ALTERNATING CURRENTS

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1 ALTERNATING CURRENTS VERY SHORT ANSWER QUESTIONS Q-1. What is the SI unit of? Q-2. What is the average value of alternating emf over one cycle? Q-3. Does capacitor allow ac to pass through it? Q-4. What is the opposition offered by an inductance to the flow of alternating current through it? Q-5. Does the current in LCR circuit lead voltage in phase if V < Vr? Q-6. What is the dimensional formula of LC? Q-7. Can we control alternating current with the help of a capacitor? Q-8. Does the current in an ac circuit remain in phase with voltage if frequency of applied voltage is equal to resonant frequency? Q-9. What is (a) maximum value (b) minimum value of power factor? Q-10. Which is more dangerous to use-alternating current or direct current? Q-11. What will be the shape of graph between inductive reactance and frequency of ac supply? Q-12. What will be the shape of graph between capacitive reactance and frequency of ac supply? Q-13. Which value of current do you measure with an ac meter? Q-14. Can a capacitor replace a choke coil in an ac circuit? Q-15. Can we use 15 cycle per second alternating current for lighting purpose? Q-16. When does LCR series circuit have minimum impedance? Q-17. What is the phase difference between voltage and current in LCR circuit at resonance? Q-18. What is the phase difference between the voltage drop across L and C in a series LCR circuit connected to an ac source? Q-19. What is the reactance of a capacitor of capacitance C at Hz? Q-20. What are the factors on which the power factor depends? 1

2 Q-21. Why a dc voltmeter and dc ammeter cannot read ac? Q-22. What is the frequency of direct current? Q-23. Q-24. Q-25. Define power factor. Define the mean value of an alternating current. Fig Shows the variation of an alternating emf with time. What is the average value of the emf for the shaded part of the graph? Q-26. The given graphs (a) and (b) of Fig represent the variation of the opposition offered by the circuit element to the flow of alternating current with frequency of the applied emf. Identify the circuit element corresponding to each graph. Q-27. Peak value of emf of an ac source is E 0. What is its rms value? Q-28. What is the power dissipated in an ac circuit in which voltage and current are given by V = 230 sin and I = 10 sin ωt? Q-29. The power factor of an circuit is 0.5. What will be the phase difference between voltage and current in this circuit? Q-30. Can the voltage drop across the inductor or the capacitor in a series LCR circuit be greater than the applied voltage of the ac source? Justify your answer. 2

3 Q-31. At resonance, What is the value of power factor in the case of LCR series circuit? SHORT ANSWER QUESTIONS Q-32. An inductor of 1 H and negligible resistance is used on the mains of frequency 50 Hz. What is the reactance of the inductor? Q-33. A small dc motor operating at 200 volt draws a current of 5 ampere at its full speed of 3000 rpm. The resistance of the armature of the motor is 8.5 Ω Suppose the windings of the armature in this dc motor cannot tolerate a current of more than 20 ampere. What do your think will happen if the armature gets jammed and cannot rotate when the motor is connected to the supply? Q-34. Show that a series LCR circuit driven by an ac source exhibits resonance at ωr =. Q-35. Show that the angular frequency of free oscillations of an LC circuit is equal to =. Q-36. For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Q-37. Explain : Voltages across L and C in series are out of phase, while for L and C parallel, currents in L and C are out of phase. Q-38. A light bulb and an open coil inductor are connected to an ac source through a key as shown in Fig The switch is closed and after some time, an iron rod is inserted into the interior of the inductor. The glow of the light bulb (a) increases (b) decreases (c) is unchanged, as the iron rod is inserted. Give your answer with reasons. Q-39. How can you improve the quality factor of a series resonance circuit? Q-40. How much power is consumed in a 3

4 I. Purely inductive, and II. Purely capacitive, ac circuit? Q-41. An air-core coil and an electric bulb are connected in series across a 220 V 5-Hz ac source. The bulb glows with some brightness. How will the glow of bulb be affected on introducing a capacitor in series in the circuit? Justify your answer. Q-42. A bulb connected in series with a solenoid is lit by ac source. If a soft iron core is introduced in the solenoid, will the bulb glow brighter? Q-43. Which is the best method of reducing current in an ac circuit and why? Q-44. Why power factor correction is must in heavy machinery? Q-45. A radio frequency choke is air-cored, whereas an audio frequency choke is iron-cored. Give reasons for this difference. Q-46. Why choke coil cannot be used in dc? Q-47. What is the importance of power factor? Q-48. If the frequency of the ac source in LCR series circuit is increased, how does the current in the circuit change? Q-49. An electric lamp connected in series with a capacitor and an ac source is glowing with certain brightness. How does the brightness of the lamp change on reducing the capacitance? Q-50. An inductor is in turn put across 220 V 50 Hz and 220 V 100 Hz supplies. Will the current flowing through it in the two cases be the same or different? Q-51. Q-52. A 100 Hz ac is flowing in a 14 mh coil. Find its reactance. With reference to alternating currents and voltage, state any one fundamental difference between resistance and reactance. Q-53. What is the function of a choke coil in a fluorescent tube? Q-54. Q-55. Q-56. Show mathematically that an ideal inductor does not consume any power in an ac circuit. Show that the impedance offered by an ideal inductor to the flow of direct current is zero. What is capacitive reactance? Give its SI unit. 4

5 Q-57. State the phase relationship between the current flowing and the voltage applied in an ac circuit for (i) pure resistor (ii) pure inductor. Q-58. A bulb B and a capacitor C are connected in series to the ac mains as shown in Fig The bulb glows with some brightness. How will the glow of the bulb change when a dielectric slab is introduced between the plates of the capacitor? Give reasons in support of your answer. Q-59. In India, domestic power supply is at 220V, 50 Hz, while in USA it is 110V, 50 Hz. Give one advantage and one disadvantage of 220 V supply over 110 V supply. Q-60. Q-61. Prove that high frequency ac can pass through a pure capacitor easily but not through a pure inductor. A bulb and a capacitor are connected in series to an ac source of variable frequency. How will the brightness of the bulb change on increasing the frequency of the ac source? Give reason. Q-62. State the condition under which the phenomenon of resonance occurs in a series LCR circuit. Plot a graph showing variation of current with frequency of ac source in a series LCR circuit. 5

6 Q-63. Sketch a graph to show how the reactance of (i) a capacitor (ii) an inductor varies as a function of frequency. Q-64. Why 220V ac is more dangerous than 220 V dc? Q-65. A capacitor blocks dc but allows as. Why? Q-66. Q-67. Distinguish between resistance, reactance and impedance for an ac circuit. An ordinary moving coil ammeter used for dc cannot be used to measure an alternating current even if its frequency is low Explain why? Q-68. At an airport, a person is made to walk through the doorway of a metal detector, for security reasons. If she/he is carrying anything made of metal, the metal detector emits a sound. On what principle does this detector work? Q-69. Write the expression for frequency of an ideal LC circuit. In an actual circuit, why do the oscillations ultimately die away? Q-70. An alternating voltage of frequency f is applied across a series LCR circuit. Let f r be the resonance frequency for the circuit. Will the current in the circuit lag, lead or remain in phase with the applied voltage when (i) f > f r, (ii) f < f r? Explain your answer in each case. Q-71. In a series LCR circuit, the voltage across an inductor, a capacitor and a resistor are 30 V, 30 V and 60 V respectively. What is the phase difference between the applied voltage and the current in the circuit? SHORT ANSWER QUESTIONS Q-72. Power factor can often be improved by the use of a capacitor of appropriate capacitance in the circuit. Is it correct? 6

7 Q-73. A light bulb is rated at 100 W for a 220 V supply. Find (a) the resistance of the bulb (b) the peak voltage of the source and (c) the rms current through the bulb. Q-74. How much inductance should be connected to 200 V, 50 cycle per second supply so that a maximum current of 0.9 A flows through it? Q-75. An inductor (L=200 mh) is connected to an ac source of peak emf 210 V and frequency 50 Hz. Calculate the peak current. What is the instantaneous voltage of the source when the current is at its peak value? Q-76. (a) A coil of self-inductance 0.16 H is connected to a condenser of capacity 0.81 μf. What should be the frequency of alternating current that should be applied so that there is resonance in the circuit? Resistance of circuit is negligible. (b) If the initial chare on capacitor in part (a) is 6 mc, what is the total initial energy stored in the circuit? Q-77. A 100 V, 50 Hz ac source is connected to a series combination of an inductance of 100 mh and a resistance of 25 Ω. Calculate the magnitude and phase of the current. Q-78. A circuit draws a power of 550 W from a 220 V 50 Hz source. The power factor of the circuit is 0.8. A current in th circuit lags behind the voltage. Show that a capacitor of about 10-2 F will have to be connected in the circuit to bring its power factor to unity. Q-79. A circuit consists of a resistance of 10 Ω and a capacitance of 0.1 μf. An alternating emf of 100 V, 50 Hz is applied. Calculate the current in the circuit. Q-80. An alternating current of 1.5 ma and angular frequency 300 radian s -1 flows through a 10 KΩ resistor and a 0.50 μf capacitor in series. Find the rms voltage across the capacitor and impedance of the circuit. Q-81. A student connects a long air-cored coil of manganin wire to a 100 V dc source and records a current of 1.5 A. When the same coil is connected across 100 V, 50 Hz ac source, the current reduces to 1 A. Calculate the reactance of the coil. Q-82. An alternating voltage E=200 sin 300t is applied across a series combination of R=10 Ω and L=800 mh. Calculate (i) the impedance of the circuit. (ii) the peak current in the circuit and (iii) the power factor of the circuit. 7

8 Q-83. A 25.0 μf capacitor, a 0.10 henry inductor and a 25.0 Ω resistor are connected in series with an ac source whose emf is given by E=310 sin 314t. (i) What is the frequency of the emf? (ii) Calculate (a) the reactance of the circuit (b) the impedance of the circuit, and (c) current in the circuit. Q-84. Q-85. Calculate the capacitive reactance of a 5 μf capacitor for a frequency of (i) 50 Hz (ii) 10 6 Hz. A capacitor, a resistor and a 40 mh inductor are connected in series to an ac source of frequency 60 Hz. Calculate the capacitance of the capacitor, if current is in phase with the voltage. Q-86. When 100 volt dc is applied across a coil, a current of one ampere flows through it. When 100 volt ac of 50 cycle per second is applied to the same coil, only 0.5 ampere flows. Calculate (i) resistance of coil (ii) impedance of coil (iii) inductive reactance of coil (iv) inductance of coil. Q-87. A capacitor of capacitance 100 μf and a coil of resistance 50 Ω and inductance 0.5 H are connected in series with a 110 V 50 Hz source. Calculate the rms value of current in the circuit. Q-88. An inductance coil has a reactance of 100 Ω. When ac signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by Calculate the self inductance of the coil. Q-89. A series circuit contains a resistor of 10 Ω, a capacitor and an ammeter of negligible resistance. It is connected to a source of 220 V 50 Hz. If the reading of an ammeter is 2.0 A, calculate the reactance of the capacitor. Q-90. A capacitor, resistor of 5 Ω and an inductor of 50 mh are in series with an ac source marked 100 V, 50 Hz. It is found that the voltage is in phase with the current. Calculate the capacitance of the capacitor and the impedance of the circuit. Q-91. A resistor, a capacitor of 100μF capacitance and an inductor are in series with an ac source of frequency 50 Hz. If the current in the circuit is in phase with the voltage, calculate the inductance of the inductor used. Q-92. A circuit containing a 80 mh inductor and a 60 μf capacitor in6 series has a resistance of 15 Ω. It is connected to a 230 V, 50 Hz supply. Obtain the average power transferred to each element of the circuit, and the total power absorbed. 8

9 Q-93. What should be the frequency of alternating 200 V so as to pass a maximum current of 0.9 A through an inductance of 1 H? Q-94. A 100 μf capacitor in series with a 40 Ω resistance is connected to a 100 V, 60 Hz supply. Calculate (i) the reactance (ii) the impedance, and (iii) maximum current in the circuit. CONCEPTUAL PROBLEMS Q-95. Why alternating current measuring instruments have a non-linear scale? Q-96. The frequency of alternating emf applied to a LCR circuit is quadrupled. What is the effect on : (i) the resistance (ii) inductive reactance (iii) capacitive reactance? Q-97. A lamp is connected in series with a capacitor. Predict your observation for dc and ac connections. What happens in each case if the capacity is reduced? Q-98. An ac source is connected to two circuits as shown. Obtain the current through R at resonance I both the circuits. Q-99. A box contains L, C and R. When 250 V dc is applied to the terminals of the box, a current of 1 A flows in the circuit. When an ac source of 250 V at 2250 rad s -1 is connected, a current of 1.25 A flows. It is observed that the current rises with frequency and becomes maximum at 4500 rad s -1. Draw the circuit diagram and justify it. Q-100. An air-core coil L and a bulb B are connected in series to the ac mains as shown in Fig The bulb glows with some brightness. How will the glow of the bulb change if an iron rod is inserted in the coil? Give reasons in support of your answer. LONG ANSWER QUESTIONS 9

10 Q-101. Give definitions of (i) mean value of ac and (ii) rms value of ac. Also write the relation between them. Derive an expression for rms value of ac. Q-102. An ac voltage E=E 0 sin ωt is applied across a capacitor of capacitance C. Derive an expressions for the current I. Q-103. An ac voltage E = E 0 sin ωt is applied across an inductor of inductance L. Derive an expression for the current I. Q-104. In an ac circuit, there is no power consumption in an ideal inductor. Explain. Why? Q-105. Define the term impedance of series LCR circuit. Derive a mathematical expression for it using phasor diagram. Q-106. Q-107. Derive an expression for mean value of first half cycle of ac. Also find an expression for virtual of ac. Drive an expression for the average power in LCR series circuit connected to ac supply. Hence define power factor. What is a resonant circuit? Q-108. What is a phasor diagram? With its help, derive an expression for the impedance of an ac series LCR circuit. Q-109. How does impedance of a circuit differ from ohmic resistance? Derive an expression for the impedance in an ac circuit containing LCR in series. Also, find an expression for resonant frequency of such a circuit. Q-110. Derive a phase relation between current and emf if an ac circuit contains a pure capacitance. Prove that dc can not pass through a pure capacitor. Q-111. Explain the term inductive reactance. Show graphically the variation of inductive reactance with frequency of the applied alternating voltage. An ac voltage E = E 0 sin ωt is applied across a pure inductance L. Show mathematically that the current flowing through it lags behind the applied voltage by a phase angle of /2. Q-112. Explain the term capacitive reactance. Show graphically the variation of capacitive reactance with frequency of the applied alternating voltage. An ac voltage E = E 0 sin ωt is applied across a pure capacitor of capacitance C. Show mathematically that the current flowing through it leads the applied voltage by a phase angle of /2. 10

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