F,Sc Physics Part II Chapter 13

ELECTRIC CURRENT
	ELECTRIC CURRENT
	"Electric current is defined as the amount of electric charge                                    passing through a cross section of a conductor in unit time."In other words                                "The rate of flow of electric charge through a cross                                                                           section of a conductor is called Electric Current". Mathematically                                          Electric current = electric charge / time
		Unit of electric current is AMPERE.      1 ampere = 1 coulomb / 1 sec
		AMPERE
	In S.I system unit of electric current is ampere. Ampere is defined as:                      “Current through a conductor will be 1 ampere if one coulomb of electric                             charge passes through any cross section of conductor in 1 second.”                                                                         1 ampere = 1 coulomb / 1 sec
		DIRECTION OF CURRENT
	There are two types of current.
	ELECTRONIC CURRENT
	Electronic current flows from negative to positive terminal.
	CONVENTIONAL CURRENT
	Direction of conventional current is taken from higher potential to the lower potential. RESISTANCE RESISTANCE Opposition offered by the material of conductor in the flow of electric current is called resistance. Resistance opposes the flow of current through a conductor. Resistance of a conductor is due to the collision of free electrons with the atoms of the conductor. It is denoted by “R” FACTORS ON WHICH RESISTANCE DEPENDS (1) Length of conductor Resistance of a conductor is directly proportional to the length of conductor .                                                         R a L…………….(a) (2) Area of cross section of conductor Resistance of a conductor is inversely proportional to area of cross section of conductor.                                                         R a 1 / A……………….(b) Combining (a) and (b)                                                 Where  r = resistivity of material of conductor RESISTIVITY Resistivity is an electrical property of material . It is defined as the resistance of a material or conductor of 1 cubic meter volume.                                         Or It is the resistance of a conductor of unit length and unit area.                                         Or Resistivity of a conductor is the resistance of 1 meter long conductor whose area of cross section is I meter square Unit:     r = ohm x m Different materials have different values of resistivity. A very high value of resistivity indicates high electrical resistance RESISTANCE AND TEMPERATURE Resistance of a conductor is directly proportional to temperature. Reason : With the increase in temperature, vibrational motion of the atoms of conductor increases. Due to increase in vibration, probability of collision between atoms and electrons increases. As a result, resistance of conductor increases. VARIATION IN RESISTANCE OF A MATERIAL AT DIFFERENT TEMPERATURES: (1) Increase in resistance of a conductor is directly proportional to original resistance.                  DR  R1..............(a) (2) Change in resistance is directly proportional to change in temperature.                                                                                 DR  DT………….(b) Combining (a) and (b)                 DR  R1 DT                 DR = (constant) R1DT Here constant = a                 DR = a R1DT Where a = temperature coefficient                                      As  DR = R2 - R1 and  DT = T2  -T1 We get                             R2 – R1 = aR1 (T2 – T1)                R2 = R1 + aR1 (T2 – T1)                          R2 = R1 {1 + aT2 – T1)}When T1 = 0 and T2 = t                Rt = R0 [1 + a((t – 0)]                  Rt = R0 {1 + at} TEMPERATURE COEFFICIENT Fractional change in resistance per unit original resistance per degree change of temperature is called temperature coefficient                DR = aR1DT                   a = DR / R1 DT UNIT 1/ K OR 1/ 0C OHM'S LAW  INTRODUCTION Ohm’s law is a quantitative relation between the potential difference across the ends of a conductor and electric current flowing through it. STATEMENT According to Ohm’s law, "The electric current passing through a conductor is directly proportional to the potential difference between the ends of conductor, if physical conditions of conductor remain constant." I a V MATHEMATICAL REPRESENTATION According to Ohm’s law, I a VI = kV Where K = constant and it is called conductivity of material of conductor. V = I/K or V = I x 1/K [ but 1/K = R (resistance of conductor)] V = I x R GRAPHICAL REPRESENTATION Graph between electric current and potential difference is a straight line. SERIES COMBINATION OF RESISTORS  CHARACTERISTICS  In series combination of resistors there is only one path for the flow of electric current.  Electric current passing through each resistor is same.  Potential difference across each resistor is different and it depends upon the value or resistance.  Equivalent resistance of circuit is always greater than any of the resistance connected in the      circuit. DISADVANTAGE OF SERIES COMBINATION In series combination, if one resistance is damaged then the other resistors will not work. EQUIVALENT RESISTANCE OF CIRCUIT Consider three resistances R1, R4 and R3 connected to one another in series circuit as shown below. Let the circuit is connected to a power supply of voltage 'V' and an electric current 'I' is passing through the circuit. Potential difference across R1 is V1 Potential difference across R2 is V2 Potential difference across R3 is V3 The sum of these Potential differences is equal to 'V'. V = V1 + V2 + V3 According to Ohm's law V = IR Putting the value of V, we get, IRe = IR1 + IR2 + IR3 OR Re = R1 + R2 + R3 PARALLEL COMBINATION OF RESISTORS  CHARACTERISTICS  In parallel combination of resistors there are more than only one paths for the flow of electric      current.  Electric current passing through each resistor is different and it depends upon the value or      resistance.  Potential difference across each resistor is the same.  Equivalent resistance of circuit is always smaller than any of the resistance connected in the      circuit. ADVANTAGE OF PARALLEL COMBINATION In parallel combination, if one resistance is damaged then the other resistors will work properly because there are more than one path for the flow of electric current. EQUIVALENT RESISTANCE OF CIRCUIT Consider three resistance R1, R4 and R3 connected to one another in parallel circuit as shown below. Let the circuit is connected to a power supply of voltage 'V' and an electric current 'I' is passing through the circuit. Electric current passing through R1 is I1 Electric current passing through R2 is I2 Electric current passing through R3 is I3 The sum of all three currents is equal to 'I'. I = I1 + I2 + I3 According to Ohm's law I = V/R Putting the value of I, we get, ELECTROMOTIVE FORCE DEFINITION We know that when electric current is passed through a conductor, energy is dissipated in the form of heat energy. Hence for maintaining a steady current continuous source of energy is required. This source when connected across the resistance maintains a P.D of constant value across its ends and hence supplies energy at the rate at which it is dissipated. The devices such as dry cell, battery or electric generator are the source of emf .This strength of these sources is known as emf. Suppose “q” coulomb of charge requires an amount of work “W” joule to be transported through the source then emf in volts is given by:  EMF = W / q EMF AND TERMINAL POTENTIAL DIFFERENCE Consider a source of emf connected to a resistance “R” through which a steady current “I” flows as shown below: Let the emf of source is E Potential difference across resistance R is V We know that A source of emf also has some resistance which is due to electrolytes and electrodes. Therefore some useful energy of emf-source is used in passing the current through the source. Let the internal resistance of the source is “r” Potential drop across emf source = Vr Since Where V = terminal potential difference When no current is drawn from the source then emf and terminal potential difference are equal. If the current is passing through the circuit then the terminal potential difference is less than that of the emf of the source. Power Dissipation in Resistors When an electric current passes through a conductor, some useful electrical energy is dissipated in the form of heat energy. This loss of electrical energy is due to the collision of charges with the atoms of conductor. Loss of electrical energy in unit time is referred to as "power dissipation in resistor".                     EXPRESSION FOR POWER LOSS Let 'q' amount of electric charge passes through a conductor in unit time, the electric current through the conductor is given by:              I = q/t                            Or              q = I x t ............... (1) During the flow of electric current energy lost in the form of heat is equal to q x V, where V is the potential difference across the ends of conductor. Energy lost = q x V Putting the value of q, we get Energy lost = I x t x V Energy lost/t = VI  But Energy /t = Power Power = VI POWER LOSS IN TERMS OF CURRENT AND RESISTANCE According to Ohm's law V = IR. putting the value of V, we get Power = (IR)I Power = I2R POWER LOSS IN TERMS OF RESISTANCE AND POTENTIAL DIFFERENCE As power = VI and according to Ohm's law I = V/R, putting the value of i, we get Power = VI Power = V (V/R) Power = V2/R     UNIT OF POWER In SI system unit of power is Watt. Other large units are: 1. Kilowatt KW (1000 watt) 2. Megawatt W(106 watt)

F,Sc Physics Part II Chapter 12 ELECTROSTATICS

                             COULOMB’S LAW

INTRODUCTION
The magnitude of the force of attraction or repulsion between two electric charges at rest was studied by Charles Coulomb. He formulated a law ,known as "COULOMB'S LAW".
STATEMENT
	According to Coulomb's law:  The electrostatic force of attraction or repulsion between two point charges is directly proportional      to the product of charges.  The electrostatic force of attraction or repulsion between two point charges is inversely proportional      to the square of distance between them.
	MATHEMATICAL REPRESENTATION OF COULOMB'S LAW
	Consider two point charges q1 and q2 placed at a distance of r from each other. Let the electrostatic force between them is F.
	According to the first part of the law:
	According to the second part of the law:
	Combining above statements:
	OR                                     ---------------------(I)
	Where k is the constant of proportionality.
	VALUE OF K
	Value of K is equal to 1/4pe0
	where eo is permittivity of free space .Its volume is 8.85 x 10-12 c2/Nm2.
	Thus in S.I. system numerical value of K is 8.98755 x 109 Nm2c-2.
	OTHER FORMS OF COULOMB'S LAW
	Putting the value of K = 1/4pe0 in equation (i)
	FORCE IN THE PRESENCE OF DIELECTRIC MEDIUM
	If the space between the charges is filled with a non conducting medium or an insulator called "dielectric", it is found that the dielectric reduces the electrostatic force as compared to free space by a factor (er) called DIELECTRIC CONSTANT. It is denoted by er . This factor is also known as RELATIVE PERMITTIVITY. It has different values for different dielectric materials.
	In the presence of a dielectric between two charges the Coulomb's law is expressed as:
	VECTOR FORM OF COULOMB'S LAW
	The magnitude as well as the direction of electrostatic force can be expressed by using Coulomb's law by vector equation:
	Where  is the force exerted by q1 on q2 and  is the unit vector along the line joining the two charges from q1 to q2.ELECTRIC FIELD - ELECTRIC INTENSITY

ELECTRIC FIELD
When an electric charge is placed in space, the space around the charge is modified and if we place another test charge within this space, the test charge will experience some electrostatic force. The modified space around an electric charge is called 'ELECTRIC FIELD'.
For an exact definition we can describe an electric field as:
Space or region surrounding an electric charge or a charged body within which another charge experiences some electrostatic force of attraction or repulsion when placed at a point is called Electric Field.
ELECTRIC INTENSITY
	Electric intensity is the strength of electric field at a point.
	Electric intensity at a point is defined as the force experienced per unit positive charge at a point placed in the electric field. or It may also be also defined as the electrostatic force per unit charge which the field exerts at a point.
	Mathematically,
	E=F/q
	UNIT
	N/C or Volt/m
	The force experienced by a charge +q in an electric field depends upon. 1. magnitude of test charge (q) 2. Intensity of electric field (E) It is a vector quantity. It has the same direction as that of force.
	ELECTRIC LINES OF FORCE
	In order to point out the direction of an electric field we can draw a number of lines called electric lines of force.
	DEFINITION
	An electric line of force is an imaginary continuous line or curve drawn in an electric field such that tangent to it at any point gives the direction of the electric force at that point.The direction of a line of force is the direction along which a small free positive charge will move along the line. It is always directed from positive charge to negative charge.
	CHARACTERISTICS OF ELECTRIC LINES OF FORCE
	Lines of force originate from a positive charge and terminate to a negative charge.
	The tangent to the line of force indicates the direction of the electric field and electric force.
	Electric lines of force are always normal to the surface of charged body.
	Electric lines of force contract longitudinally.
	They and expand laterally.
	Two electric lines of force cannot intersect each other.
	Two electric lines of force proceeding in the same direction repel each other.
	Two electric lines of force proceeding in the opposite direction attract each other.  The line of force are imaginary but the field it represents as real.
	There are no lines of force inside the conductor. ELECTRIC INTENSITY DUE TO A POINT CHARGE Consider a point charge q called SOURCE CHARGE placed at a point ‘O’ in space. To find its intensity at a point ‘p’ at a distance ‘r’ from the point charge we place a test charge 'q'. The force experienced by the test charge q’ will be: F = Eq’----(1) According to coulomb's law the electrostatic force between them is given by: Putting the value of 'F' we get :                     This shows that the electric intensity due to a point charge is directly proportional to the magnitude of charge q and inversely proportional to the square of distance. EFFECT OF DIELECTRIC MEDIUM If there is a medium of dielectric constant (er) between the source charge and the field charge,intensity at a point will decrease er times i.e. VECTORIAL FORM

                                                                          ELECTRIC FLUX

GENERAL MEANING    OF ELECTRIC FLUX
In common language flux refers to the flow or stream of any thing from one point to another point. In the similar way electric flux is the total number of lines of force passing through a surface.
PHYSICAL MEANING OF ELECTRIC FLUX
	In physical sense, electric flux is defined as:
	"The total number of lines of force passing through the unit area of a surface held perpendicularly."
	MATHEMATICAL MEANING OF ELECTRIC FLUX
	Mathematically the electric flux is defined as:
	"The dot product of electric field intensity (E) and the vector area (DA) is called electric flux."
	Where q is the angle between E and DA
	MAXIMUM FLUX
	If the surface is placed perpendicular to the electric field then maximum electric lines of force will pass through the surface. Consequently maximum electric flux will pass through the surface.
	ZERO FLUX
	If the surface is placed parallel to the electric field then no electric lines of force will pass through the surface. Consequently no electric flux will pass through the surface.
	Flux is a scalar quantity .
	UNIT OF FLUX

                                   ELECTRIC FLUX THROUGH A SPHERE

Consider a small positive point charge +q placed at the centre of a closed sphere of radius "r". The relation is not applicable in this situation because the direction of electric intensity varies point to point over the surface of sphere. In order to overcome this problem the sphere is divided into a number of small and equal pieces each of area DA. The direction of electric field in each segment of sphere is the same i.e. outward normal.
Now we will determine the flux through each segment. Electric flux through the first segment:
	Electric flux through the second segment:
	Similarly,
	Electric flux through other segments:
	Being a scalar quantity, the total flux through the sphere will be equal to the algebraic sum of all these flux i.e.
	This expression shows that the total flux through the sphere is 1/eO times the charge enclosed (q) in the sphere.
	The total flux through closed sphere is independent of the radius of sphere . GAUSS’S LAW INTRODUCTION Gauss’s law is a quantitative relation which applies to any closed hypothetical surface called Gaussian surface to determine the total flux (Ø) through the surface and the net charge(q) enclosed by the surface. STATEMENT "The total electric flux through a closed surface is equal to 1/eo times the total charge enclosed by the surface." PROOF Consider a Gaussian surface as shown below which encloses a number of point charges q1,q2,q3…….qn Draw imaginary spheres around each charge. Now we make use of the fact that the electric flux through a sphere is q/eo Flux due to q1 will be Ø1 = q1/eo Flux due to q2 will be Ø2 = q2/eo Flux due to q3 will be Ø3 = q3/eo Flux due to qn will be Øn = qn/eo Hence the total flux Øe will be the sum of all flux i.e Ø = Ø1 + Ø2+ Ø3 +Ø4 ……….+ Øn                        Ø = q1/eo+ q2/eo+ q3/eo+……….. +qn/e Ø = 1/eo(q1+ q2+ q3+……….. +qn)                 Ø = 1 /eo  x ( total charge)                                 This shows that the total electric flux through a closed surface regardless of its shape or size is numerically equal to 1 /eo times the total charge enclosed by the surface. ELECTRIC INTENSITY DUE TO A SHEET OF CHARGES Consider a plane infinite sheet on which positive charges are uniformly spread. Let , The total charges on sheet = q  Total area of sheet =A  Charge density (s)= q/A (charge per unit area ) Take two points p and p’ near the sheet. Draw a cylinder from P to P'. Take this cylinder as a Gaussian surface. Consider a closed surface in front of cylinder such that p lies at one of its end faces. The angle between E and normal n to the cylindrical surface is 90 .So the flux through the cylindrical surface:  Ø = E A cos q  Ø = E A cos90Ø = E A(0) Ø = 0              The angle between E and normal n at the end of the surface P and P' is 0.hence the flux through one end surface P: Ø1 = E A cos q Ø1 = E A cos 0 Ø1 = E A (1) Ø1 = E A             Similarly the flux through other end face P': Ø2 = E A              Since electric flux is a scalar quantity, therefore, total flux through both surfaces is: Øt = D Ø1 + D Ø2 Øt = E A + E A            Øt = 2EA ...........(i) According to gauss’s law : Total flux through a closed surface is 1/ eO x (charge enclosed) i.e.             Øt = 1/ eO x q.............(ii) Comparing equations (i) and (ii) 2EA = 1/ eO x q        E = q/ eO x 1/2A or E = q/ eO 2A             E = (q/A) X 1/2 eO But q/A = s, therefore, In vector formate: Which is the expression for electric intensity due to a infinite sheet of charge. ELECTRIC INTENSITY BETWEEN TWO OPPOSITELY CHARGED PLATES Consider two oppositely charged plates placed parallel to each other. Let these plates are separated by a small distance as compared to their size. Surface density of charge on each plate is 's' .Since the electric lines of force are parallel except near the edges, each plate may be regarded as a sheet of charges. Electric intensity at a point between the plates due to positive plate:  Electric intensity at a point between the plates due to negative plate: Since both intensities are directed from +ve to –ve plate hence total intensity between the plates will be equal to the sum of E1 and E2 CAPACITOR CAPACITOR Capacitor is an electronic device, which is used to store electric charge or electrical energy A system of two conductors separated by air or any insulating material forms a capacitor as shown below: WE CANNOT STORE ELECTRIC CHARGE ON A SINGLE CONDUCTOR The size of a conductor required to store large amount of electric charge becomes very inconvenient because as the charge increases potential of plate also increases. Electric charge generated by a machine can not be stored on a conductor beyond a certain limit as its potential rises to breaking value and the charge starts leaking to atmosphere. PRINCIPLE OF CAPACITOR The principle of capacitor is based on the fact that the potential of a conductor is greatly reduced and its capacity is increased without affecting the electric charge in it by placing another earth connected conductor or an oppositely charged conductor in its neighborhood. This arrangement is therefore able to store electric charge. Capacitor are designed to have large capacity of storing electric charge without having large dimensions. PARALLEL PLATE CAPACITOR A parallel plate capacitor consists of two conducting plates of same dimensions. These plates are placed parallel to each other. Space between the plates is filled with air or any insulating material (dielectric). One plate is connected to positive terminal and other is connected to negative term- inal of power supply. The plate connected to positive terminal acquires positive charge and the other plate connected to negative terminal acquires equal negative charge .The charges are stored between the plates of capacitor due to attraction. DEPENDENCE OF CHARGE STORED IN A CAPACITOR Electric charge stored on any one of the plates of a capacitor is directly proportional to the potential difference between the plates . i.e.,                                                                                  Q a V                                                                                      OR                                                                                  Q = (constant) V                                                                                  Q = CVWhere C = capacitance of capacitor CAPACITANCE OF CAPACITOR The ability of a capacitor to store electric charge between its plates is its capacity or capacitance. DEFINITION The capacitance of a capacitor is defined as:                                          "The ratio of electric charge stored on any one of the                                   plates of capacitor to potential difference between the plates." Mathematically C = Q / V UNIT OF CAPACITANCE In S.I. system unit of capacitance is                                  Coulomb / volt                                              OR                                           Farad Farad is a large unit therefore in general practice we use small units (1) uF (microfarad) 1 uF = 1x10-6 F (2) uuF (Pico farad) 1 uuF = 1x10-12 F CAPACITANCE OF A PARALLEL PLATE CAPACITOR Consider a parallel plate capacitor as shown below: Let The area of each plate = A The separation between plates = d Medium = air Surface density of charge on each plate = s  The electric field intensity between the plates of capacitor is given by E = s / eo Potential difference between the plates of capacitor can be calculated by the following relation V = Ed Putting the value of "E" V = (s/eo) x d But s = Q/A V = Qd/A.eo AeoV = Qd…………(a) We know that The electric charge stored on any one of plate of capacitor is Q = CV……………(b) Putting the value of Q in (a) AeoV = CVd Cd = Aeo C = Aeo/d CAPACITANCE IN THE PRESENCE OF DIELECTRIC 1-When dielectric is completely filled between the plates Let the space between the plates of capacitor is filled with a dielectric of relative permittivity er. The presence of dielectric reduces the electric intensity by er times and thus the capacitance increases by er times.  C'= C x er     1-When dielectric is partially filled between the plates CONCLUSION 1- Capacitance can be increased by increasing the dimensions of plates. C a A 2- Capacitance can be increased by decreasing the separation between the plates. C a 1/d 3- Capacitance of a capacitor increases by the presence of dielectric medium between the plates. C a er