Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road, New Delhi , Ph. : ,

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1 1 EMI & AC 1. Derive an expression for the impendance of a coil in AC ciruit. A current of 1.1 A flows through a coil when connected to a 110 V DC. When 110 V AC of 50 Hz is applied to the same coil, only 0.5 A current flows. Calculate the resistance, impendance and inductance of the coil. 2. (a) Express Quality factor (Q) in terms of L, C and R. What does the Quality factor (Q) signify in a LCR AC circuit? 3. (a) How can you obtain wattless current in an AC circuit? Name one device through which power consumed an AC circuit is zero. 4. Derive an expression for the work done in maintaining a steady current i 0 in an inductor. 5. Derive an expression for the impendance of a LCR series AC circuit. A 40 resistor, 3 mh inductor and 2µF capacitor are connected in series to a 110 V, 50 Hz AC source. Calculate the value of the current in the circuit. 6. What is the phase relationship between current and voltage in an inductor and a capacitor in an AC circuit. 7. Define Poynting s vector and give its SI unit. 8. (a) What are eddy currents? How are eddy currents produced? Give two application of eddy currents. 9. Discuss the phenomenon of resonance in a LCR series AC circuit. A capacitor, a 15 resistor and 80 mh inductor are placed in series with a 50 Hz AC source. Calculate the capacity of the capacitor if the current is observed in phase with the voltage. 10. How much power is consumed in a purely inductive and purely capacitative, AC circuit? 11. Why can t tranformer be used to step up d.c. voltage? 12. Define the term self-induction. Write two factors which the self-inductance of a coil depends. 13. Derive the expression for the impendance of an a.c. circuit with an inductor L and a resistor R in series. An a.c. source of 100 V r.m.s. 50 Hz is connected across a 20 ohm resistor and a 2 mh inductor in series. Calculate. impendance of the circuit. r.m.s. current in the circuit. 14. Magnetic flux of 5 micro-weber is linked with a coil, when a current of 1 ma flows through it. What is the self-inductance of the coil? 15. A pure inductor is connected across an a.c. source. Show mathematically that the current in its lags behind the applied emf by a phase angle of /2. What is its inductive reactance? 16. An a.c. voltage E = E 0 sin t is applied across an inductor L. Obtain an expression for current I. 17. Draw the graphs to show the variation of X L, and X C with the frequency of the a.c. source used. A 200 V variable frequency a.c. source is connected to a series combination of L = 5 H, C = 80 µf and R = 40. Calculate angular frequency of the source to get maximum current in the circuit, the current amplitude at resonance and the power dissipation in the circuit.

2 2 18. If the self-inductance of an air core inductor increases from 0.01 mh to 10 mh on introducing an iron core into it, what is the relative permeability of the core used? 19. Draw a labelled diagram of an a.c. generator. Write the principle on which it works. An a.c. generator consists of a coil of 100 turns and cross-sectional area of 3 m 2, rotating at a constant angular speed of 60 radian/sec in a uniform magnetic field of 0.04 T. The resistance of the coil is 500 ohm. Calculate maximum current drawn from the generator and maximum power dissipation in the coil. 20. Explain the terms reactance and impedance as applied to components of an a.c. circuit. A variable frequency 230 V alternating voltage source is connected across a series combination L = 5.0 H, C = 80 µf and R = 40 Calculate the angular frequency of the source which drives the circuit in resonance, the amplitude of the current at resonating frequency and rms potential drop across the inductor at resonating frequency. 21. Twelve wires of equal lengths are connected in the form of a skeleton-cube which is moving with a velocityv in the direction of a magnetic field B. Find the emf in each arm of the cube. 22. Show mathematically that the average power supplied to an ideal capacitor by a source over a complete cycle of a.c. is zero. A variable-frequency 220 V alternating voltage source is connected across a series combination of L = 4.0 H, C = 100 µf and R = 55. Calculate the angular frequency of the source which drives the circuit in resonance, the impendance of the circuit, and amplitude of the current at resonance. 23. A coil A is connected to a voltmeter V and the other coil B to an alternating current source D. If a large copper sheet C, is placed between the two coils, how does the induced e.m.f. in the coil A change due to current in coil B? 24. Prove that an ideal inductor does not dissipate power in an a.c. circuit. A bulb of resistance 10, connected to an inductor of inductance L, is in series with an a.c. source marked 100 V, 50 Hz. If the phase angle between the voltage and current is 4 radian, calculate the value of L. 25. A circular copper disc 10 cm in radius rotates at 20 rad/s about an axis through its centre and perpendicular to the disc. A uniform magnetic field of 0.2 T acts perpendicular to the disc. Calculate the potential difference developed between the axis of the disc and the rim. What is the induced current, if the resistance of the disc is 2 ohm? 26. Derive the expression for the self inductance of a long solenoid. A capacitor of 50µF, a resistor 10, an inductor L, are in series with an a.c. source of frequency 50 Hz. Calculate the value of L, if the phase angle between current and voltage is zero. 27. Calculate the current drawn by the primary of a transformer, which steps down 200 V to 20 V to operate a derive of resistance 20. Assume the efficiency of the transformer to be 80%. 28. What is the power dissipation in an a.c. circuit in which voltage and current are given by : V = 300 sin ( t + /2) and I = 5 sin t? 29. Define the term root-mean-square (rms) value of a.c. Derive the relation between rms and peak value of a.c. A 1 µf capacitor is connected to a 220 V, 50 Hz a.c., source. Calculate the rms value of the current through the circuit. Also find the peak value of voltage across the capacitor.

3 30. An a.c. source E = E 0 sin t is applied across an inductor of inductance L. Show mathematically that the current lags the voltage by a phase angle of Sketch the variation of inductive reactance and capacitance reactance with the frequency of the a.c. source. A 100 mh inductor, a 20 µf capacitor and a 10 ohm resistor are connected in series to a 100 V, 50 Hz a.c. source. Calculate : Impendance of the circuit at resonance Current at resonance Resonant frequency 32. The output voltage of an ideal transformer, connected to a 240 V a.c. mains is 24 V. When this transformer is used to light a bulb with rating 24 V, 24 W, calculate the current in the primary coil of the circuit. 33. The instantaneous voltage from an a.c. source is given by E = 300 sin 314 t.what is the r.m.s. voltage of the source? 34. For a given a.c. circuit, distinguish between resistance, reactance and impendance. An a.c. source of frequency 50 hertz is connected to a 50 mh inductor and a bulb. The bulb glows with some brightness. Calculate the capacitance of the capacitor to be connected in series with the circuit, so that the bulb glows with maximum brightness. 35. A rectangular coil of N turns and area of cross-section A, is held in a time-varying magnetic field given by B sin t, with the plane of the coil normal to the magnetic field. Deduce an expression for the e.m.f. induced in the coil. 36. If the number of turns of a solenoid, keeping the other factors constants, how does the selfinductance of the solenoid change? 37. Prove mathematically that the average value of alternating current over one complete cycle is zero. A resistance of 2 ohms, a coil of inductance 0.01 H are connected with a capacitor and put across a 200 V and 50 Hz supply. Calculate the capacitance of the capacitor so that the circuit resonates. the current and voltage across the capacitor at resonance. (Take = 3). 38. A rectangular coil of N turns, area A is held in a uniform magnetic field B. If the coil is rotated at a steady angular speed, deduce an expression for the induced emf if the coil at any instant of time. 39. Distinguish between reactance and impandance. When a series combination of inductance and resistance are connected with a 10 V, 50 Hz a.c. source, a current of 1 A flows in the circuit. The voltage leads the currents by a phase angle of 3 radians. Calculate the values of resistance and inductance. 40. How are eddy currents produced? Mention two applications of eddy currents. 41. Define mutual induction and write its units. State two factors on which the mutual inductance between a given pair of coils depends. 42. What is the power factor of an LCR series circuit at resonance? 3

4 4 43. What is the phase difference between the voltage across inductor and capacitor in an LCR series circuit? 44. (a) Write the principle on which an a.c. generator works. Draw its labelled diagram. An a.c. generator consists of a coil of 50 turns and area 2.5m 2 rotating at an angular speed of 60 rad s 1 in a uniform magnetic field B = 0.2 T between the two fixed pole pieces. The resistance of the circuit including that of the coil is 500 ohm. Calculate the maximum current drawn from the generator. What is the flux when the current is zero? Would the generator work if the coil were stationary and instead of pole pieces rotated together with the same speed as above? Give reason. 45. An air-core solenoid is connected to an a.c. source and a bulb. If an iron-core is inserted in the solenoid, how does the brightness of the bulb change? Give reason for your answer. 46. What is the phase difference between the voltage across inductor and capacitor in an LCR series circuit? kW of electric power can be trasmitted to a distant station at 220 V, or 22,000 V. Which of the two modes of transmission should be preferred and why? Support your answer with possible calculations. 48. An ideal 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? 49. How does the mutual inductance of a pair of coils change when; the distance between the coils is increased? the number of turns in each coil is decreased? Justify your answer in each case. 50. An a.c. circuit having an inductor and a resistor in series draws a power of 560 W from an a.c. source marked 210 V, 60 Hz. If the power factor of the circuit is 0.8, calculate the impedance of the circuit, and the inductance of the induced used. 51. When an alternating voltage of 200 V is applied across a device Z, a current of 0.5 A flows through the circuit and is in phase with the applied voltage. When the same voltage is applied across another device Y, the same current again flows through the circuit but it leads the applied voltage by /2 radians. (a) name the devices X and Y. Calculate the current flowing in the circuit when same voltage is applied across the series combination of X and Y. 52. Give the phase difference between the applied a.c. voltage and the current in an LCR circuit at resonance. 53. Distinghish between average value and r.m.s. value of an alternating current. A 60 V - 10 W electric lamp is to be run on 100 V-60 Hz mains. (a) Calculate the inductance of choke coil required. If a resistor is to be used in place of choke coil to achieve the same result, calculate its value. 54. Distinguish between reactance and impedance. When a series combination of a coil of inductance L and a resistor of resistance R is connected across a 12V, 50 Hz supply, a current of 0.5 A flows through the circuit. The current differs in phase from applied voltage by /3 radian. Calculate the value of L and R.

5 55. An electric heater and an electric bulb are rated 500 W, 220 V and 100 W, 200 V respectively. Both are connected in series to a 220 V a.c. mains. Calculate the power consumed by the heater and electric bulb. 56. Prove that an ideal resistor connected to an a.c. source dissipates power = V 2 /R. A capacitor, eff a resistor and a 40 mh inductor are connected in series to an a.c. source of frequency 60 Hz. Calculate the capacitance of the capacitor, if the current is in phase with the voltage. 57. Distinguish between the terms rectance and impedance of an a.c. circuit. Prove that an ideal capacitor connected to an a.c. source does not dissipate power. 58. (a) Define self-inductance. Write down the expression for the self-inductance of a long solenoid of length having N turns. Give two factors on which selfinductance of an air core coil depends. 59. Prove that an ideal inductor does not dissipate power in an a.c. circuit. 60. If a rate of change of current of 4 A/s induces an e.m.f. of 20 mv in a solenoid, what is the selfinductance of the solenoid? 61. What is Lenz s law? Show that Lenz s law in accordance with the law of conservation of energy. 62. A choke coil and a bulb are connected in series to an a.c. source. The bulb shines brightly. How does its brightness change when an iron core is inserted in the choke coil? 63. Explain, with the help of a diagram, the principle, construction and working of a step-up transformer. Why is its conlaminated. 64. Sketch a graph showing the variation of reactance of capacitor with frequency of the applied voltage. 65. Distinguish between resistance, reactance and impedance for an a.c. circuit. Draw graphs showing variation of reactance a capacitor an inductor, with frequency of the applied voltage. 66. An alternating voltage E = 200 sin 300 t is applied across a series combination of R = 10 and an inductor of 800 mh. Calculate impendance of the circuit peak value of current in the circuit. power factor of the circuit. 67. A student connects a long air core coil of manganin wire to a 100 V d.c. source and records a current of 1.5 A. When the same coil is connected across 100 V 50 Hz a.c. source the current reduces to 1.0 A. Give reasons for this observation. Caclulate the value of the reactance of the coil. 68. Prove that total energy stored in an inductor is ½LI 2, where I is the maximum current max max through the inductor. In which form is this energy store. 69. Magnetic flux of 5 micro Weber is linked with a coil, when a current of 2mA flows through it. What is the self-inductance of the coil? 70. Define (I) 1 weber (II) 1 henry 5

6 6 71. Give the direction of induced current (if any) in the metal ring when the magnet is moved away form the rig as shown. 72. Why do we prefer carbon brushes than copper in an a.c. generator? 73. v-i graph for two series LCR circuit A and B is shown below. Which of the two has larger value of resistance. 74. Why do we prefer a choke coil in place of a resistor in any safety devise? 75. Give the direction of induced current (if any) in metal rings I and II. 76. In which case shown below mutual inductance is (a) maximum minimum 77. A coil is rotating in magnetic field about its axis as shown. In which orientation of coil with respect to magnetic field is the induced emf maximum minimum. 78. State Flemings Right hand rule for finding direction of induced current. 79. A magnet is moved in the direction indicated by an arrow between two coils AB and CD as shown in figure. Suggest the direction of current in each coil.

7 80. Explain how will the brightness of bulb be affected if (I) frequency of ac is increased (II) a resistor is put in series A capacitor blocks d.c., favours a.c. why? 82. What is the role of transformers in long distance transmission of electrical power. Illustrate your answer with an example. 83. In the adjoining figure magnetic field is of strength Band rectangular loop of length l and breadth w. Show graphically 84. In a series L-C-R circuit L = 5mh, c = 8MF and R = 6ohm. Voltage drop across inductor is 286v in resonance state. What is the voltage drop across capacitor in this state. 85. Calculate inductance using graph. 86. Using graph calculate average of a.c. over one complete cycle. over half cycle. virtual value and (iv) frequency of a.c.