result of collision of gas molecules with walls of container. The collision of gas molecules is elastic i.e. total kinetic energy and momentum remain conserved. The average KE of gas molecules is directly proportional to the absolute temperature. The Newton’s laws can be applied on gas molecules. At standard conditions, there are 3x10²⁵ molecules in a cubic meter. The molecules are separated by distance large as compared to their own dimension. The diameter of a molecules -10 considered as a sphere, about 3x10 meter. Expression for Pressure; 𝟏 ̅̅̅𝟐 ̅ 𝑷 = 𝝆𝑽 𝟑 Page 2 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  Relationship between Average KE and temperature; 𝟏 ̅̅̅𝟐 = 𝟑 𝑲𝑻 𝒎𝒗 𝟐 𝟐 Where ‘K’ is called Boltzmann’s constant; 𝑹 𝑲= = 𝟏. 𝟑𝟖 × 𝟏𝟎−𝟐𝟑 J/molecules.K. 𝑵𝑨 ROOT AND ROOT MEAN SQUARE VELOCITY Mean square velocity is directly proportional to temperature and Boltzmann's constant but inversely proportional to mass. Root mean square velocity is directly proportional to temperature and Boltzmann's constant but inversely proportional to mass. ̅𝑽̅̅𝟐̅ = 𝟑𝑲𝑻 𝑽𝒓𝒎𝒔 = √ 𝟑𝑲𝑻 𝒎 𝒎 GASES LAW 1. BOYLE’S LAW It deals with the relationship of volume and pressure of gas at constant temperature and given amount. It is applied on isothermal process. Statement: the volume of gas is inversely proportional to the pressure at constant temperature. OR The product of pressure and volume is constant at constant temperature. 𝟏 𝑷𝟏 𝑽𝟏 𝑷𝟐 𝑽𝟐 V∝ , PV=K, 𝑷𝟏 𝑽𝟏 = 𝑷𝟐 𝑽𝟐 , = 𝑷 𝒎𝟏 𝒎𝟐 The graph of Boyle’s law is parabola. If (PV) product increases than temperature also increases. 2. CHARLE’S LAW It deals with the relationship between volume and absolute temperature at constant pressure. This is valid for isobaric process. Statement: the volume of gas is directly proportional to the absolute temperature at constant pressure. 𝑽 V∝ Tabs:, = 𝑲, 𝑽 𝟏 𝑻𝟐 = 𝑽 𝟐 𝑻𝟏 𝑻 The graph of Charles’s law is straight line. The (V/T) ratio is inversely proportional to the temperature. Absolute Temperature: The temperature at which volume of gas becomes zero and all motion will be ceased and pressure and KE become zero. 3. PRESSURE LAW It deals with relationship between pressure and absolute temperature. The pressure of gas is directly proportional to the absolute temperature. This law is applied on isochoric process. Its Graph is straight line. 𝑷 P∝ T, = 𝑲, 𝑷 𝟏 𝑻𝟐 = 𝑷 𝟐 𝑻𝟏 𝑻 GENERAL GAS EQUATION This equation can be obtained by combining the Boyle’s law and Charles’s law. 𝑷𝟏 𝑽𝟏 𝑷𝟐 𝑽𝟐 = , PV=nRT 𝑻𝟏 𝑻𝟐 “R” is universal gas constant having value i.e. 8.314Jmol.K Universal gas constant depends upon nature of gas. Relationship between (K) and (R); 𝒎𝑹𝑻 𝑲 𝑴𝑲 𝑲 = 𝒏𝑹𝑻 = , 𝑹= = 𝑴 𝒏𝑻 𝒏𝑻 HEAT CAPICITY The amount of heat required to rise the temperature of substance through 1K. ∆𝑸 ∆𝑸 = 𝑪∆𝑻, 𝑪= ∆𝑻 Its SI unit is joule per kelvin (J/K). Heat capacity depends upon nature and mass of substance. SPECIFIC HEAT CAPACITY It is heat capacity per unit mass. 𝒉𝒆𝒂𝒕 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 ∆𝑸 𝒄= , 𝒄= 𝒎𝒂𝒔𝒔 𝒎∆𝑻 Its SI unit is joule per kg per kelvin (J/kg.k). It is amount of heat required to rise the temperature of 1Kg through 1 mole. It is independent of mass of substance and it only depend upon nature of substance. The specific heat capacity of water is 4180J/Kg.K or 4200J/Kg.K. Specific heat capacity is directly proportional to time for heat up. Page 3 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) MOLAR HEAT CAPICITY The amount of heat required to rise the temperature of 1 mole through 1K. ∆𝑸 𝑪𝒎 = 𝒏∆𝑻 Its SI unit is joule per mole per kelvin (J/mol.K). The product of molecular weight and specific heat capacity is called molar specific heat capacity. There are two types of molar specific heat capacities i.e. Molar Heat Capacity at constant volume (C v) and Molar Heat Capacity at constant pressure (Cp). Cv: The amount of heat required to rise the temperature of 1 mole of substance through 1K at constant volume. Cp: The amount of heat required to rise the temperature of 1mole through 1K at constant pressure. Some important relations; Cp>Cv, Cp=Cv x𝜸, 𝜸 =Cp/Cv, Cv=Cp/ 𝜸 1. MONOATOMIC GASES 𝟑 𝟓 𝟓 𝑪𝒗 = 𝑹, 𝑪𝒑 = 𝑹, 𝜸 = 𝑹 = 𝟏. 𝟔𝟔 𝟐 𝟐 𝟑 2. DIATOMIC GASES 𝟓 𝟕 𝟕 𝑪𝒗 = 𝑹, 𝑪𝒑 = 𝑹, 𝜸 = 𝑹 = 𝟏. 𝟒𝟏 𝟐 𝟐 𝟓 3. POLYATOMIC GASES 𝟒 𝜸 = 𝑹 = 𝟏. 𝟑𝟑 𝟑 LAW OF HEAT EXCHANGE Statement: Heat is lost by hot body is equal to heat is gained by cold body. This law is used to determine the specific heat capacity of the substance. THERMODYNAMICS Greek word ( therm=heat+ dynamics=power) It deals with the conversion of heat energy into other forms of energy mostly mechanical work. Types of systems; 1. Open system: Matter and Energy both can be transferred. 2. Close system: Only energy can transferred not matter. 3. Isolated system: Neither Energy not Matter can be transferred. WORK DONE IN THERMODYNAMICS W=F.d W=P∆V Its SI unit is joule. 1. WORK DONE BY SYSTEM ON SURROUNDING Work will be positive and change in volume will also be positive. Volume will increases (expansion). 2. WORK DONE ON SYSTEM BY SURROUNDING Work will be negative and change in volume will also be negative. Volume will decreases (compression). 3. WORK DONE IS ZERO No change in volume. It is Isochoric process. FIRST LAW OF THERMODYNAMICS Statement: the heat supplied to system is equal to sum of change in internal energy and work done. ∆Q= ∆U + ∆W ∆U = ∆Q − ∆W The internal energy of system can be changes by either supplying heat or doing work. The internal energy of system working in cyclic process is conversed i.e. Carnot cycle. The internal energy of isolated system is always conversed. This law gives the concept of conversation of energy. Work and Heat both are not state functions but they are path functions. SIGN AND CONVECTIONS ∆U = +ve (internal energy increases), ∆U = −ve (internal energy decreases) ∆W = +ve (expansion, work done by system) , ∆W= −ve (compression, work done on system) ∆Q= +ve( heat supplied), ∆Q= −ve (heat emitted) ZEROTH LAW OF THERMODYNAMICS  If (A) body is in thermal equilibrium with body (B) and (B) body is in thermal equilibrium with body (C) then (A and C) bodies are also in thermal equilibrium.  Bodies (A, B and C) are mutually in thermal equilibrium. Page 4 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) SPECIAL CASES OF THERMODYNAMICS 1. ISOBARIC PROCESS (iso=same + baric=pressure) A process in which pressure remain constant. ∆Q= ∆U + ∆W For isobaric expansion: ∆Q=+ve, ∆U=+ve, ∆W=+ve For isobaric compression: ∆Q=-ve, ∆U=-ve, ∆W=-ve PV diagram is horizontal line on x-axis. Charles’s law is applied. 2. ISOCHORIC PROCESS (iso=same + choric=volume) The process in which volume remain constant. Work done is zero. ∆Q = ∆U If the temperature and pressure increases then internal energy also increases. If the temperature and pressure decreases then internal energy also decreases. If ∆Q is positive then ∆U is also positive and vice versa. Pressure law is applied. PV diagram is straight vertical line. There is no expansion or compression in system because volume is constant. 3. ISOTHERMAL PROCESS (iso=same + thermal=temperature) The process in which temperature remains constant Internal energy in this process also remains constant. ∆Q = ∆W Boyle’s law is applied. It is slow process i.e. heat given very slowly. For isothermal expansion: +∆Q = +∆W For isothermal compression: −∆Q = −∆W In isothermal expansion, temperature remains constant but volume increases due to decreases in pressure. In isothermal compression, temperature remains constant but volume decreases due to increases in pressure. Phase conversion is a isothermal process. 4. ADIABATIC PROCESS The process in which no heat leaves or enter in system. Adiabatic process is also called isotropic process because in this process entropy remains constant. ∆U = ∆W It is fast process. For adiabatic expansion: +∆W= −∆U For adiabatic compression: −∆W = +∆U In adiabatic expansion, temperature and pressure will decreases while volume will increases. In adiabatic compression, temperature and pressure will increases while volume will decreases. Adiabatic expansion is cooling process while adiabatic compression is heating process. Formation of clouds, puncture of tier, etc are examples of adiabatic process. Adiabatic Constant:𝑷𝑽𝜸. Work Done: 𝑾𝒊𝒔𝒐𝒃𝒂𝒓𝒊𝒄 > 𝑾𝒊𝒔𝒐𝒕𝒉𝒆𝒓𝒎𝒂𝒍 > 𝑾𝒂𝒅𝒊𝒂𝒃𝒂𝒕𝒊𝒄 > 𝑾𝒊𝒔𝒐𝒄𝒉𝒐𝒓𝒊𝒄 HEAT ENGINE An engine that convert heat energy into mechanical energy. Efficiency of heat engine is never be 100%. Efficiency of petrol engine is 25-30%. Efficiency of diesel engine is 35-40%. Parts of heat engine; 1. Source ( hot reservoir, high temperature) 2. Sink ( cold reservoir, low temperature) 3. Cooking substance 4. Piston cylinder arrangement CARNOT ENGINE An engine which work on Carnot cycle. It consist of four process; 1. Isothermal expansion 2. Isothermal compression 3. Adiabatic expansion 4. Adiabatic compression At the end of Carnot cycle the internal energy remains same. In Carnot engine, heat is supplied in isothermal expansion only. Page 5 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  It is ideal engine because friction losses are neglected. The efficiency of Carnot engine is not be 100% but it is called ideal heat engine because losses due to frictions are ignored. It has maximum efficiency. Efficiency of Carnot engine; 𝒐𝒖𝒕𝒑𝒖𝒕 ∆𝑾 𝑸𝟏 𝑻𝟏 𝒏=[ ] × 𝟏𝟎𝟎, 𝒏=[ ] × 𝟏𝟎𝟎, 𝒏 = [𝟏 − ] × 𝟏𝟎𝟎, 𝒏 = [𝟏 − ] × 𝟏𝟎𝟎 𝒊𝒏𝒑𝒖𝒕 ∆𝑸 𝑸𝟐 𝑻𝟐 T2 is sink temperature and T1 is source temperature. Efficiency of Carnot engine can be increases by lowering T2/T1 or by increasing T1 or by decreasing T2 If the temperature of sink (T2) would be zero kelvin then efficiency of Carnot cycle would be 100%. If T1=T2, then efficiency of Carnot engine will be zero. SECOND LAW OF THERMODYNAMICS It describes the possibilities of process which may happens. Kelvin statement: the continuous supply of heat by cooling a body coldest to its surrounding is not possible. Celsius statement: it is impossible to cause heat to flow from cold body to hot body without expenditure of energy. Plank’s Kelvin statement: the efficiency of any heat engine can never be 100%. Heat engine works on Kelvin statement. Refrigerator works on Celsius statement. ENTROPY It is measure of disorder of molecules of substance. It is a state function. If phase conversion occurs then entropy increases. ∆𝑸 ∆𝑺 = ∆𝑻 Its SI unit is J/k. In isothermal expansion, entropy increases while in isothermal compression, entropy decreases. Entropy of body can be increases, decreases or remain constant. Entropy is greater order: Gases>liquids>Solids In adiabatic process, entropy remain constant The entropy of unidirectional processes always increases. The entropy of bidirectional (cyclic) processes always remain same. Entropy is also called time arrow or death of heat. The entropy of Carnot engine remains same. The entropy of universe always increases. Page 6 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) CHAPTER NO.12 ELECTROSTATICS CHARGE  It is a property of substance which is obtained by adding or removing electron(s).  There are two types of charges; 1. Positive Charge  Deficiency of electrons or loss of electrons. 2. Negative Charge  Excesses of electrons or gain of electrons.  Charge is always conserved and quantized.  Charge of any substance is integral multiple of electrons. 𝑸 = N𝒆̅  Electron is smallest unit of charge.  -19 1electron= 1.602x10 C  18 1C= 6.25x10 electrons. ELECTRIFICATION  The process of creating charge on objects. 1. CHARGE BY FRICTION  In this method two neutral substance are rubbed and get charges.  This takes place in insulators. 2. CHARGE BY CONDUCTION  In this method, there is physical contact. This take place only in conductors. 3. CHARGE BY INDUCTION  In this method, there is no physical contact.  This take place in insulators.  Repulsion is sure test of electrification. COULOMB’S LAW OF ELECTROSTATICS  st 1 law’s statement: Similar charges repel each other and opposite charges attract each other.  nd 2 law’s statement: The force of attraction or repulsion between two charges is directly proportional to the product of magnitude of charges and inversely proportional to the square of distance between them. 𝑸𝟏 𝑸𝟐 𝑸𝟏 𝑸𝟐 𝑭=𝑲 𝟐 , 𝑭= 𝒓 𝟒𝝅𝜺𝒐 𝒓𝟐  Coulomb’s law is mutual force.  Electrostatic force depends upon medium, magnitude of charges and square of distance between charges.  Coulomb’s force decreases due to presence of dielectric.  Coulomb’s law is inverse square law.  Electrostatic force depends upon field charge and test charge.  Coulomb’s law agrees with 3rd law of motion.  -15 Coulomb’s law is applicable when r>10 m. COULOMB’S CONSTANT (K)  K is called coulombs constant.  It depends upon the medium between charges and system of units.  9 2 2 Its value is 9x10 Nm /C.  Its value is maximum is air.  2 2 Its SI unit is Nm /C. 𝟏 𝑲= 𝟒𝝅𝜺𝒐 PERMEATIVITY OF FREE SPACE  𝝐𝒐 is called as permittivity of free space.  -12 2 2 Its value is 8.85x10 C /Nm. 𝟏 𝜺𝒐 = 𝟒𝝅𝑲 RELATIVE PERMEATIVITY  𝜺𝒓 is called relative permittivity or dielectric constant.  It has no unit.  Relative permittivity is the ratio of electrostatic force in vacuum to electrostatic force in medium.  The value of relative permittivity is greater than one for any non-metal, one for air and infinite for metal 𝑨𝒃𝒔𝒐𝒍𝒖𝒕𝒆 𝑷𝒆𝒓𝒎𝒊𝒕𝒕𝒊𝒗𝒊𝒕𝒚 𝑹𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝑷𝒆𝒓𝒎𝒊𝒕𝒕𝒊𝒗𝒊𝒕𝒚 = 𝑷𝒆𝒓𝒎𝒊𝒕𝒕𝒊𝒗𝒊𝒕𝒚 𝒐𝒇 𝒇𝒓𝒆𝒆 𝒔𝒑𝒂𝒄𝒆 Page 7 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) ABSOLUTE PERMITTIVITY  𝝐 Is absolute permittivity.  -1 Its SI unit is Farad.m.  Absolute permittivity= relative permittivity x permittivity of free space. ELECTRIC FIELD  It is modified region around a charge where another charge experience a force.  It is intrinsic property.  It introduced by Michael Faraday.  The presence of dielectric decreases the electric field.  Electric potential increases in opposite direction of electric field.  Electric potential decreases in direction of electric field.  It depends upon magnitude of charges, distance between charges and medium between charges.  Point charge: the charge whose size is small as compare to distance between charges.  Properties of test charges; 1. It is positive charge 2. It has very weak field. 3. It has negligible magnitude. 4. Force on test charge is larger, then field is strong. 5. Force on test charge is lesser, then field is weak. ELECTRIC FIELD INTENSITY  It is force per unit charge. 𝑭 𝑲𝒒 𝑽 𝑬= , 𝑬= , 𝑬= 𝒒𝒐 𝒓𝟐 𝒅  Its SI unit N/C or V/m.  It is vector quantity.  It depends upon only field charge and distance from field charge.  It is independent of test charge.  It is directed from positive charge to negative charge.  Electric field intensity is maximum in air. PROPERTIES OF ELECTRIC LINES OF FORCES  These lines are imaginary lines.  For positive charge these lines are radially outward and for negative charges these lines are radially inward.  Two electric lines of same charges never intersect.  If these electric lines are parallel than electric field is uniform.  If these electric lines are crowded than electric field in strong.  These electric lines start from positive charge and terminate at negative charges.  These lines can’t passed through conductors.  The direction of electrical field can be obtained by taking tangent at that point.  Electric lines are always normal to surface. ELECTRIC FLUX  The number of electric lines crossing through a surface normally or perpendicularly OR it is dot product of electric field intensity and vector area. ∅ = 𝑬. 𝑨 ∅ = 𝑬∆𝑨𝒄𝒐𝒔𝜽  Electric flux is directly proportional to electric field and vector area.  It is scalar quantity.  Electric flux is independent of area, charge position and shape of hypothetical surface.  o If the angle is less than 90 then, electric flux is positive.  o If the angle is greater than 90 then, electrical flux is negative.  o If the angle is 0 then, electrical flux is maximum.  Electrical flux is maximum when normal area is parallel to electric field and surface area is perpendicular to electrical field.  Electrical flux is zero when normal area is perpendicular to electric field and surface area is parallel to electrical field. ELECTRICAL FLUX DENSITY  The number of electric force crossing through a surface held normally per unit area is called electric flux density.  Electric flux per unit area is called electric flux density. ∅ 𝑬= 𝑨  Its SI unit is N/m or V/m. Page 8 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)   It is vector quantity.  It gives concept of electric field intensity.  The electric flux density of a surface can be increased by increasing magnitude of charge enclosed in surface. GAUSS’S LAW  Statement: The total electric flux of any hypothetical Gaussian surface is equal to 1/𝝐𝒐 times the total charge enclosed in surface. 𝟏 ∅= ∑𝒒 𝜺𝒐  Gaussian surface is always a closed surface.  If the total outward flux of any close surface is zero than net charge within surface is zero.  Gauss’s law is used to determine electric field.  The total outward electric flux of any hypothetical Gaussian surface is independent of area of surface, shape of surface and orientation of charge inside the surface.  It only dependent on the magnitude of charge enclosed inside surface.  Application of Gauss’s law; 1. ELECTRIC FIELD INTENSITY OF UNIFORMLY CHARGES SHPERE Inside the sphere→ 𝑬 = 𝟎 At the surface → 𝑬 =𝝈/𝜺𝒐 2. ELECTRIC FIELD INTENSITY OF INFINITE CHARGE SPHERE 𝝈 𝑬= 𝟐𝜺𝒐 3. ELECTRIC FIELD INTENSITY BETWEEN TWO OPPOSITELY CHARGED PLATES 𝝈 𝑬= 𝜺𝒐 4. ELECTRIC FIELD INTENSITY BETWEEN TWO SIMILAR CHARGED PLATES 𝑬=𝟎 ELECTRIC POTENTIAL DIFFERENCE  It is defined the work per unit charge between two points. 𝑾 ∆𝑽 = 𝒒𝒐  Its SI unit is volt (J/C).  Absolute Potential: it is work done per unit charge to move the charge from infinity to that point.  It is scalar quantity.  If the field charge is positive than potential is positive.  If the field charge is negative than potential is negative.  If the number of positive charges is equal to negative charges than potential difference is zero.  If the number of positive charges is not equal to negative charges than potential difference is not zero.  Electric potential varies 1/r from a point charge.  Relationship between field intensity and potential difference; 𝑽 = 𝑬. 𝒅 , 𝑬 =𝑽/𝒅 ELECTRIC POTENTIAL GRADIENT  The rate of change of potential wrt distance in an electric field. −∆𝑽 𝑬= ∆𝑺  Negative of electric potential gradient gives the concept of electric field intensity.  The electric potential decreases in direction of electric field and increases in opposite direction of electric field.  Electric potential gradient is vector quantity. ELECTRON VOLT  The KE acquired by an electron while falling through Pd of 1 volt.  It is smallest unit of energy. 𝑲𝑬 = 𝒒∆𝑽  -19 18 1ev= 1.602x10 J and 1J=6.25x10 eV. EQUIPOTENTIAL SURFACE  A surface where all the points have same potential.  The potential gradient at equipotential surface is zero.  In equipotential surface the work done is zero because electric field lines are always perpendicular to the displacement and electric field lines are normal to surface.  Two equipotential surfaces can never intersect because every surface have unique potential. CAPACITANCE AND CAPACITOR  Capacitance is the capacity of conductor to store the charge. 𝒒 ∝ 𝑽 , 𝒒 = 𝑪𝒗  Where C is capacitance Page 9 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)   The SI unit of capacitance is Farad(C/V).  Capacitance is ratio of charge and voltage.  Capacitor is device which is used to store charges. OR it is device which store the electrical energy in form of electric field.  Old name of capacitor is condenser.  Capacitor is system of two conductors separated by air or any other insulating medium.  Capacitance of conductor depends upon shape and doesn’t depend upon charges and voltage.  Net charge on capacitor is zero. PARALLEL PLATE CAPICATOR  A capacitor which consist of two plates surrounded by a distance, r with the help of air or any other insulating material. 𝑨𝜺𝒐 𝑪= 𝒅  Presence of dielectric increases the capacitance.  When a capacitor is connected to battery then voltage remains constant but charge and capacitance will increases.  When a capacitor is disconnected from battery then charge remains constant, voltage decreases but capacitance will increases.  Energy stored in capacitors; 𝟏 𝟏 𝑬 = 𝑪𝑽𝟐 , 𝑬 = 𝒒𝑽 𝟐 𝟐 COMBINATIONS OF CAPACITORS 1. SERIES COMBINATION  In this combination, each capacitor are connected end to end.  In series combination, the charge in capacitors remain same but voltage in each capacitor will be different. 𝟏 𝟏 𝟏 𝟏 𝟏 = + + +⋯+ 𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐 𝑪𝟑 𝑪𝒏  By series combination, the equivalent capacitance will decreases.  The “Ceq” will be smaller than the smallest value of combination.  For decreasing capacitance, the capacitor must be connected in series. 𝑪𝟏 × 𝑪𝟐 𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 2. PARALLEL COMBINATION  In this combination, capacitors are connected side by side through common point.  In parallel combination, the voltage in capacitor remains same but charge in each is different.  𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 + 𝑪𝟑 + ⋯ + 𝑪𝒏  By parallel combination, the equivalent capacitance will increases.  The “Ceq” will be larger than the large value of combination. CHARGING AND DISCHARGING OF CAPACITOR  When the capacitor is fully charges then its voltage is equal to voltage of battery.  Fully charged capacitor acts as open circuit.  In DC, capacitor acts as open circuit.  In AC, capacitor acts as close circuit.  RC for charging 1. After 1RC------ 63% charged and 37% uncharged 2. After 5RC--------99.3%charged  Capacitor take infinite time to charged 100%.  RC unit is second (Ohm X Farad= second). TYPES OF CAPACITORS 1. Multi plate Capacitor  A capacitor having more than two plates.  If capacitor have (n) numbers of plates than there will be (n-1) capacitors. 𝜺𝜺𝒓 𝑨 𝑪 = (𝑵 − 𝟏) 𝒅 2. Electrolytic Capacitor  Aluminum borate used as electrolyte.  It consists of two metal plates and an electrolyte used as dielectric.  This capacitor has polarity.  This capacitor has high capacitance because a thin layer act as dielectric. Page 10 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  3. Variable Capacitor  A capacitor whose capacitance can be changed.  This capacitor consists of semicircular plates, one is fixed and other is movable.  The capacitance of variable capacitor can be varied by varying area between plates.  It is used in radio for turning purpose. In this process frequency is directly proportional to the capacitance. 4. Compound Capacitor  A capacitor which is partially filled with dielectric and partially filled with air. 𝜺𝒐 𝑨 𝑪= 𝒕+(𝒅−𝒕) 𝜺𝒓 Page 11 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) CHAPTER NO.13 CURRENT ELECTRICITY INTRODUCTION The conductor is the substance having free electrons. Universal best conductor is silver. Conductance: Sliver>Copper>Gold>Aluminum Insulator is the substance having no free electrons. The importance of insulator is that, it is used for safety purpose. Eg: Wood, Plastic, etc. DRIFT VELOCITY It is average velocity acquired by electrons due to external electric field. This velocity is responsible for drift the electrons against the electric field. -3 Its value is 10 m/sec or 0.001m/sec or 1mm/sec. The drift velocity is small in magnitude but it is responsible for current production. 𝑰 𝑽𝒅 = 𝒏𝑨𝒆 THERMAL VELOCITY In conductor, electrons are moving in a random direction with a velocity called thermal velocity. This is velocity when conductor is not connected with voltage. 6 Its value is 10 m/sec. Thermal velocity is always greater than drift velocity. ELECTRONIC GAS The free electrons of conductor collectively known as electronic gas. In semiconductors, current is flowing due to holes and electrons. In conductor, current only flow due to electrons. In electrolytes, current flow due to ions. In gases, current flow due to electrons and ions. ELECTRIC CURRENT The rate of flow of electronic charges is called electric current. Its SI unit is Ampere(C/sec). 𝒒 𝑵𝒆 𝑰= = 𝒕 𝒕 The current flowing in a conductor is said to be 1ampere if 1C of charge crossing at appoint inside the conductor in one second. Current is scalar quantity. Relationship between drift velocity and current; 𝑰 = 𝒏𝑨𝒆𝑽𝒅 Direction of electric current; 1. CONNVECTIONAL CURRENT The current which flows from high potential to low potential. It is current due to flow of positive charges. 2. ELECTRONIC CURRENT The current which flow from low potential to high potential. It is current due to negative charges. Note: current always flows due to potential difference. OHM’S LAW It deals with relationship between voltage and current. Statement: the current flowing in a conductor is directly proportional to potential difference across the end of conductor provide the physical state remain same. 𝑰 𝟏 𝑰 ∝ 𝑽, 𝑰 = 𝑲𝑽, 𝑲 = = 𝑽 𝑹 Where K is conductance. Conductance is ratio of electric current or voltage. OR it is reciprocal of resistance. -1 The SI unit of conductance is mho (ohm ). The ohm’s graph is straight line. The slope of ohm’s graph gives the conductance or reciprocal of resistance. The conductors who obey ohm’s law are called ohmic conductors otherwise are called as non-ohmic conductors. Blub is non-ohmic conductor. ELECTRIC RESISTANCE The hindrance experienced by charges to flow in an electric circuit is called electric resistance. It is due to collision between atoms and electrons. Resistance is the ratio of voltage to current. The SI unit of resistance is ohm (Ω). Page 12 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  𝑽 𝟏 R= = 𝑰 𝑲 Resistance of conductor depends upon length of conductor and area of conductor. Resistance is directly proportional to length of conductor while inversely to area of conductor. 𝝆𝑳 𝑹= , ∆𝑹 = 𝜶𝑹𝒐 ∆𝑻 , 𝑹′ = 𝑹𝒐 (𝟏 + 𝜶∆𝑻) 𝑨  Where ‘𝜶’ is called temperature co-efficient of resistance. SPECIFIC RESISTANCE (RESISTIVITY) It is resistance of a unit cube. Its SI unit is ohm.m (Ωm). It depends upon nature and temperature. It is independent of length and area of conductor. Resistance of unit conductor is called resistivity. When the temperature of a conductor increases the resistance will increases. Resistance of conductor is directly proportional to rising temperature. The resistance of semiconductor decreases with increased in temperature. Resistance of semiconductor is inversely proportional to rising temperature. At zero kelvin, semiconductor behaves as insulators. 𝑹𝑨 𝝆= , ∆𝝆 = 𝜶𝝆𝒐 ∆𝑻 , 𝝆′ = 𝝆𝒐 (𝟏 + 𝜶∆𝑻) 𝑳 ‘𝜶’ is temperature coefficient of resistance. Temperature coefficient of resistance is defined as the fractional change in resistance per degree rise in temperature. -1 The SI unit of temperature coefficient is k. For conductors, temperature coefficient is positive. For semiconductors, temperature coefficient is negative. For insulators, temperature coefficient is zero. COMBINATION OF RESISTORS 1. SERIES COMBINATION Current remain same but voltage changes. The (R) is added in series to limit the current. 𝑹𝒆𝒒 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + ⋯ + 𝑹𝒏 In series the working of an element depends upon others. If one is damage than other elements will be effected or not work anymore. By connecting resistors in series, the resistance of circuit will increases. 2. PARALLEL COMBINATION Voltage remain same but current changes 𝟏 𝟏 𝟏 𝟏 𝟏 = + + + ⋯+ 𝑹𝒆𝒒 𝑹𝟏 𝑹𝟐 𝑹𝟑 𝑹𝒏 In parallel combination, equivalent resistance will be smaller than smallest ratio of combination. By connecting the resistor in parallel, the resistance of circuit will decreases. 𝑹𝟏 ×𝑹𝟐 𝑹𝒆𝒒 = 𝑹𝟏 +𝑹𝟐 In parallel combination, all devices work independently. All domestic connections are in parallel. POWER DISSIPATION IN RESISTORS Resistors always in form of heat. Power dissipation is the amount of heat generated in 1sec when current is flowing in the resistor. 𝑬 𝒒𝑽 𝑽𝟐 𝑷= , 𝑷= , 𝑷 = 𝑽𝑰 , 𝑷 = 𝑰𝟐 𝑹, 𝑷 = 𝒕 𝒕 𝑹 For series combination of resistor, P=I²R (P∝R). For parallel combination of resistor, P=V²/R (P∝𝟏/𝑹). EMF (ELECTROMOTIVE FORCE) A source is required to maintain current in circuit. Its concept is closely related to voltage. It is work done per unit charge. It is independent of resistance of circuit. It is potential difference across the terminal of battery when no load is connected. The terminal voltage becomes zero when battery is short circuited. Emf is amount of energy converted into electricity energy per charge by source. Source of Emf; 1. Battery: convert chemical energy to electrical energy 2. Solar cell: convert solar energy to electrical energy Page 13 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  3. Generator: convert mechanical energy to electrical energy  Terminal Potential Difference: Voltage across the terminals of battery or cell when it supplies current to the external resistance.  Internal Resistance: It is opposition to the flow of current inside the battery.  When battery is connected with load (E>V); 𝑬 𝑬 = 𝑽 + 𝑰𝒓 = 𝑰(𝑹 + 𝒓), 𝑽 = 𝑬 − 𝑰𝒓, 𝑰= (𝑹+𝒓)  When battery is connected with charge (V>E); 𝑬 𝑽 = 𝑬 + 𝑰𝒓, 𝑬 = 𝑽 − 𝑰𝒓 = 𝑰(𝑹 − 𝒓), 𝑰= (𝑹−𝒓) KIRCHOF’S LAWS 1. KIRCHOF’S LAW OF CURRENT Statement: The sum of current enter and current leaves at a node is always equal to zero. It is accordance with the law of conservation of charge. It is placed in junction or node. 2. KIRCHOF’S LAW OF VOLTAGE Statement: The sum of voltage in close loop is always equal to zero. This law is applied in close loop. It is accordance with the law of conservation of energy. JOULE’S LAW  When current is flowing in a resistor heat will produce. 𝑽𝟐 𝒕 𝑬 = 𝑷 × 𝒕, 𝑬 = 𝑽𝑰 × 𝒕, 𝑬 = 𝑰𝟐 𝑹𝒕, 𝑬= 𝑹 Page 14 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) CHAPTER NO.14 ELECTROMAGNETISM AND ELECTROMAGNETIC INDUCTION ELECTROMAGNETISM It is magnetic effect of electric current. Its idea was given by Hans Oersted. Magnetic field is perpendicular to electric field. The change in electrical flux produce magnetic field. Magnetic Field: Region around a magnetic in which it can attract or repel other magnet and attracts magnetic material. Methods of magnetization: Single touch method, double touch method and by applying DC current. Methods of demagnetization: Heating, Hammering, by applying reverse AC current. Permeability of free space (Uo):4πx10-7Wb/Am(T.m/A) MAGNETIC INDUCTION Magnitude of magnetic field -2 Its SI unit is Tesla (N/Am) or Wb.m. Magnetic induction depends upon magnitude of current, distance from conductor and presence of magnetic material. Magnetic induction is directly proportional to magnitude of applying current while inversely proportional to distance from conductor. 1 Tesla=10⁴Gauss (CGS unit of magnetic induction). If the distance form current carrying conductor is increased then, distance between magnetic lines will increases. MAGNETIC MATERIAL 1. DIAMAGNETIC MATERIAL (Ur>1) Those materials which have large number of unpaired electrons and their magnetic field is always greater than original magnetic field i.e. Fe, Ni, Co, etc. SHAPE OF MAGNETIC FIELD Shape of magnetic field depends upon shape of conductor. When there is a straight conductor, magnetic field will be circular. Loop or solenoid conductor behave as bar magnetic. In bar magnetic, magnetic lines are from north to south from outside which creates weak magnetic field. In bar magnetic, magnetic lines are from south to north from inside which creates strong magnetic field. DIRECTION OF MAGNETIC FIELD The direction of magnetic field depends upon direction of current. For straight conductor, Grasp Right Hand Rule is used while for Loop or solenoid Curl Right Hand Rule is used. Grasp Right Hand Rule states that Grip the current carrying conductor in right hand in such a way that thumb point out the direction of current while curl fingers shows the direction of magnetic field. Grasp Right Hand Rule is used for conventional current. If two parallel conductors carrying current in same direction then these conductors will attract each other and magnetic field between these conductors will be weak while outside is strong. If two parallel conductors carrying current in opposite direction then these conductors will repel each other and magnetic field between these conductors will be strong while outside will weak. Force between two parallel conductors carrying current; 𝝁𝒐 𝑰𝟏 𝑰𝟐 𝑭= 𝟐𝝅𝒓 Curl Right Hand Rule states that Rotation of fingers show direction of current while direction of thumb show magnetic field. The two facing loops carrying current in same direction then these loops will attract each other. The two facing loops carrying current in opposite direction then these loops will repel each other. AMPERE’S LAW Ampere's law states that Magnetic induction is directly proportional to current flowing through conductor and inversely proportional to distance from conductor. 𝑰 𝝁𝒐 𝑰 𝝁𝒐 𝑰 𝝁𝒐 𝑰 𝑩∝ , 𝑩= × , 𝑩= , 𝑩= 𝒓 𝟐𝝅 𝒓 𝟐𝝅𝒓 𝑳 It is analogous to Gauss’s law and used to determine magnetic field. Page 15 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) AMPERE’S CIRCUITAL LAW Ampere's circuital law states that the sum of product of tangential components of magnetic field of induction and length of element of the curve taken in magnetic field is equal to the 𝝁𝒐 times of the current flowing in bounded curve. ∑B. ∆L = 𝝁𝒐 𝑰 Ampere’s circuital law is used to determine magnetic field intensity inside a current carrying solenoid. SOLENOID AND TOROID Solenoid is coil wounded on long cylinder with close turns of insulated copper. 𝝁𝒐 𝑰 𝝁𝒐 𝑰 𝑩=𝑵 , 𝑩=𝑵 𝑳 𝟐𝝅𝒓 Magnetic field of solenoid is along its axis. Its magnetic field just like bar magnet. Magnetic field of solenoid is independent of its area while directly proportional to the thickness of wire from which solenoid is made. Toroids are circular solenoid. It is coil of circular core with closed turns of insulated copper. The magnetic field of toroid is within core. MAGNETIC FORCE ON CURRENT CARRYING CONDUCTOR Magnetic force on current carrying conductor is due to interaction of magnetic field. 𝑭 = 𝑰𝑳𝑩𝑺𝒊𝒏𝜽, 𝑭 ⃗ = 𝑰(𝑳 ⃗ ×𝑩⃗⃗ ) Magnetic force is perpendicular to vector length and magnetic field. To determine direction, Palm Right Hand Rule and Fleming Left Hand Rule are used. Palm Right Hand Rule and Fleming Left Hand Rule are used for convectional current. Magnetic force on current carrying conductor is maximum when angle is 90° or 270°. Magnetic force on current carrying conductor is equal to half of maximum when angle is 30°. Magnetic force on current carrying conductor is zero when angle is 0° or 180°. Palm Right Hand Rule states that On right hand, thumb show direction of current, fingers show magnetic field while palm show direction of magnetic force. Fleming Left Hand Rule states that on left hand, thumb shows direction of magnetic force, 1st finger show direction of current and middle finger show direction of magnetic field. MAGNETIC FORCE ON MOVING CHARGE Magnetic force on moving charge behave like centripetal force. Magnetic force is deflecting force so work done by magnetic force is zero due to KE remains constant. 𝑭 = 𝒒𝑽𝑩𝑺𝒊𝒏𝜽, 𝑭 ⃗ = 𝒒(𝑽⃗ ×𝑩 ⃗⃗ ) Magnetic force is perpendicular to velocity vector and magnetic field. Palm Right Hand Rule and Fleming Left Hand Rule is used to determine direction of positive charge. Magnetic force on moving charge will be maximum when angle is 90° or 270°. Magnetic force on moving charge will equal to half of maximum when angle is 30°. Magnetic force on moving charge will be zero when angle is 0° or 180°. Path of moving charge depend upon angle between velocity vector and magnetic field. When angle is 90°, then path of moving charge in magnetic field will be circular. When angle is not 90°, then path of moving charge in magnetic field will be helical. Magnetic force can’t exerted on particle when; 1. Neutral body 2. Rest charge (velocity=zero) 3. No magnetic field 4. Particle move along or opposite to magnetic field. E/m OF ELECTRON E/m of electron is also called specific charge of electron. e/m of electron is 1.7x10¹¹C/Kg (constant value). 𝒆 𝒗 𝒆 𝝎 = , = 𝒎 𝑩𝒓 𝒎 𝑩 The deflection of charge particle is depend upon mass, radius, time period and e/m value. The deflection of charge particle is inversely proportional to mass, radius and time period while only directly proportional to e/m value. deflection order: electron> proton> alpha particle e/m order: electron> proton> alpha particle E/m of electron is 1836 times of e/m of proton. TRAJECTORY OF CHARGE When charge enters in magnetic field perpendicular then its trajectory is circular. 𝒎𝒗 𝑷 𝒓= , 𝒓= 𝒒𝑩𝑺𝒊𝒏𝜽 𝒒𝑩𝑺𝒊𝒏𝜽 If the electron and proton move in uniform magnetic field in perpendicular direction with same speed then electron experiences greater deflection. Page 16 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE) SELECTOR VELOCITY The velocity at which a charged particle enters in the region of electric and magnetic field and passed without deflection. V=E/B Its SI unit is m/sec. Selector velocity is independent of charge and mass of particle. LORENTZ FORCE It is combination of electric force and magnetic force. F=Fe+FB Electric field and magnetic field will disturb each other when they are perpendicular. When electric field and magnetic field are perpendicular then electric force and magnetic force will be parallel. When electric field and magnetic field are parallel then electric force and magnetic force will be perpendicular. BIOT AND SAVRAT LAW Biot and Savrat's law states that Magnetic field is directly proportional to twice of current and inversely proportional to the distance from the conductor. 𝟐𝑰 𝝁𝒐 𝟐𝑰 𝝁𝒐 𝑰 𝝁𝒐 𝑰 𝑩∝ , 𝑩= × , 𝑩= , 𝑩= 𝒓 𝟒𝝅 𝒓 𝟐𝝅𝒓 𝑳 MAGNETIC FLUX The number of magnetic lines crossing through a surface held normally. It is dot product of magnetic field of induction and vector area. ∅ m = B∆ACosθ Its SI unit is Weber (T.m²) or (NmA-¹). Magnetic flux is scalar quantity. If the angle is less than 90° then magnetic flux is positive while if the angle is greater than 90° then magnetic flux is negative. If angle is 0° then magnetic flux is maximum while if angle is 90° then magnetic flux is minimum. When magnetic flux is maximum then surface area will be normal to magnetic field and vector area will be parallel to magnetic field. When magnetic flux is minimum then surface area will be parallel to magnetic field and vector area will be normal to magnetic field. MAGENTIC FLUX DENSITY Magnetic flux density is magnetic flux per unit area. ∆∅𝒎 𝑩= ∆𝑨 It give concept of magnetic field of induction. Its SI unit is Tesla (Wb/m²). Magnetic field is measured by fluxometer. ELECTROMAGNETIC INDUCTION The phenomenon in which Emf is generated in a conductor due to relative motion between conductor and magnetic field is called electromagnetic induction. OR it is production of induce current and induce Emf due to change of magnetic flux. Induce Emf is directly proportional to rate change of magnetic flux and independent of resistance. Induce current is directly proportional to rate change of magnetic flux and inversely proportional to resistance. Induce Emf and induce current can be increases by strong magnet with greater number of turns. LENZ’S LAW Lenz's law states that the direction of induced current is in such a way that it oppose the cause which is given to it. It is special case of law of conservation of energy. It is used to determine the direction of induced current. FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION 1st statement: The magnitude of induced Emf is directly proportional to rate of change of flux. 𝒅∅𝒎 𝑩∆𝑨𝑪𝒐𝒔𝜽 −𝑵∆∅ 𝑵∆∅ 𝑬 = −𝑵 ( ) , 𝑬 = −𝑵 ( ) , 𝑬= , 𝑬= 𝒅𝒕 𝒅𝒕 ∆𝒕 ∆𝒕 2nd statement: Average induce Emf in a conducting coil of N loops is equal to the negative of the rate at which the magnetic flux through the coil is changing with time. SELF INDUCTION AND MUTUAL INDUCTION 1. SELF INDUCTION The phenomenon in which Emf induced in the conductor of its own current. 𝑳∆𝑰 𝑬= ∆𝒕 “L” is self-inductance and its SI unit is Hennery (V.sec/A or ohm.sec). It is also called back Emf. Page 17 of 36 COMPOSED BY: ADBUL RAZAQUE MALLAH (CEO OF MK TESTING SERVICE)  Hennery/ohm is equivalent to seconds. 2. MUTUAL INDUCTION It is phenomenon in which Emf is induced in the secondary coil due to change in current of primary coil. 𝑴∆𝑰𝒑 𝑬𝒔 = ∆𝒕 “M” is mutual inductance and its SI unit is Hennery (V.sec/A or ohm.sec). Inductor coil store energy in the form of magnetic field; 𝟏 𝑼 = 𝑳𝑰𝟐 𝟐 Self-induction and mutual induction depends upon geometry of coil i.e. Number of turns, area of coil and length of coil. Self-induction and mutual induction is directly proportional to area and number of turns of coil while inversely proportional to length of coil. TRANSFORMER It is device which step up or step down voltage. Transformer work on AC only not DC. Transformer work on principle of mutual induction. Types of transformer; 1. STEP UP TRANSFORMER: Ns>Np, Vs>Vp, IsNs, Vp>Vs, Ip