Unit 4ab tủ tài liệu training

VERY SHORT AND SHORT-ANSWERS QUESTIONS 41 What is the function of a transformer ? 42 In the given diagram will the acceleration of the magnet equal to the acceleration due to gravity g ? 43 Two similar coaxial circular loops carry equal currents in the same direction If the loops be brought nearer, what will happen to the currents in them? 44 A rectangular loop PQRS is taken away from a long straight Y current carrying wire XY.Give the direction of induced Q current, if any, in the loop [Fig A.6] 45 Why we experience a force in dragging a metallic block out of a magnetic field ? 46 An oscillating magnet stops soon if a metallic plate is placed i below it Why? 47 Fig A.7 (a) shows an irregular wire loop expanding into a circular loop in a magnetic field perpendicular to the paper in the downward direction Fig A.7(b) shows a circuP lar loop shrinking into a narrow rectangular loop in a field X directed upward Find the direction of induced current in each case S Chand & Company Limited S N Fig A.5 S R Fig A.6 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x D A x x x x x x x x x B C C B D A Fig A.7 (b) Fig A.7 (a) 48 In figure A.8 the magnitude of the electric current through the wire AB is increasing Is there any induced current in the loop ?If yes , what is its direction ? A B Fig A.8 49 The Resistance R in circuit (a) in Fig A.9 is increased What will be the direction of induced current in circuit (b)? S Chand & Company Limited R (a) (b) Fig A.9 50 Which factors govern the magnitudeof the e.m.f induced in a coil 51 A train is moving with uniform speed from north to south Does any induced e.m.f appear across the ends of its axle ? 52 A closed loop of wire is being moved without changing its orientation so that it remains inside a uniform magnetic field Is there a current induced? 53 Write one application of electromagnetic damping 54 When is the magnetic flux linked with a coil held in a magnetic field zero? 55 Does the induced e.m.f depend upon the material of the coil? 56 Why does the transformer core become hot when current passing through the primary is changed ? 57 How is the electrical energy transferred from the primary to the secondary coil of a transformer? 58 A wire of length 0.1 m moves with a speed of 10 m/s perpendicular to a magnetic field of induction Wb/m2 What is the value of the induced e.m.f.? 59 How can you increase the efficiency of a transformer? 60 What are the factors which reduce the efficiency of a transformer 61 A magnetic field of flux density 10 testa acts normal to a 50 turn coil of 100 cm2 area Find the e.m.f induced in it if this coil is removed from the field in 0.1 second S Chand & Company Limited 62 A transmission line feeds input power at 2300 V to a step down transformer having 4000 turns in its primary What should be the number of turns in the secondary to get the output power at 230 V? 63 When a magnet moves towards a coil having 1000 turns, the magnetic flux linked with the coil per turn increases from to 1.6 × 10–5 Wb in 0.1 s Calculate the induced e.m.f 64 An aeroplane, having a wingspan of 30 m, flies in the N - S direction at a horizontal speed of 80 ms– Calculate the potential difference between the tips of the wings, if the vertical component of earth’s magnetic field is × 10–5 T 65 Calculate the induced e.m.f in a 10 H induction coil in which current changes from A to A in 0.2 seconds 66 An iron bar falling vertically through the hollow region of a thick cylindrical shell made of copper experiences a retarding force What can you conclude about the iron bar ? 67 What is noninductive wiring of coils ? 68 A lamp connected in parallal with a large inductor glows brilliantly before going off when the switch is put off Why ? 69 Magnetic flux φ ( in weber) in a closed circuit of resistance 10 Ω varies with time according to the equation φ = t2 – 4t + Calculate the magnitude of the induced current in the circuit at t = 0.2 second 70 A metal piece and a stone are dropped from the same height near the earth’s surface Which one will reach the earth earlier? Neglect air friction 71 Why is the induced e.m.f at the breaking of a circuit larger than that while making the circuit? S Chand & Company Limited 72 A copper sheet oscillates between the pole pieces of a strong magnet Its oscillations are highly damped Why ? 73 Why inductance is called electrical inertia ? 74 A thick copper cylinder is filled with water and is placed in a changing magnetic field Can the water start boiling ? 75 When the current on a high voltage line is switched on or off, the birds sitting on it fly away Why ? 76 Can the magnetic flux linked with a coil placed in a uniform magnetic filed be zero ? When ? 77 The induced e.m.f is sometimes called back e.m.f Why? 78 Show that the rate of change of magnetic flux has the same unit as the potential 79 Derive the expression for the e.m.f induced between the ends of a metallic rod moving perpendicular to a uniform magnetic field (AISSCE 1993 C) 80 Show that the induced e.m.f produced by changing the area of a rectangular coil placed perpendicular to a magnetic fields is Blv, where the symbols have their usual meanings (AISSCE 1992) 81 Define mutual inductance State two factors on which the mutual inductance between a given pair of coils depends (AISSCE Delhi1999) 82 Briefly explain how lenz’s law supports the law of conservation of energy (AISSCE 1999) 83 If the number of turns is doubled in a solenoid, keeping the other factors constant, how does the self-inductance of the solenoid change ? (AISSCE Delhi - 2000) S Chand & Company Limited 84 A rectangular coil of N turns and area of cross section A is held in a time varying magnetic field given by B = B0 sin ωt, with the plane of the coil normal to the magnetic field Deduce an expression for the emf induced in the coil (AISSCE Delhi - 2000) 85 Give the direction in which the induced current flows in the wire loop when the magnet moves towards it as shown in Fig A.10 (AISSCE Delhi 1997) N S Fig A.10 ANSWERS 41 A transformer is used to convert A.C at low voltage into A.C at high voltage and vice versa 42 No The acceleration of the magnet will be less than g The direction of induced current in the metallic loop will be such as to opposes the motion of the magnet 43 The current in each loop will decrease 44 The flux linked with the loop due to the current in the wire is directed into the paper If the loop is moved away, this flux tends to decrease According to Lenz’s law, the induced current should produce inward flux Hence the current will be clockwise 45 Eddy currents are set up in the metallic block which oppose the motion of the block So we experience a force S Chand & Company Limited 46 Eddy currents are produced in the plate which oppose the motion of the magnet and hence the magnet stops soon 47 (a) When the loop becomes circular the magnetic flux (into the paper) linked with it increases due to increase in area The direction of induced current would oppose it by producing a magnetic flux out of the paper So the direction of induced current is along ABCDA, i.e., anticlockwise (b) In this case the area enclosed by the loop decreases and therefore the flux which is out of the paper decrease The induced current will produce flux out of the paper Hence the current will be anticlockwise, i.e., along ABCDA 48 The magnetic flux linked will the loop due to the current in the wire is out of the paper As the current increases this flux increases According to Lenz’s law, the induced current produces an inward flux Hence this current is clockwise 49 The direction of induced current in circuit (b) will be clockwise 50 It is equal to rate of change of magnetic flux 51 There is an induced e.m.f across the ends of axle as the axle cuts the vertical component of earth’s magnetic field 52 No, since there is no change in the magnetic flux linked with the loop 53 Electromagnetic damping is used in a dead beat galvanometer to stop the coil quickly 54 When the plane of coil is parallal to the magnetic field 55 No 56 Due to eddy currents produced in the core 57 By mutual induction 58 The induced e.m.f.is given by ε = BvL S Chand & Company Limited Here B = T, v = 10 m/s, L = 0.1 m So, ε = × 10 × 0.1 = volt 59 The efficiency of a transformer can be increased by (a) laminating the transformer core to minimize the eddy currents, (b) using core of a material for which the hysterisis loss is small, and (c) using thick copper windings to minimize joule heat 60 The different factors which reduces the efficiency of a transformer are: (a) Heating of primary and secondary coils, (b) Hysteresis loss due to loss of energy in magnetising and demagnetising the core (c) Leakage of magnetic flux (d) Eddy currents in the core 61 B = 10 T, n = 50, A = 100 cm2 = 100 × 10–4 m2 ∆ t = 0.1 s We have ε=n ∆φ n (BA – 0) = ∆t ∆t 50 × 10 × 100 × 10 –4 = 50 V 0.1 NS ES 62 Transformer ratio is given by N = E P P Here EP = 2300 V, NP = 4000 ES = 230 V = S Chand & Company Limited NS = ES 230 × NP = × 4000 2300 EP = 400 nd φ 63 | ε | = dt Here n = 1000, dφ = 1.6 × 10–5 Wb, dt = 0.1 s ∴ | ε |= 1000 × 1.6 ×10 –5 0.1 = 1.6 ×10 –1 = 0.16 V 64 ε = BvL Here B = Vertical component of earth’s magnetic field = × 10–5 T V = 80 m/s L = 30 m ∴ ε = × 10–5 × 80 × 30 = 0.19 volts 65 |ε| = L Here ∴ di dt L = 10 H di = – = 4.0 A dt = 0.2 s |ε | = 10× 4.0 = ×102 V 0.2 S Chand & Company Limited 66 The iron bar is a magnet When it falls, eddy currents are produced in the shell due to change in magnetic flux These eddy currents oppose the fall of the magnet 67 Noninductive coils are made of doubled up insulated wires In such coils, the current in the two wires flow in opposite directions, so that the net magnetic field linked with the coil is always zero and hence no inductive effect takes place 68 When the switch is put off, large induced e.m.f is set up in the coil which makes the bulb glow brilliantly 69 φ = 5t2 – 4t + Wb, R = 10 Ω, t = 0.2 s dφ d Induced e.m.f | ε | = = 5t – 4t +1 dt dt = (10 t – 4) volt ( At ) t = 0.2 s the induced e.m.f will be ε = [ 10 × 0.2 – 4] = 2V ε = 0.2 A Current i= = R 10 70 Due to the earth’s magnetic field, eddy currents are produced in the falling metal piece These eddy currents oppose the motion of the metal piece However, no such currents are produced in the stone Therefore the stone will reach the earth earlier 71 Breaking of a circuit reduces the current to zero suddenly and therefore the induced e.m.f is extremely large 72 The motion of copper sheet is damped due to eddy currents 73 Inductance is called electrical inertia because it opposes the change of current S Chand & Company Limited 74 The water can boils due to the heat produced by eddy currents in the cylinder 75 When the current on the line is switched on or off, induced current are produced in the body of the birds They experience a repulsive force and fly away 76 Yes, when the plane of coil is parallal to the magnetic field 77 The induced e.m.f due to self induction opposes the current change Therefore it is sometimes called back e.m.f 78 Rate of change of magnetic flux weber NA –1 m = second s Nm J = = = JC –1 = volt As C 79 Consider a conducting rod AC of length l in a uniform magnetic field B perpedicular to the plane of the paper downward The rod is moved with a velocity v towards right In metals there are free electrons They also move along with the rod in a direction perpendicular to the magnetic field So they will experience a magnetic Lorentz force Fm = Bev According to Fleming’s left hand rule, the force on the electron will be towards C = S Chand & Company Limited x x x x x x x x x x x x x x x x x x x x x x Fe x x x x x e x x x x x x x x x x x x x x x x x x A ++ Fm C Fig A.12 As a result the electrons accumulate at the end C, making the end A of the rod positively charged and end C negatively charged Thus an electric potential difference V is created between the ends of rod The electric field E within the rod is E = V/l (1) This electric field exerts a force Fe on each electron within the rod, where Fe = eE The direction of this force is towards A Thus the directions of Fm and Fe are opposite to each other When Fe and Fm become equal, we have S Chand & Company Limited eE = Bev or E = Bv From (1) and (2) (2) V = Bv l 80 Consider a straight conductor CD moving with a velocity v towards right along a U – shaped conductor placed in a uniform magnetic field B directed into the paper [Fig 4A.13] As the conductor moves, the area of the loop CDFG increases, causing a change in flux and hence an e.m.f is induced in the loop If l is the length of the conductor and FD = x, then the area of the loop is A = lx x x x x l x x x x x Induced emf is or x x x x x x C x x x x x x x x x x x x x x x x x F x x xD x x x G Flux φ = BA = Blx |ε |= x dφ dx = Bl dt dt | ε| = Blv 81 See Q.No 15 and Q No 20 x B Fig A.13 82 See Q No 21 83 Self inductance of a solenoid is µ0 N A l Thus if N is doubled, L becomes four times L= S Chand & Company Limited v 84 Flux linked with the coil φ = NBA sinωt Induced emf ε=– dφ –d = (NBA sinωt ) dt dt = –NBA ω cosωt 85 Anticlockwise S Chand & Company Limited ... sometimes called back e.m.f Why? 78 Show that the rate of change of magnetic flux has the same unit as the potential 79 Derive the expression for the e.m.f induced between the ends of a metallic