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Chapter 3, , Current Electricity, , e Introduction, © Electric Current, , e Electric Current in, Conductors, , © Ohm's Law, , © Drift of Electrons and the, Origin of Resistivity, , e Limitations of Ohm's Law, e Resistivity of Various, Materials, , © Temperature Dependence of, , Resistivity, e Electrical Energy, Power, , e Combination of Resistors, ~ Series and Parallel, , e Cells, emf, Internal, Resistance, , © Cells in Series and Parallel, ¢ Kirchhoff's Rules, , ® Wheatstone Bridge, , ¢ Meter Bridge, , e Potentiometer, , Some Important Definitions, e@ Formulae Chart, , @ Quick Recap, , Chapter Contents, , Introduction, , We considered all charges whether free or bound to be at rest in, previous two chapters. Charges in motion constitute an electric, current. Such currents occur naturally as well as artificially. Lightening, is one of the natural phenomena in which charges flow from clouds to, earth through the atmosphere. The current produced during lightening, is not steady., , Artificially, current is generated by dynamo, inverters, cells etc. The, currents through devices like cell-driven clocks, torch etc., are steady., , In this chapter we study some basic laws concerning steady electric, current and their applications., , ELECTRIC CURRENT, , Consider a small area A kept perpendicular to the direction of flow of charges, as shown in figure., , A, , , , %, , , , , , 42%, q, , , Positive charges q, are flowing from left to right and negative charge q_ are, flowing from right to left across the area. Net charge flowing through the area, in the interval ¢ from left to right, q = q, - q_., , For steady current q is proportional to ft., , The quotient = 1 is defined as the current across the area in the direction, , left to right. If the quotient is negative then the current is in the direction, right to left., , Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456

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192 Current Electricity Board & Competitive Exams., , But currents are not always steady. In that case we define current in two ways, , 1. Average current, , 2. Instantaneous current, , If AQ charge flows through any cross-section of conductor in the interval t to tf + Af, then average current, , in that interval is defined as the ratio of AQ to Af; /,, = Be., If the limit of At is tending to zero, then the current is defined to be instantaneous current at time ¢,, r= we 42.89, , At—0 At at”, , Direction of current is taken as direction of motion of positively charged particles and opposite to the direction, of negatively charged particles., , SI unit of current is ampere (A), , Order of currents in domestic appliances is 1 A, , Order of currents in our nerves is 1 pA, , Order of current in lightening is 10* A, , Example 1: 10° positrons are flowing normally through an area in forward direction and same amount of, electrons are flowing in backward direction in the interval of 10 ms. Find the current through the, area., , Solution : q. = 108 x 1.6 x 10-9 C = 1.6 x 10°C, , q_ = 108 x (-1.6 x 10-9 C) = -1.6 x 10°C, = 1.6 « 10-13 C — (-1.6 x 10-9 C), =3.2«10-3C, , , , , , Net charge through the area q = q, — q., , ~13, Current through the area pad 82x10 76 32x10 A, t 10x10~ s, , , , Example 2: Charge through a cross-section of a conductor is given by Q = (2f? + 5t)C. Find the current through, the conductor at the instant t = 2 s., , Solution : Charge Q = (2f? + 5t) C, dQ_d,.2, Instantaneous current / = — = —, I at an +5t), =4t+5, Att=2s,/=(4* 2)+5=13A, , , , =, , Example 3: /n neon gas discharge tube 2.9 x 10'® Ne* ions move to the right through a cross-section of the, tube each second, while 1.2 = 101° electrons move to the left in this time. The electronic charge, is 1.6 x 10-'? coulomb. What is the net electric current in the tube?, , Solution : Here since positive and negative charges are moving in opposite directions their equivalent current, is in the same direction i.e. in the direction in which the positive ions are moving. So the total, current will be the sum of the currents due to individual positive and negative charges., , (a, +n,ye _ (2.9 10" + 1.210") x 1.6 x 107", , Hence net current = qs, , t, direction in which the positive charge is moving., , nay, Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road, New Dethi-110005 Ph. 011-47623456, , = 0.66 A to the right i.e. the

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Board & Competitive Exams. Current Electricity 193, , , , Example 4: /n the Bohr’s model of hydrogen atom, the electron is assumed to rotate in a circular orbit of radius, 5% 10-" m, at a speed of 2.2 « 10° m/s. What is the current associated with electron motion?, , q_ Ww (= Setange - 2%), , Solution: = / = + * Onn speed v, , 1.6 x10" Cx 2.2«10°m/s 3, ee F112 107 A, 2nx5x10"'m *, , 1.12 mA, , , , , , Example 5: The current in a wire varies with time according to the relation i = 2.0A + (0.6A/s?)t?. (a) How many, coulomb of charge pass a cross-section of the wire in the time interval between, t = 0 and t = 10s? (b) What constant current would transport the same charge in the same time, , , , , , , , interval?, tos, Solution : (@) q= fia = Je 0A +(0.6As ?)t? Jot, = fasarsomnnt, 3 lo, = (2.0 A) (10s) + (0.6 As~2) fost = 20 As + 200 As, , = 220 As = 220 coulomb, , (b) Constant current i = 9 _ 220C _a5,, t 10s, Try Yourself, , 1. Charge through a cross-section of a conductor is given by Q = 5f — 2t coulomb. Find the, average current through the conductor in the interval t, = 2 s to t, = 4 s., (1) 144A (2) 28A, (3) 56A (4) 7A, , 2. If 1,, 1, and /, are the orders of the currents through our nerves, domestic appliances and, average lightening, then the correct order of currents is, (1) > h>ly 2) >k>h, 8) 4<h<h 4 L=h=h, , 3. For driving current of 2 A for 6 minute in a circuit, 1000 J of work is to be done. The emf of, the source of the circuit is, (1) 1.38 V (2) 1.68V, (3) 2.03 V (4) 3.10V, , Hint : emf = work,, it, , 4. The potential difference applied to an X-ray tube is 5 kV and the current through it is 3.2 mA., Then the number of electrons striking the target per second is, (1) 2x 10°6 (2) 5 x 10%, (3) 1x 107 (4) 4x 1018, , Hint : 1=%.. t= 2x10", , , , , , , , Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456

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194, , , , Current Electricity Board & Competitive Exams., , Knowledge Cloud, , Instantaneous current through a cross-section | = 22, , Charge passed through the cross-section in the interval t to t+ ot, dQ = Idt, Total charge in the interval f, to t,, , fe, Q= Jiat = Area below / versus tf graph in the interval t, to t, as shown in figure., 4, , Average current in the interval f, to t, , ‘a, l= Q -4 _ Area below / versus t graph, " b-t tb-t Time interval, , , , , , » Did You Know?, , Blood flow in human body can be simulated by current flow in electrical circuits and hence this, , chapter finds several direct and indirect biological applications like, , 1. In technique of a impedance plethysmography the electrical resistance of a part of body is, measured to diagnose deep venous thrombosis (blood clotting in the veins), , 2. Heart pace-makers incorporate RC circuits to control the timing of voltage pulses that are, delivered to a malfunctioning heart to regulate its beating cycle., , , , , , , , ELECTRIC CURRENT IN CONDUCTORS, , , , If an electric field is applied to an electric charge, it will experience a force. If it is free to move, then it will, contribute to a current., , In atoms and molecules, negatively charged electrons and positively charged nuclei are bound to each other, and thus are not free to move in electric field., , In some materials, the electrons will still be bound so when electric field is applied, they will not accelerate, to develop current. These materials are generally called insulators. In electric solutions both positive and, negative ions move to develop current., , In bulk matter these molecules are so closely packed that electrons no longer are attached to individual, nuclei. If an electric field is applied some of the electrons are practically free to move within the bulk material, to develop currents in them. These materials are generally called conductors and these electrons are known, as free electrons., , In the absence of electric field, the electrons move with their thermal motion. During their motion they collide, with fixed ions such that their speed before collision is equal to speed after collision but the direction of, velocity after collision is completely random. Therefore, number of electrons in any direction will be equal, to the number of electrons travelling in opposite direction, so there is no net electric current., , , , Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road. New Delhi-110005 Ph. 011-47623456

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Board & Competitive Exams. Current Electricity 195, , Now electric field E is produced along the conductor AB by using two charged insulating discs carrying, charge +Q and —Q as shown in figure., , The electrons will be accelerated due to this field E from end B to A to neutralise the charges on discs, gradually. The motion constitute an electric current. The current will stop after a short time. If the charges, in the discs are maintained to keep E constant by some mechanism then a steady continuous current can, , be established in the conductor. To maintain the steady electric field, cells or batteries are used across the, conductor., , , , Example 6 : What do you mean by thermal motion of free electrons in conductors?, Solution : In conductors some of the electrons are practically free to move within the conductor. Kinetic, , energy of these electrons depends on the temperature T of conductor i.e., E = gar, where, k = Boltzmann constant. So, the motion in these electrons is known as thermal motion., , , , _ —___ Example 7: Can electrons produce current due to their thermal speed. Explain., , Solution : No, velocity of free electrons during thermal motion is random. So, their net flow through any cross, section is zero., , , , , , Try Yourself, , 5. Aconductor is at T Kelvin. Find the thermal speed of free electrons of the conductor., , 6. How does electric current flow along a conductor, when electric field is applied along the length, of conductor?, , , , , , , , OHM’S LAW, , It was discovered by G.S. Ohm in 1828. If V be the potential difference between the ends of the conductor, through which a current / is flowing, then Ohm's law states that, , , , Ve lorV=RI, where R is the proportionality constant known as Resistance of the conductor, SI unit of resistance are VA-!, or ohm (Q)., , Resistance of the conductor depends on, 1. Dimensions of conductor and, 2. Material of conductor, , Dependence of Resistance on Length of Conductor, Consider a conductor satisfying V = Ri/ to be in the form of a slab of length / and cross-sectional area A., + /—, , , , A, , , , , , —*), , , , —_v—, , , , Resistance of slab = 7 =R «-(1), , Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456