Notes
Electromagnetic Induction — 60 MCQs
Faraday's & Lenz's laws, AC generators, eddy currents, self/mutual inductance, energy in inductors, transformers and losses. Questions range from basic concepts to advanced applications.
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1. Faraday's law of electromagnetic induction states the induced emf in a closed circuit equals:
easyExplanation: Faraday: ε = − dΦ/dt (flux linkage change). Negative sign indicates Lenz's law. -
2. The negative sign in Faraday's law corresponds to which principle?
easyExplanation: Lenz's law gives direction such that induced current opposes change in flux — represented by minus sign. -
3. Lenz's law ensures the induced current direction is such that it:
easyExplanation: Lenz's law enforces conservation of energy by opposing the cause of induction. -
4. If the magnetic flux through a loop increases into the page, the induced current will produce a magnetic field:
easyExplanation: To oppose increasing into-page flux, induced field must be out of page; use right-hand rule to set current direction. -
5. A coil of N turns is rotated in a uniform magnetic field with angular frequency ω. The peak induced emf amplitude is:
mediumExplanation: If angle between normal and B varies as ωt, emf amplitude = N B A ω (sinusoids give max N B A ω). -
6. If a rectangular loop moves out of a uniform magnetic field region, the induced emf appears because:
easyExplanation: Flux change (due to area in field changing) induces emf per Faraday. -
7. Motional emf produced when a conductor of length l moves with velocity v perpendicular to B is:
easyExplanation: Motional emf from v × B acting on charges across length: ε = B l v (for perpendicular orientation). -
8. A conductor moves parallel to B (no component perpendicular). The motional emf is:
easyExplanation: If v parallel to B then cross product zero so no motional emf. -
9. An induced emf in a closed loop can be produced by:
mediumExplanation: Flux changes can occur by varying B, A, or angle between B and area vector. -
10. If magnetic flux through a coil changes sinusoidally with time, the induced emf is:
mediumExplanation: Emf = -dΦ/dt; derivative of sine is cosine (90° phase shift). -
11. A single-turn loop and a 10-turn coil experience identical flux change ΔΦ. The induced charge magnitude passing during change is:
mediumExplanation: Total induced emf ∝ N; for same rate, more turns produce greater total emf and integrated charge (assuming same resistance per turn aggregate). -
12. When a bar magnet is pushed quickly into a coil, the induced current in coil will:
easyExplanation: Induced currents create fields opposing the change; work must be done to push magnet, appearing as mechanical resistance. -
13. Eddy currents are:
easyExplanation: Eddy currents are loops inside conductors; cause heating and magnetic damping. -
14. An example where eddy currents are useful is:
mediumExplanation: Eddy currents are exploited for non-contact braking and for detecting conductive objects. -
15. An example where eddy currents are a nuisance is:
easyExplanation: Eddy currents in solid cores cause significant I^2R losses; cores are laminated to reduce them. -
16. To reduce eddy current losses in a transformer core you:
easyExplanation: Lamination increases electrical resistance of current paths, reducing eddy currents. -
17. Self-inductance L of a coil is defined by relation:
easyExplanation: Inductance relates flux linkage to current; L depends on coil geometry and medium. -
18. Mutual inductance M between two coils means:
easyExplanation: M = Φ21 / I1 (flux through coil 2 due to current I1) assuming linearity; symmetric property M12=M21. -
19. Mutual inductance M between two coils depends on:
mediumExplanation: Mutual coupling determined by how well flux from one links the other and by turns. -
20. A key use of mutual inductance is in:
easyExplanation: Transformers use mutual inductance to transfer energy between circuits at different voltages. -
21. Energy stored in an inductor with inductance L carrying current I is:
easyExplanation: Magnetic energy stored in inductor = 1/2 L I². -
22. If current in an inductor changes rapidly, voltage across it is v = L (dI/dt). This property is called:
easyExplanation: An inductor resists change in current; induced emf = L dI/dt. -
23. Inductive reactance X_L of an inductor in AC circuit is:
easyExplanation: Inductive reactance increases with frequency; X_L = 2π f L. -
24. In an ideal inductor the current lags the applied voltage by:
mediumExplanation: Voltage leads current by 90° in ideal inductance (v = L di/dt). -
25. Back emf in an inductor opposes change of current according to:
easyExplanation: Induced emf opposes change in current (Lenz), magnitude L dI/dt. -
26. If two inductors are connected in series with coupling coefficient k, total inductance is:
hardExplanation: Mutual inductance adds or subtracts depending on aiding or opposing orientation; M = k sqrt(L1 L2). -
27. Coupling coefficient k ranges between:
mediumExplanation: k = M / sqrt(L1 L2), limited to [0,1] for non-pathological cases. -
28. A coil wound on an iron core has larger inductance than same coil in air because:
easyExplanation: Magnetic core increases flux linkage per current, increasing inductance. -
29. Self inductance of a solenoid of N turns, length l, cross-sectional area A is approximately:
mediumExplanation: Inductance of long solenoid: L = μ N² A / l where μ = μ0 μ_r. -
30. When current in primary coil changes, induced emf in secondary equals:
easyExplanation: Φ2 = M I1, so emf in coil2 = − dΦ2/dt = − M dI1/dt. -
31. A simple AC generator (alternator) produces emf by:
easyExplanation: AC generator: coil rotates in B producing sinusoidal flux change and induced emf. -
32. Output emf of ideal AC generator with N turns, area A, B field, rotating at ω is:
mediumExplanation: Flux = N B A cos(ωt); ε = − dΦ/dt = N B A ω sin(ωt). -
33. Slip rings in an AC generator are used to:
easyExplanation: Slip rings maintain electrical contact to rotating coil for AC output; brushes slide on rings. -
34. Commutator is used in DC machines to:
easyExplanation: Commutator (split ring) reverses connection each half rotation to produce DC from rotating coil. -
35. In an AC generator, maximum power transfer to a purely resistive load occurs when load is:
hardExplanation: Maximum power transfer occurs when load equals internal source impedance (for complex sources matching both R and reactive parts). -
36. When flux through a stationary coil is changed by a time-varying current in nearby coil, the phenomenon is:
easyExplanation: Changing current in one coil induces emf in nearby coil via mutual inductance. -
37. If mutual inductance between two coils is M and the rate of change of current in coil1 is dI1/dt, induced emf in coil2 magnitude equals:
easyExplanation: Emf magnitude = M times absolute rate of change; sign determined by Lenz's law. -
38. A transformer transfers power between circuits most efficiently when:
easyExplanation: High μ concentrates flux and lamination limits eddy currents, increasing efficiency. -
39. Ideal transformer equations (turns N1,N2) relate voltages by:
mediumExplanation: Ideal transformer: voltage ratio equals turns ratio; current ratio inversely so power approximately conserved ignoring losses. -
40. In a step-up transformer the secondary has:
easyExplanation: Step-up increases voltage by increasing turns N2 > N1. -
41. Energy stored in magnetic field of inductor is recovered when current decreases; this energy originally came from:
mediumExplanation: Energy stored in magnetic field equals work done to build current against back emf. -
42. Transformer core hysteresis loss depends mainly on:
mediumExplanation: Hysteresis loss per cycle ∝ loop area; total loss increases with frequency. -
43. Other principal transformer losses include:
easyExplanation: Transformers lose energy via core eddy currents, winding I²R (copper) losses, leakage flux, dielectric and stray losses. -
44. Eddy current loss in transformer core increases with:
hardExplanation: Eddy current loss ~ k_e f² B_m² for simple models; lamination reduces it. -
45. Copper loss in transformer windings is proportional to:
easyExplanation: I²R loss in windings increases with square of current and winding resistance. -
46. Open-circuit test on a transformer is used to measure primarily:
hardExplanation: OC test applies rated voltage with secondary open to observe no-load current and core losses. -
47. Short-circuit test on a transformer is used to determine:
hardExplanation: SC test applies reduced voltage to cause rated current and measures I²R (copper) losses and leakage reactance. -
48. Leakage flux in transformer is undesired because it:
mediumExplanation: Leakage flux contributes to series leakage reactance limiting short-circuit current and voltage regulation. -
49. Power transformer efficiency improves when:
mediumExplanation: Efficiency high when losses small relative to output; design and load factor influence losses and efficiency. -
50. Autotransformer differs from two-winding transformer by:
mediumExplanation: Autotransformer uses tapped single winding; economical but no full isolation. -
51. If primary of ideal transformer has N1 turns and secondary N2 turns, flux per turn Φ is determined by applied voltage V1 and frequency f by:
hardExplanation: RMS voltage V = 4.44 f N Φ_m for sinusoidal flux amplitude Φ_m; used in transformer design. -
52. If frequency in transformer is reduced (with same applied voltage), flux in core will:
mediumExplanation: V ∝ f Φ, so lower f increases flux for same V; core design must account for frequency to avoid saturation. -
53. Core saturation in transformer leads to:
hardExplanation: Saturation reduces permeability causing nonlinear magnetization, increased magnetizing current and distortion. -
54. A single-phase AC generator output frequency depends on:
hardExplanation: Electrical frequency determined by mechanical rotation speed and pole pairs. -
55. In eddy-current dampers used in meters, the damping force is proportional to:
mediumExplanation: Eddy currents proportional to rate of change of flux (velocity) and produce damping force ∝ v. -
56. A rotating loop in a magnetic field that produces emf also experiences a torque resisting rotation. This torque is due to:
mediumExplanation: Mechanical input must do work against electromagnetic torque; energy converted to electrical form. -
57. In a transformer's iron core, adding silicon to the iron alloy primarily:
hardExplanation: Silicon steel reduces core losses by decreasing hysteresis and eddy currents via higher resistivity. -
58. For an ideal lossless transformer, input and output power are related by:
hardExplanation: Ideal transformer conserves real power (accounting for phase), V1I1 = V2I2 if phase same; often simplified for resistive loads. -
59. A clamp-on iron-core device that uses induction to detect current in a conductor is called:
mediumExplanation: CT uses magnetic coupling to sense current in primary conductor via transformer action. -
60. Lenz's law and Faraday's law together guarantee conservation of energy because:
mediumExplanation: Opposing induced currents require input work; energy converted consistently between mechanical and electrical forms.