2. Electric Current. E.M.F. of a cell is defined as the maximum potential difference between the two electrodes of the

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1 2. Electric Current The net flow of charges through a etallic wire constitutes an electric current. Do you know who carries current? Current carriers In solid - the electrons in outerost orbit carries current in solid In liquid but in liquids the current carriers are ions (cations and anions) So, EMF is a force required to ove electrons. What is the source of electrootive force? Battery, dynao etc. are the source of E.M.F. How source of EMF works (battery, generator or dynao)? For battery- In gases Actually gases are insulator of current. But in soe special cases, it is possible to ake current flow in gases. The gases can be ionized at low pressure and high potential differences although gases contain positive ions and electrons. Why do gases conduct at low pressure? The electrons don't get enough tie to get accelerated.... When the gas pressure is low (but not too low), the electrons get enough tie (or distance) to accelerate. By the tie they collide with an ato, they have gained enough kinetic energy fro the electric field to ionize other atos. ELECTROMOTIVE FORCE: Response on electrootive force is different fro different author. But I will tell you a short trick to learn electrootive force. Electro eans electron and otive eans otion and force is force, so in short force required oving electron in solid. This is an electrolytic cell. Such arrangeent which does work to ove charge fro lower potential to higher potential energy is known as source of ef. Let us see how it works. An electrolytic cell consists of two rods (cathode and anode) +ve and ve rods. And an electrolyte (is a solution in tank) When electrodes are iersed in electrolyte, they exchange charges with the electrolyte due to difference in concentration of free electrons in the and electrolyte. The positive electrode acquires positive potential and negative electrode acquires negative potential. Then the axiu potential difference between the two electrodes of the cell is E =v + -(-v ) = v + +v 0 E.M.F. of a cell is defined as the axiu potential difference between the two electrodes of the

2 cell when no current is drawn fro the cell. E = E. dl SI UNIT OF E.M.F IS VOLT OR JOULE/COULOMB. ELECTRIC CURRENT: The rate of flow of charges in a definite direction is known as electric current. Electric current = total charge flown Tie taken Electric current, I= q t If in a solid conductor the net charges is q=ne (because the charges can be quantized) Then, I= ne t If Q be the net aount of positive charge flowing in a direction in a tie interval fro t+ t. Then current in a conductor q I = Liit t 0 t = dq dt Unit of current is Apere. One apere ay be defined as, if 1C of charge is flowing per second through any section of wire. Electronic current- The direction of flow of electrons is known as electronic current. Note: The flow of electric current is opposite to that of electronic current. Current is a scalar quantity because it does not follow vector law of addition. DRIFT VELOCITY: When conductor is subjected to an electric field E, each electron experiences a force. F =k q 1q 2 r 2, E= k q r 2 fro electrostatics. Force experienced by electron- F = ee F = a, a = F, a = ee here Negative sign shows that the direction of force is opposite to electric field. Here, = ass of election, e = charge, E = electric field. If solid conductor is not subjected to any electric field or under the influence of electrootive force then, the otion of all electrons are rando. And their average initial velocity is zero. As shown in figure. Direction of electric current: Conventional current or electric current The direction of flow of positive charges gives the direction of electric current. If initial velocity of 1 st, 2nd, 3rd,n th electrons is u1, u2, u3, un. u avg = u 1 + u 2 + u 3 + u n = 0 n fro 1st equation of otion v = u + at if tie taken by 1st electron is τ 1

3 τ avg = τ 1 + τ 2 + τ 3 + τ n n for 1st electron, u 1 = v 1 + aτ 1 for 2nd electron, u 2 = v 2 + aτ 2 siilarly for n th, u n = v 3 + aτ n The average velocity of all the free electrons in the conductor under the effect of external electric field is the drift velocity of the free electrons. v d or v avg = u avg + aτ avg v d = u 1 + u 2 + u 3 + u n n v d = ee τ avg, v d = 0 + a τ avg + a τ 1 + τ 2 + τ 3 + τ n n (i. e. ) a = ee τ avg = average relaxation tie, MOBILITY: Mobility of charge carrier (electron and holes) Holes in seiconductors Electrons in solid conductors ay be defined as ratio of drift velocity to electric field. Represented by µ (u) μ = v d E For electrons μ e = v d E = eτ Volue of conductor = area length V = A l Assue that there are n nubers of electrons in this conductor then Total electrons = Aln Total charge on solid, q = Alne Fro this equation we can write that E OR V= E. dl E = V l Speed = distance, tie = distance tie speed, t = l v d I = q Alne t = l v d I = Anev d and in ters obility, v d = μe So, I = AneμE OHM S LAW: At constant pressure, teperature and echanical strain etc. I V OR V I V = IR Or For holes μ h = v d E = eτ Si unit of obility is 2 s 1 V 1 RELATION BETWEEN CURRENT AND DRIFT VELOCITY: R = V I R is known as resistance.

4 Deduction of oh s law: v d = ee τ avg, E = V l v d = ev τ l Putting the value of v d in I = Anev d Suppose you have to pass through a narrow alley if it is short then easy to cross. But if it is long then we will have to suffer a little bit long. R 1/A This eans that whenever we increase the area of cross section of wire the resistance decreases and so on. In siple language if you have to go across a alley which is wide it will be easy to pass. So here ass, length, nuber, tie and area all are constant. V I = l ne 2 = R, a constant τa ELECTRICAL RESISTANCE: The physical quantity which opposes the flow of electric current is known as resistance. Si unit of resistance is oh. (Ω) Diensional forula of resistance is R = V W displaceent I = q I = F q I R = MLT 2 L A = ML2 T 2 AT A = ML 2 T 3 A 2 Cause of resistance is frequent collision of electrons with ions or atos of the conductor while drifting. RESISTIVITY OR SPECIFIC RESISTANCE: Resistance depends upon certain factors. R l This eans that whenever we increase the length of wire resistances also increases. I will ake it siple for you. R l A, R = l A ρ, ρ = R A l Here ρ is a constant known as resistivity or specific resistance Resistivity ay be defined as the resistance of a 1 long and 1 2 areas of cross section. SI unit of resistivity is oh/eter. Diensional forula ρ = R A l, ρ = ML 2 T 3 A 2 L2 L = ML 3 T 3 A 2 ρ = R A where R = l l Ane 2 τ ρ = l Ane 2 τ A l = ne 2 τ ρ = ne 2 fro this equation if τ we assue and e is constant Then ρ 1 n ρ 1 we can see that τ the value of ρ depends upon nuber of electron n and τ, the average relaxation tie. CURRENT DENSITY: Current density ay be defined as the aount of current (I) pass through any cross sectional area A. Denoted by J, J = I A J = Anev d = nev A d The SI unit of current density is A/ 2 Relation between current density and electric field

5 J = I Ane 2 Eτ A = = ne2 τe A Relation between resistivity and obility I = Anev d, v d = μe and J = I A = E ρ = nev d = neμe or ρ = 1 neμ EFFECT OF TEMPERATURE ON RESISTANCE: The value of resistance increases with increase in teperature. Suppose that RT Is resistance R at teperature T. RT=R 0 (1 + αt + βt 2 ) α AND β are teperature cofficients, their values vary fro etal to etal If T teperature is not as large as in ost cases so above expression can be expressed as RT=R 0 (1 + αt) Or we can write it as α = R T R 0 R 0 T R 2 R 1 α = R 1 (T 2 T 1 ) EFFECT OF TEMPERATURE ON RESISTIVITY: It is as sae as that of resistance just replace resistance with resistivity. ρt=ρ 0 (1 + αt) ρ 2 ρ 1 α = ρ 1 (T 2 T 1 ) = dρ dt. 1 ρ 1 GRAPHS: FOR METALS Metals: In ost etals, nuber density n of free electrons does not change with teperature but an increase in teperature increases the aplitude of vibration of lattice ions of the etal. Therefore, the Collision of free electrons with ions or atos while drifting towards the positive end of the conductor becoes ore frequent, resulting in a decrease in relaxation tie. Thus resistivity of conductor increases with increase in teperature. The value of α is positive, showing that their resistivity increase with increase in teperature. For ost etals the resistivity increases linearly with increase in teperature over a teperature range of about 500 k, above the roo teperature. Sei conductors: In case of sei- conductors, the value of α is negative. It eans the resistivity of seiconductor decreases as teperature increases Insulators: The resistivity increases exponentially with decrease in teperature in case of seiconductors. It becoes infinitely large at teperature near absolute zero i.e. the conductivity is alost zero at o k. The teperature dependence of resistivity of sei-conductors and insulators is given by: ρ = ρ 0e E g/2kt Where K= Boltzann constant ( j ole -1 k -1 )

6 T= absolute teperature E=Energy band gap between conduction band and valence band or activation energy for conduction The classification of non-conduction aterials into insulators and seiconductors depends upon the E. (i) If E= 1eV, the value of resistivity is not very high therefore, the aterials are called sei-conductors. (ii) If E 1eV, the value of resistivity is very high and the aterials are called insulators. NON-OHMIC DEVICES: The device which does not follow oh s law is known as non-ohic devices. Such as LED. (LIGHT EMITTING DIODE). (GaAs). It is a non-ohic device. Graph of voltage and current is not straight line (linear). Graph of V and I depends on the sign of V. In this graph the value of current for certain value of voltage will not be sae if the direction is changed. Graph of V and I is not unique. Here you can see that in this graph 3 dotted line are drawn parallel to each other. Each of the cuts voltage on different points. But the value of current in this graph is sae at two different values of voltage. SUPER-CONDUCTIVITY: As we already know that the value of resistance decreases with decrease in teperature. At a certain teperature (called critical teperature) the value of resistance becoes zero. This is known as superconductivity. For exaple Mercury at 4.2k Lead at 7.25k And niobiu at 9.2k becoes superconductors. RESISTANCE: IN SERIES Many students got confuse in series and parallel connection while deterining. Here is a easy ethod.

7 Suppose you are aking a huan chain holding one hand of other student and so on. V1 = IR1, V2 = IR2 and V3 = IR3. PARALLEL in volt? EMF can also be called as ter potential difference of battery like 6V OR 12V. But, this is when there is no current drawn fro battery. In other hand terinal potential difference is also potential difference as per nae but this is when the current is drawn fro battery. Assue you have a glass of water and the aount of water in glass is x. this x is EMF And soe aount of water is drawn out of glass ( x). Now the aount of water in glass is x x. this is terinal potential difference. Here question arises who draws out water or where does it go. Answer is, it is consued by resistance offered by electrolyte (solution in battery) and electrodes (cathode and anode). This well known resistance is INTERNAL RESISTANCE Of battery. Equations Internal resistance is r Capacity or EMF of battery is Here full glass of water is EMF( ) Sall aount of water drawn, v = Ir Reaining water in glass is TERMINAL P.D V = v or V = Ir r = V I, r = V V R In this case suppose you are holding both hands of your friend GROUPING OF CELLS: IN SERIES DIFFERNCE BETWEEN EMF AND TERMINAL POTENTIAL DIFFERENCE: EMF eans electrootive force is actually the capacity of battery. Which is calculated Let potential difference across 1 st cell is V 1 2 ND cell is V 2 Fro terinal P.D. forula V 1= 1 Ir 1 V 2= 2 Ir 2 So potential difference of 2 cells is algebraic su V 1 + V 2= 1 Ir Ir 2

8 = I(r 1 + r 2 ) eq = r eq = r 1 + r 2. V= eq + r eq IN PARALLEL r eq = r 1r 2 r 1 + r 2 1 Dividing eq by r eq r eq = 1 r r 2 eq r eq = 1 r r 1 r 1 + r 2 r 1 r 2 r 1 + r 2 eq r eq = 1 r r 2 n r n MIXED GROUPING OF CELLS: I = I 1 + I 2 (1) V = 1 I 1 r 1, V = 2 I 2 r 2 I 1 = 1 V r 1, I 2 = 2 V r 2 I = 1 V r V r 2 = ( 1 r r 2 ) V ( 1 r r 2 ) V = 1r r 1 r 1 +r 2 Ir 1r 2 r 1 +r 2 V = eq r eq eq = 1 r r 1 r 1 + r 2 IN each row, there are n cells. Total no. of cells in a row in series is n Their internal resistance is = nr Their EMF = n Now in colun their nubers is and are in parallel. Their internal resistance is= 1 = 1 r p nr upto ters nr = nr or r p = nr total resistance in circuit = R + nr HERE In parallel cobination of cells does affect the EMF of each cell but increase the nuber of cathode and anode. So total EMF of cells = n Current in ext. resistance,

9 I=effective EMF/Total resistance I = n R + nr or I = n R + nr Current will be axiu when R + nr will be iniu. So it can be written as ( R) 2 + ( nr) 2 2nRr + 2nRr = iniu ( R nr) 2 + 2nRr = iniu and it will be inu only when ( R nr) 2 = 0 or R nr = 0 R = nr = R = nr So we can get axiu current only when if the value of external resistance is equal to total internal resistance of the cell. Thank you Divya Ranjan Teacher (The institute of physics)