ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT (Assignment)

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1 ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT (Assignment) 1. In an A.C. circuit A ; the current leads the voltage by 30 0 and in circuit B, the current lags behind the voltage by What is the ratio of their power factors? 2. A copper loop and an identical constantan loop are moved out of a magnetic field in same time interval. In which of the two loops will the (i) induced emf be greater (ii) induced current be greater? 3. An electric lamp and a capacitor are connected in series to an A.C. How will the brightness of the lamp change on increasing the frequency of the A.C.? Give reason. 4. How will the answer toq.3 change if the capacitor is replaced by inductor? 5. In a series LCR A.C. circuit; the potential difference across resistor and capacitor is 20 V each and the across the inductor is 40 V. What is the power factor of the circuit? 6. A series LCR circuit resonates at 50 hertz. What will be the change in impedance of the circuit if the frequency changed to (i) 40 hertz (ii) 60 hertz? 7. Give two advantages of D.C. over A.C. 8. Give two advantages of A.C. over D.C. 9. Show that a pure capacitor consumes no energy in a complete cycle of A.C. 10. State the principle of working of a transformer. Give one use of the device. The laminations used in the core of the transformer are electrically insulated from each other. Give reason. 11. What does the term phasors in A.C. circuit analysis mean? An A.C. source of emf E = E 0 sin t is connected across a pure inductor of inductance L. Obtain an expression for the current I flowing in the circuit. Also draw the (i) phasor diagram (ii) graphs for E and I versus t for this circuit. Explain the difference in graphs of E and I if any. 12. An A.C. source of emf E = E 0 sin t is connected one by one, to three elements X, Y and Z. It is observed that the current flowing (i) lead the applied voltage in phase by π/2 for element X. (ii) lags behind the applied voltage in phase by π/2 for element Y. (iii) is in phase with the applied voltage for the element Z. Identify the three circuit elements. If the same A.C. source is connected across series combination of the elements X, Y and Z, find an expression for (a) current flowing in the circuit (b) net impedance of the circuit. If the frequency of the applied voltage is varied, set up the condition of the frequency when the current in the circuit is the maximum. Write the expression for this maximum current. 13. Represent variation of R, X L and X C with frequency of an A.C. source. 14. The number of turns and length of a solenoid are doubled. How does it affect the self-inductance of the solenoid? 15. What is the phase difference between the voltage across an inductor and a capacitor in an A.C. circuit? physicswithoutfear Page 1

2 16. Write any four causes of energy loss in a transformer. 17. A rectangular coil of area A having N turn is rotated at f revolutions per second in a uniform magnetic field BH perpendicular to the coil. Prove that the peak emf induced in the coil is 2 f NBA. 18. A 200 mh inductor, a capacitor with capacitance C and a 10 ohm resistor are connected in series to a 100 V, 50s -1 A.C. source. If the current and the voltage are in phase with each other, calculate C. 19. Obtain an expression for the energy stored in an inductor. What is the seat of the energy? 20. A capacitor of capacitance 1 F is connected across a 10 V supply. The battery is then disconnected and an inductor of 1 H is connected across the capacitor. What will be the maximum current in the inductor? 21. With the help of neat and labelled diagram, describe the principle, construction and working of an A.C.generator. 22. With the help of neat and labelled diagram, describe the principle, construction and working of transformer. 23. Can the current produced by an A.C. generator be measured with a moving coil galvanometer? Give reason. 24. Find the inductance of an inductor which when used in series with a bulb of resistance 10 ohm connected to an A.C. source of 80 V, 50 Hz gives the circuit a power factor of 0.5. What will be the power dissipated in the circuit? 25. Distinguish between reactance and impedance. When a series combination of a coil of inductance L and a resistance R is connected across a 20 V, 50 Hz supply, a current of 0.5 A flows through the circuit. The current differs in phase from the applied voltage by /3. Calculate the value of L and R kw of electric power can be transmitted to a distant consumer at (i) 220 V (ii) V. Which of the two modes of transmission should be preferred and why? Support your answer with possible calculations. 27. The primary coil of an ideal step-up transformer has 200 turns and the transformation ratio is also 100. The input voltage and power are 220 V and 11k W respectively. Calculate. (i) the number of turns in the secondary (ii) the current in the primary (iii) the voltage across the secondary (iv) the current in the secondary (v) the power in the secondary. 28. State Faraday s laws of electromagnetic induction. 29. State Lenz s law. Show that the law is a consequence of the principle of energy conservation. 30. In India the domestic supply is at 220 V, 50 Hz while in USA it is 110 V, 50 Hz. Give on advantage and one disadvantage of 220 V supply over 110 V supply. 31. An A.C. generator consists of a coil of 50 turns and area 2.5 m 2 rotating at an angular speed of 60 rad s -1 in a uniform magnetic field B = 0.3 T between two fixed pole pieces of a magnet. The resistance of the circuit including the coil is 500. (i) (ii) Find the maximum current drawn from the generator. What will be the orientation of the coil with respect to the magnetic field to have (a) minimum magnetic flux (b) maximu8m physicswithoutfear Page 2

3 induced emf (c) an instantaneous value of current equal to half the maximum? (iii) Would the generator work if the coil were held stationary and the pole pieces rotated with same speed as above. 32. What is meant by impedance? Give its SI unit. Using a phasor diagram, derive the expression for the impedance of an A.C. circuit containing L, C and R in series. Find the expression for resonant frequency. 33. Derive an expression for self inductance of a long solenoid. 34. Show mathematically that the current flowing through an ideal inductor is wattles current. 35. An A.C source of emf E = E 0 sin t is applied across an inductor of inductance L. Show mathematically that the current lags behind the voltage by a phase angle of π/2? 36. An A.C. source of emf E = 100 sin 100 t is applied across a capacitor of capacitance 0.5 F. Calculate the peak current through the circuit. Obtain the equation for instantaneous value of current. Hence show that the current leads the emf in the circuit by π/2? 37 A 100 ohm resistance is connected across an alternating potential V = 200 sin (100 t). Calculate time taken by the current to change from its peak value to rms value. What will be the rms value of current? 38. Obtain dimensional formula for magnetic flux. 39. Show that JA -1 is SI unit of magnetic flux. 40. For what orientation of the coil with magnetic field, will the magnetic flux linked with the coil become (i) maximum (ii) Zero? 41. Sensitive electrical instruments around an electromagnet sometimes get damaged. Give reason. 42. A square loop of side 10 cm and resistance of 125 m per cm is placed vertically in the east-west plane. A uniform magnetic field of 0.20 T is set up across the loop in north-east direction. The magnetic field is reduced to zero in 0.40 sec at a steady rate. Calculate the (i) initial magnetic flux (ii) final flux (iii) induced emf (iv) induced current during this time interval. 43. A 100 cm 2, 200 turn coil of resistance 2 is placed with its plane perpendicular to the horizontal component (0.03 mt) at a place. Estimate the magnitude of induced emf in the coil if it is rotated about its vertical diameter through in 0.20 sec. State superfluous data, if any. 44. A large circular metal ring of radius 1 m has a metal rod connecting its centre and touching the ring with a uniform magnetic field of one tesla perpendicular to its plane. The rod is rotated about an axis through the centre of the ring with a frequency of 50 revolutions/sec. Calculate the emf induced between the centre and the rim. How will the answer to the above change if four rods connect the centre to the rim? 45. Name the phenomenon which causes rotation of a shiny metal disc in analogue electric power meters. 46. A magnet is made to fall through two long identical pipes but made of physicswithoutfear Page 3

4 different materials : PVC and aluminium. Will the time of fall be equal in the two cases. Explain the difference in time, if any. 47. An exerciser being paddled has a coil of 100 turns of area 0.10 m 2 is rotating at 30 rpm. The coil is used to power a digital meter attached to the exerciser. Calculate the maximum e.m.f. generated in the coil if it is placed in a uniform magnetic field of 0.01 T perpendicular to the axis of rotation of the coil. 48. Show that the electric charge flowing through a coil due to electromagnetic induction is independent of time in which the flux change takes place. 49. Obtain dimensional formula for the ratio of mutual inductance to emf. 50. Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency alternating current? 51. What is the average value of the a.c. voltage represented by V = 220 sin 314 t volts over the time interval (i) 0 to π/ω(ii) 0 to 2π/ω? 52. What is the nature of impedance of a series LCR circuit if the current I (i) is in phase with the voltage? (ii) leads the voltage in phase? (iii) lags behind the voltage in phase? 53. Calculate the power loss in a 20 turn, 10 circular coil of radius 8 cm rotating about its vertical diameter at 50 radius s -1 in a uniform horizontal magnetic field of 30 mt. 54. Calculate the power factory of an A.C. circuit having a resistance R and inductance L connected in series. Give angular frequency of the source is. 55. The primary coil of a transformer with turn ratio 2 carries a current of 4A. What will be the current in the secondary coil? 56. A current of 4A flowing through a coil reverses its direction in 0.05 sec. If an emf of 16V is induced in the coil, calculate self inductance of the coil. 57. In an oscillating LC circuit; the peak charge on the capacitor is Q 0. What is the charge on the capacitor when the energy in the circuit is equally divided between the electric and the magnetic fields. 58. A coil of 50 turns having a resistance 2 is connected to a galvanometer of 8. Calculate the induced current in the circuit if the magnetic flux changes from 0.1 weber to 0.2 weber in 0.1 sec. 59. A 10 m long horizontal straight wire extending from east to west is falling with a speed of 5 ms -1 at right angles to the 0.3 x 10-4 tesla horizontal component of the earth s magnetic field. Determine (i) instantaneous emf in the wire (ii) sense of the emf induced. (iii) the end of the wire at higher potential. If the resultant intensity of earth s magnetic field at the place is 0.5 x 10-4 tesla, Determine. What is the value of the vertical component of earth s magnetic field at the place? What are the answers to (i), (ii) and (iii) alone due to the vertical component of the field? 60. A pair of adjacent coils with mutual inductance 1.5 H have the current through one coil changing from 10 A to 20 A in 0.5 s. Calculate (i) the change in flux linked with the other coil (ii) emf induced in the other coil. 61. Obtain the dimensional formulae for (i) resistance (ii) inductance (iii) physicswithoutfear Page 4

5 inductive reactance (iv) impedance. 62. What is the ratio of (i) the peak voltage to the rms voltage in an a.c. circuit? 63. A d.c. ampere is defined in terms of magnetic force between two infinitely long straight current carrying conductors. But a.c. reverses its direction after regular intervals of time and its magnitude also change. How is one ampere of a.c defined? 64. In an a.c. circuit A ; the current leads the voltage by 30 0 and in circuit B, the current lags behind the voltage by What is the ratio of their power factors? 65. In a d.c. circuit; the potential difference across a series combination of a number of circuit elements is equal to the sum of the potential differences across the individual elements. The same is not true for a.c. circuits. Explain. 66. A copper loop and an identical constantan loop are moved out of a magnetic field in same time interval. In which of the two loops will the (i) induced emf be greater (ii) induced current be greater? 67. A step up transformer provides a high voltage output for a low voltage input. How does it confirm to the law of energy conservation? 68. An electric lamp and a capacitor are connected in series to an a.c. source. How will the brightness of the lamp change on increasing the frequency of the a.c.? Give reason. 69. An a.c source has an inductor and a capacitor joined to it in series. The frequency of the a.c. source is gradually increased from a very low value. Discuss the variation of phase difference between the emf and the current with change in angular frequency. 70. In a series LCR a.c. circuit; the potential difference across resistor and capacitor is 20 V each and that across the inductor is 40 V. What is the power factor of the circuit? 71. Represent variation of reactance X C X L with frequency graphically. Explain the shape of the graph. 72. The instantaneous voltage and current in an a.c. circuit are given by V = 230 sin ( t - π/2 volts and I = 1.5 sin t amperes. What is the power dissipated in the circuit. 73. Represent the variation of (i) resistance(ii) capacitive reactance (iii) inductive reactance (iv) impedance of series LCR circuit connected to an a.c source with increase in frequency of the a.c. 74. A series LCR circuit resonates at 50 hertz. What will be the change in impedance of the circuit if the frequency changed to (i) 40 hertz (ii) 60 hertz? 75. A pure inductance; a pure capacitance and a series LCR circuit are connected in turn to an a.c. source of variable frequency. Represent the variation of current in the circuit with increase in frequency of the a.c. source. 76. Give two advantages of d.c. over a.c. 77. What is the phase difference between V and I in an a.c. circuit containing: (i) pure resistance (ii) pure inductor (iii) pure capacitor (iv) series LCR circuit. 78. Give two advantages of a.c. over d.c. 79. A step-down transformer is used to reduce the supply voltage of 220 V to 11 V. The primary coil draws a current of 5 A. The current in secondary coil is found to be 90 A. Calculate the efficiency of the transformer. 80. Show that pure capacitor consumes no energy in a complete cycle of a.c. physicswithoutfear Page 5

6 81. A sinusoidal alternating current has a peal value I 0.What will be the mean power delivered by this a.c. if it is passed through a heater coil of resistance R. 82. State the principle of working of a transformer. Give one use of the device. The laminations used in the core of the transformer are electrically insulated from each other. Give reason. 83. The coefficient of mutual inductance of two circuits A and B is 3 mh and their respective resistances are 10 ohm and 4 ohm. By how much should the current change in 0.02 second in the circuit A so as to make an induced current of 0.012A flow through the coil B? 84. What does the term phasors in a.c. circuit analysis mean? An a.c. source of emf E = E 0 sin t is connected across a pure inductor of inductance L. Obtain an expression for the current I flowing in the circuit. Also draw the (i) phasor diagram (ii) graphs for E and I versus t for this circuit. Explain the difference in graphs of E and I if any. 85. An alternating voltage source produces an emf represented by V = 220 sin t). volts. The source is connected to a 10 ohm resistance. Calculate (i) rms current (ii) the time taken by current to fall from its peak value to rms value. 86. An a.c. source of emf E = E 0 sin t is connected one by one, to three elements X, Y and Z. It is observed that the current flowing (i) lead the applied voltage in phase by π/2for element X. (ii) lags behind the applied voltage in phase by π/2for element Y. (iii) is in phase with the applied voltage for the element Z. Identify the three circuit elements. If the same a.c. source is connected across series combination of the elements X, Y and Z, find an expression for (a) current flowing in the circuit (b) net impedance of the circuit. If the frequency of the applied voltage is varied, set up the condition of the frequency when the current in the circuit is maximum. Write the expression for this maximum current. 87. The magnetic flux through a coil perpendicular to the plane of the coil varies with time t according to the equation : = (4t 3 + 2t 7) weber. The coil has a resistance of 1 ohm is connected to an electric lamp of resistance 3 ohm. Calculate the induced current through the coil at t = 2 sec. 88. A coil connected to an a.c. source of frequency (25/π) k Hz offers a reactance of 50 ohm. Find the inductance of the coil. 89. An emf of E = 20 sin ( t + π/8? applied to a circuit results in an alternating current I = 5 sin ( t - n an element X in the circuit. Calculate (i) the impedance of the circuit (ii) the power factor of the circuit. Is the circuit inductive or capacitive? 90. A capacitor connected to an a.c. source of frequency 5/ π khz offers a reactance of 100 ohm. Find the capacitance of the capacitor. 91. When a 100 V d.c. is applied across a coil, a current of 1 A flow through it. When a 100 V, 50 hertz a.c. is applied; the same coil allows only 0.5 A current. Calculate the resistance, the impedance, the inductance and the power factor of the a.c. circuit. 92. Represent variation of R, X L and X C with frequency of an a.c. source. physicswithoutfear Page 6

7 93. Find the capacitance of the capacitor required to be connected across a 5H inductor coil of a motor so as to draw the maximum power from a 50 hertz a.c. source. 94. What is the phase difference between the voltage across an inductor and a capacitor in an a.c. circuit? 95. A coil of inductance 0.50 H and resistance 100 is connected to a 240 V, 50 Hz a.c. supply. (a) What is the maximum current in the coil? (b) What is the time lag between voltage maximum and the current maximum? 96. Write any four causes of energy loss in a transformer. 97. An alternating voltage of 220 V applied across a device X makes a current of 0.5 A flow through it and is in phase with the applied voltage. When the same device X is used in series combination with another device Y and connected to the same source; the power factor is found to be 1/ 2. Calculate the impedance of the circuit using X and Y in series. Name the devices X and Y if the current is found to lead the voltage in the series circuit of X and Y. What is the reactance offered in the series combination? 98. In a series LCR circuit, the voltage across the inductor, capacitor and resistor are 40V, 20V and 20 V respectively. (a) What is the net operative voltage across the combination? (b) What is the power factor of the circuit? (c) Will the voltage lead or lag behind the current in the circuit? Justify your answer in each case. 99. A rectangular coil of area A having N turn is rotated at f revolutions per second in a uniform magnetic field B perpendicular to the coil. Prove that the peak emf induced in the coil is 2 π f NBA A 200 mh inductor, a capacitor with capacitance C and a 10 ohm resistor are connected in series to a 100V, 50 s -1 a.c. source. If the current and the voltage are in phase with each other, calculate C Obtain an expression for the energy stored in an inductor. What is the seat of the energy? 102. A radio frequency choke is air cored coil whereas an audio frequency choke is iron cored. Give reasons for this difference A capacitor of capacitance 1 µf is connected across a 10 V supply. The battery is then disconnected and an inductor of 1 µh is connected across the capacitor. What will be the maximum current in the inductor? 104. With the help of neat and labelled diagram, describe the principle, construction and working of an a.c. generator With the help of a neat and labelled diagram, describe the principle, construction and working of a transformer Can the current produced by an a.c. generator be measured with a moving coil galvanometer? Give reason Find the inductance of an inductor which when used in series with a bulb of resistance 10 ohm connected to an a.c. source of 80 V, 50 Hz gives the circuit a power factor of 0.5. What will be the power dissipated in the circuit? 108. Distinguish between reactance and impedance. When a series combination of a coil of inductance L and a resistance R is connected across a 20V, 50 Hz physicswithoutfear Page 7

8 supply, a current of 0.5 A flows through the circuit. The current differs in phase from the applied voltage by π /3. Calculate the value of L and R kw of electric power can be transmitted to a distant consumer at (i) 220V 9ii) 22000V. Which of the two modes of transmission should be preferred and why? Support your answer with possible calculations The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The input voltage and power are 220 V and 1100 W respectively. Calculate (i) the number of turns in the secondary. (ii) the current in the primary. (iii) the voltage across the secondary. (iv) the current in the secondary (v) the power in the secondary State Faraday s laws of electromagnetic induction State Lenz s law. Show that the law is a consequence of the principle of energy conservation In India the domestic supply is at 220 V, 50 Hz while in USA it is 110 V, 50 Hz. Give one advantage and the one disadvantage of 220 V supply over 110 V supply An a.c. generator consists of a coil of 50 turns and area 2.5 m 2 rotating at an angular speed of 60 rad s -1 in a uniform magnetic field B = 0.3 T between two fixed pole pieces of a magnet. The resistance of the circuit including the coil is 500. (i) (ii) (iii) Find the maximum current drawn from the generator. What will be the orientation of the coil with respect to the magnetic field to have (a) minimum magnetic flux (b) maximum induced emf (c) an instantaneous value of current equal to half the maximum? Would the generator work if the coil were held stationary and the pole pieces rotated with same speed as above What is meant by impedance? Give its SI unit Using a phasor diagram, derive the expression for the impedance of an a.c. circuit containing L, C and R in series. Find the expression for resonant frequency Derive an expression for self inductance of a long solenoid Show mathematically that the current flowing through an ideal inductor is wattles current An a.c. source of emf. E = E 0 sin t is applied across an inductor an inductor of inductance L. Show mathematically that the current lags behind the voltage by a phase angle of π /2? physicswithoutfear Page 8

15. the power factor of an a.c circuit is.5 what will be the phase difference between voltage and current in this

15. the power factor of an a.c circuit is.5 what will be the phase difference between voltage and current in this 1 1. In a series LCR circuit the voltage across inductor, a capacitor and a resistor are 30 V, 30 V and 60 V respectively. What is the phase difference between applied voltage and current in the circuit?