# Electromagnetic Iinduction & Alternating Current

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1. Three identical coils A, B and C are placed with their planes parallel to one another. Coils A and C
carry current as shown. Coil B and C are fixed. The coil A is moved towards B with uniform motion. Is
there any induced current in B?

2. Two coils are being moved out of magnetic field- one coil is moved rapidly and the other slowly. In which case is more work done and why?

3The figure shows two identical rectangular loops (1) and (2), placed on a table along with a straight line current carrying conductor between them.
(i) What will be the directions of the induced currents in the loops when they are pulled away from the conductor with same velocity?
(ii) Will the e.m.f. induced in the two loops be equal? Justify your answer.

4 Give the direction in which the induced current flows in the coil mounted on an insulating stand when a bar magnet is quickly moved along the axis of the coil from one side to the other as shown.

5. A bar magnet M is dropped so that it falls vertically through the coil C. The graph obtained for voltage produced across the coil vs time is shown in figure (b). (i) Explain the shape of the graph. (ii) Why is the negative peak longer than the positive peak?

6.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?

7. A cylindrical bar magnet is kept along the axis of a circular coil, when the magnet is rotated (a) about its own axis, and (b) about an axis perpendicular to the length of the magnet, in which case the induced emf will be more?

8.How does the self inductance of an air core coil change, when (i) the number of turns in the coil is decreased, (ii) an iron rod is introduced in the coil? A copper coil L wound on a soft iron core and a lamp B are connected to a battery E through a tapping key K. When the key is suddenly opened, the lamp flashes for an instant to much greater brightness. Explain.

9. How is the mutual inductance of a pair of coils affected when separation between the coils is increased? The number of turns of each coil is increased? A thin iron sheet is placed between the two coils, other factors remaining the same? Explain your answer in each case.

10. A rectangular wire frame, shown below, is placed in a uniform magnetic field directed upward and normal to the plane of the paper. The part AB is connected to a spring. The spring is stretched and released when the wire AB has come to the position A’B’ (t = 0). How would the induced emf vary with time? Neglect damping.

11. Why does metallic piece become very hot when it is surrounded by coil carrying high frequency alternating current?

12. Three students X, Y, and Z performed an experiment for studying the variation of alternating current with angular frequency in a series LCR circuit and obtained the graphs as shown. They all used a.c sources of the same r.m.s. value and inductances of the same value. What can we (qualitatively) conclude about the (i) capacitance value (ii) resistance values Used by them? In which case will the quality factor be maximum? What can we conclude about nature of the impedance of the set up at frequency wo?

13.In the circuit shown below, R represents an electric bulb. If the frequency of the supply is doubled, how should the values of C and L be changed so that glow in the bulb remains unchanged?

14 An air cored coil L and a bulb B are connected in series to the mains as shows in the given figure: The bulb glows with some brightness. How would the glow of the bulb change if an iron rod is inserted in the coil? Give reasons in support of your answer

15. When a circuit element ‘X’ is connected across an a.c. source, a current of √2A flows through it and this current is in phase with the applied voltage. When another element ‘Y’ is connected across the same a.c. source, the same current flows in the circuit but it leads the voltage by π/2 radians.(i) Name the circuit elements X and Y. (ii) Find the current that flows in the circuit when the series combination of X and Y is connected across the same a.c. voltage.

16. Fig shows a light bulb (B) and iron cored inductor connected to a DC battery through a switch (S). (i) What will one observe when switch (S) is closed? (ii) How will the glow of the bulb change when the battery is replaced by an ac source of rms voltage equal to the voltage of DC battery? Justify your answer in each case

17. A circuit containing a 80 mH inductor and a 60 μF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible. (a) Obtain the current amplitude and rms values. (b) Obtain the rms values of potential drops across each element. (c) What is the average power transferred to the inductor? (d) What is the average power transferred to the capacitor? (e) What is the total average power absorbed by the circuit?

18. A series LCR-circuit with L = 0.12 H, C = 480 nF, R = 23 Ω is connected to a 230 V variable frequency supply. (a) What is the source frequency for which current amplitude is maximum? Obtain this maximum value. (b) What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power. (c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies? (d) What is the Qfactor of the given circuit?

19. An LC-circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0(a) what is the total energy stored initially. Is it conserved during the LC-oscillations? (b) What is the natural frequency of the circuit? (c) At what times is the energy stored (i) Completely electrical (i.e., stored in the capacitor)? (d) At what times is the total energy shared equally between the inductor and the capacitor? (e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

20. Define self-inductance in terms of work done against the induced emf.

21. A circuit with a vertical copper wire bends as shown supports a small wooden piece W which floats in mercury. What do you expect when key is closed and current flows through the circuit?

22. Draw the wave form of out put current. Substantiate your answer

23. 23. An electron beam is deflected in a given field. Identify whether it is an electric field or a magnetic field in the following cases?
(i) The trajectory of the beam is a parabola and its K.E changes.
(ii) The trajectory of the beam is circular and its K.E. remains the same. Justify your answer.

24. A resting electron near a stationery bar magnet does not set into motion. But a moving magnet near an electron set it into motion. Why?

25. An irregularly shaped flexible current carrying loop when placed in an external magnetic field will assume a circular shape. Give reason

26. Alpha particles (m = 6.68 X 10-27 Kg., q = +2e) accelerated through a potential difference V to 2 kV, enter a magnetic field B = 0.2 T perpendicular to their direction of motion. Calculate the radius of their path.

27.

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The above figure shows a horizontal solenoid connected to a battery and a switch. A copper ring is placed on a frictionless track near the solenoid, the axis of the ring being along the axis of the solenoid. What will happen to the ring as the switch is closed? Justify your answer.

28. A particle with charge ‘q’ and mass ‘m’ is shot with kinetic energy K into the region between two plates as shown in the figure. If the magnetic field between the plates is B and as shown, how large must B be if the particle is to miss collision with the opposite plate?

29.For the circuit shown below, find the magnitude and direction the force on wire AC, wire BC and wire AB. Also show that net force is zero.

30. A bar PQ of mass M is suspended by two wires as shown below. Assume that a uniform magnetic field B is directed into the page. Find the tension in each supporting wire when the current through the bar is I.

31. A bar of mass M is suspended by two springs as shown below. Assume that a magnetic field B is directed out of the page. Each spring has a spring constant K. Describe the bar’s displacement when a current I is sent through it in the direction shown.

32.An equilateral triangle is formed from a piece of uniform resistance wire. Current is fed into one corner and led out of the other as detailed in the figure below. Show that the current flowing through the sides of the triangle produces no magnetic field at its centre ‘O’ (the intersection of the medians).

33. In the following figure, the rectangular loop of wire is being pulled to the right, away from the long straight wire through which a steady current i flows upward as shown. Does the current induced in the loop flow in the clockwise sense or in the counter clockwise sense ? Justify

34. Determine the separate effects on the induced emf of a generator if (a) the flux per pole is doubled, and (b) the speed of the armature is doubled.

35. An electromagnet has stored 648 J of magnetic energy when a current of 9A exists in its coils. What average emf is induced if the current is reduced to zero in 0.45 s?

36. A 40 Ohm resistor is connected across a 15 V variable frequency electronic oscillator. Find the current through the resistor when the frequency is (a) 100 Hz and (b) 100 kHz. What is the current if the 40 Ohm resistor is replaced by a 2 mH inductor?

37. The axes of two magnets are collinear. One has poles of strength 80 Am separated by 125 mm, and the second has a magnetic moment of 12 A-m2 with poles of strength 160 Am. Find the attractive force between the magnets if the north pole of one is 45 mm from the south pole of the second

38. A coil A is connected to voltmeter V and the other coil B to an alternating current source D. If a large copper sheet CC is placed between the two coils, how does the induced e.m.f in the coil A change due to current in coil B?

39. A magnet is moved in the direction indicated by an arrow between two coils A and B as shown below. Suggest the direction of induced current in each coil L.

40. An electromagnet has stored 648 J of magnetic energy when a current of 9 A exists in its coils. What average emf is induced if the current is reduced to zero in 0.45 sec.

41. What is the magnitude of the induced current in the circular loop-A B C D of radius r, if the straight wire PQ carries a steady current of magnitude I ampere?

42. Two identical loops, one of copper and another of aluminum are rotated with the same speed in the same M.F.In which case, the induced (a) e.m.f (b) current will be more and why?

43. Why is spark produced in the switch of a fan, when it is switched off?

44. Coils in the resistance boxes are made from doubled up-insulated wire. Why?

45. A galvanometer connected in an A.C. circuit does not show any deflection. Why?

46. A capacitor blocks D.C. but allows A.C to pass through it. Explain. Why?

47. Can we use transformer to step up D.C. voltage? If not, why?

48. Calculate the r.m.s value of alternating current shown in the figure.

49. The algebraic sum of potential drop across the various – elements in LCR circuit is not equal to the applied voltage. Why?

50. A copper ring is held horizontally and bar magnet is dropped through the ring with its length along the axis of the ring. Will the acceleration of the falling magnet be equal to, greater than or less than that due to gravity?

51. A magnet is moved in the direction indicated by an arrow between two coil A B and C D as shown in the figure. Suggest the direction of current in each coil.

52. Figure shows an inductor L and a resistance R connected in parallel to a battery through a switch. The resistance R Which of the bulbs lights up earlier, when K is closed? Will the bulbs be equally bright after same time?

53. How does the self inductance of a coil change, when Number of turns in the coil is decreased? An iron rod is introduced into it. Justify your answer in each case.

54. Figure shows two electric circuits A and B. Calculate the ratio of power factor of the circuit B to the Power factor of the circuit A.

55. An inductor L of reactance XL is connected in series with a bulb B to an A.C. source as shown in the figure. Briefly explain, how does the brightness of the bulb change when (a) Number of turns of the inductor is reduced and (b) A capacitor of reactance XC =XL is included in series in the same circuit.

56. When a series combination of a coil of inductance L and a resistor of resistance R is connected across a 12 V-50 Hz supply, a current of 0.5.A flows through the circuit. The current differs in phase from applied voltage by π / 3 radian. Calculate the value of L and R.

57. An A.C. generator is connected to a sealed box through a pair of terminals. The box may contain R L C or the series combination of any two of the three elements. Measurements made outside the box reveal that:

E=75 Sin ωt (in volt) and

I= 1.2 Sin ( ω t + π / 5 ) ( in ampere )

Name the circuit elements

What is the Power factor of the circuit? What is the rate, at which energy is delivered by the generator to the circuit?

58. Figure (a), (b) and (c) Show three alternating circuits with equal currents. If frequency of alternating emf be increased, what will be the effect on currents In the three cases. Explain.

59. Does the current in an A.C. circuit lag, lead or remain in phase with the voltage of frequency u applied to the circuit when
(i) u = ur (ii) u < ur (iii) u > ur
where ur is the resonance frequency.

60. Two different coils have self inductance L1=8 mH and L2 = 2 mH. At a certain instant, the current in the two coils is increasing at the same constant rate and the power supplied to the two coils is same. Find the ratio of (a) induced voltage (b) current and (c) energy stored in the two coils at that instant?

CBSE Physics (Chapter Wise With Hint / Solution) Class XII (By Mr. Sreekumaran Nair)