Unit 4ab tủ tài liệu training

4 A.7 a shows an irregular wire loop expanding into a circular loop in a magnetic field perpendicular to the pa-per in the downward direction.. When is the magnetic flux linked with a co

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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

cur-rents in them?

44. A rectangular loop PQRS is taken away from a long straight

current carrying wire XY.Give the direction of induced

current, if any, in the loop [Fig 4 A.6]

45. Why do 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

below it Why?

47. Fig 4 A.7 (a) shows an irregular wire loop expanding into

a circular loop in a magnetic field perpendicular to the

pa-per in the downward direction Fig 4 A.7(b) shows a

circu-lar loop shrinking into a narrow rectangucircu-lar loop in a field

directed upward Find the direction of induced current in

each case

S

N

Fig 4 A.5

X

Y

Q

S

i

Fig 4 A.6

B

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 x x

x x x x x x x

Fig 4 A.7 (a)

D

C

Fig 4 A.7 (b)

A

B C

D

48. In figure 4 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 ?

B A

Fig 4 A.8

49. The Resistance R in circuit (a) in Fig 4 A.9 is increased What will be the direction of induced current in circuit (b)?

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Fig 4 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 1 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 cm2area Find the e.m.f induced in it if this coil is removed from the field in 0.1 second

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 0 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– 1 Calculate the potential difference between the tips of the wings, if the vertical component of earth’s magnetic field is 8 × 10–5 T

65. Calculate the induced e.m.f in a 10 H induction coil in which current changes from 8 A to 4 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 = 5 t2 – 4t + 1 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?

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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 perpendicu-lar 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

per-pendicular 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)

84. A rectangular coil of N turns and area of cross section A is held in a time varying magnetic field given by B = B0sin 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 4 A.10 (AISSCE Delhi 1997)

Fig 4 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

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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

Here B = 1 T, v = 10 m/s, L = 0.1 m So,

ε = 1 × 10 × 0.1 = 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

–4

( – 0)

50 10 100 10

0.1

n BA n

∆φ

ε =

50 V

62. Transformer ratio is given by S = S

Here EP = 2300 V, NP= 4000

ES = 230 V

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230 4000 2300

S

P

E

E

=400

63. | | = n d

dt

φ

ε

Here n = 1000, dφ = 1.6 × 10–5 Wb, dt = 0.1 s

–5

–1

1000 1.6 10

0.1

=

0.16 V

64. ε = BvL

Here B = Vertical component of earth’s magnetic field = 8 × 10–5 T

V = 80 m/s

L = 30 m

∴ ε= 8 × 10–5× 80 × 30

= 0.19 volts

65. | | =L di

dt

ε

Here L = 10 H

di = 8 – 4 = 4.0 A

dt = 0.2 s

10× 4.0

0.2

2 ×10 V

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 + 1 Wb, R = 10 Ω, t = 0.2 s

Induced e.m.f | | d d 5t – 4t 1

dt dt

φ

= (10 t – 4) volt

At t = 0.2 s the induced e.m.f will be

ε = [ 10 × 0.2 – 4] = 2V

2

10

i R

0.2 A

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

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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

–1

–1

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 perpen-dicular to the magnetic field So they will experience a magnetic Lorentz force

F m = Bev

According to Fleming’s left hand rule, the force on the electron will be towards C

Fig 4 A.12

++

Fe

Fm e

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 x x x x x x x

C A

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 be-tween 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 F e are opposite to each

other When F e and F m become equal, we have

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eE = Bev

From (1) and (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

Flux φ = BA = Blx

Induced emf is

| | =d Bl dx

dt dt

φ

or | ε| = Blv

81. See Q.No 15 and Q No 20

82. See Q No 21

83. Self inductance of a solenoid is

2 0 µ

L l

Thus if N is doubled, L becomes four times.

C

D F

G

Fig 4 A.13

B

84. Flux linked with the coil

φ = NBA sinωt.

Induced emf

–

NBA t

dt dt

φ

ω ω

85. Anticlockwise