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C5b Induction Essay Essay 83-2 Hall effect and Search coil Describe briefly the methods adopted in the measurement of (a) a steady magnetic field using a Hall probe, and (b) an alternating magnetic field using a search coil. Compare the different physical mechanisms in these tow methods and derive any necessary mathematical expressions. Comment briefly on the main factors that might affect the accuracy of the measurements. [15] Essay 84-6a (a) Inductor inductance L current I resistance R Key K e.m.f. E Figure 1 Write down a differential equation for the current I in the circuit in Figure 1 after the key K has been closed at a time t = 0, explaining clearly each term in the equation. [3] Essay 84-6b (b) Generator rotation axis perpendicular to paper magnetic field of uniform flux density B starting position of coil ( t = 0) Figure 2 A coil of N turns, each of area A, is situated initially (at time t = 0) with the plane of the coil perpendicular to a magnetic filed of uniform flux density B. The coil is then rotated at a uniform angular velocity about an axis perpendicular to the magnetic field and passing through the centre of the coil, as shown in Figure 2. Derive an expression for the e.m.f. induced in the coil at any subsequent time t. [3] Essay 86-4a DC motor Using the rotating coil of a simple d.c. motor as an example, describe, with the aid of a diagram, the force effects of a magnetic field on an electrical current. (Details of the commutator are not required.) [3] Essay 90-4cd DC motor c) Using suitable diagrams, explain the working of a simple d.c. motor, where the magnetic field is produced by a permanent magnet. [4] d) For this motor explain, in detail, the observed sequence of physical effects of i) switching it on with no mechanical load and, ii) after a while, applying such a load. [4] Essay 98-4a DC motor i) Draw a labeled diagram of a simple d.c. motor using permanent magnets. Indicate the direction of rotation of the motor and state the function of the commutator. ii) Describe and explain THREE modifications for improving the turning effect in practical d.c. motor. iii) The magnetic fields of some electric motors are provided by electromagnets. Give the advantages of using electromagnets over permanent magnets. [7] Essay 96-4 Transformer Source of energy Generator Transformers Consumers The above block diagram shows how electric power is supplied to consumers. a) i) Name ONE major source of energy that is currently used in electric power stations in Hong Kong. Briefly describe how the energy released from the source can be used to drive a generator in the power station. ii) Draw a labelled diagram of a simple a.c. generator. State the conditions for the output to be sinusoidal a.c. of frequency of 50 Hz. [6] b) For steady power transmission, show that the power loss in the cables is inversely proportional to the square of the output voltage from the power station. [2] c) i) Electric power companies usually use overhead power cables for transmitting electricity over large distance, however the general public often prefer cables to be underground. Give TWO supporting reasons for each party. ii) An overhead power cable usually consists of a central core of several steel wires, which is surrounded by many strands of aluminium wire. Give ONE advantage and ONE disadvantage of using aluminium instead of copper. Why is it necessary to include several steel wires in the cable? [6] d) Low voltage steady d.c. is required for charging a battery inside a Walkman. Draw a circuit diagram to show how the mains supply of 220 V a.c. can be stepped down by a transformer, rectified by a bridge rectifier consisting of four diodes, smoothed by a circuit consisting of two capacitors and an inductor, and finally connected to the battery. [2] Essay 97-4 Generator a) You are given two bar magnets, a long copper wire and a light beam galvanometer. Describe how you would use the apparatus to investigate qualitatively the factors affecting the e.m.f. induced in a coil by electromagnetic induction. [5] b) i) Consider a rectangular coil of N turns rotating uniformly in a uniform magnetic field about an axis perpendicular to the field. Derive an expression for the e.m.f. produced. With the aid of a labelled diagram, describe the construction of a generator to provide a d.c. to a light bulb using the methods in (I) [ smoothing is not required ]. Show that the current generated is always flowing in one direction through the bulb. ii) Explain carefully why a greater driving torque is needed to maintain the coil of the generator rotating at the original speed when an identical light bulb is connected in parallel with the first one. Also explain how this change agrees with the principle of conservation of energy. [11] Essay 98-3a Induced emf a) i) The figure below shows a rectangular metallic loop ABCD being pulled with constant speed out of magnetic field, which points into the paper. State Lenz’s law and use it together with the idea of changing flux to find the direction of the induced current flowing in the loop. Briefly explain your answer. ii) What do you understand by the principle of conservation of energy? Referring to the above example, justify whether Lenz’s law satisfies the principle of conservation of energy. [6] Essay 98-4 Motor 4. a) i) Draw a labeled diagram of a simple d.c. motor using permanent magnets. Indicate the direction of rotation of the motor and state the function of the commutator. ii) Describe and explain THREE modifications for improving the turning effect in practical d.c. motors. iii) The magnetic fields of some electric motors are provided by electromagnets. Give the advantages of using electromagnets over permanent magnets. [7] b) The figure below shows a simple motor circuit, in which a constant voltage V is applied to a motor M with coil resistance r while the current flowing is I. i) Explain why a back e.m.f. (Eb) is generated when the motor rotates and express Eb in terms of I, V and r. Hence explain carefully why the coil of a motor is liable to be damaged when a motor is first switched on or when a running motor is suddenly jammed. ii) Discuss the variation of current in the above circuit and describe the corresponding changes in the motor’s rotation speed and driving torque when:I) the switch S is closed and the motor does not carry any mechanical load; II) a mechanical load is connected to a steadily running motor. [9] Essay 99-5 Induced emf 5. a) i) Using a solenoid connected to an a.c. source of variable frequency, describe a simple experiment to investigate how the induced e.m.f. in a coil depends on the rate of change of the magnetic flux linkage through it. List the apparatus used and describe the observation. ii) State THREE factors that would affect the magnetic flux linkage through a coil. [9] b) Referring to appropriate physical laws, explain the following: i) Sparks occur when opening the switch of a circuit with an electromagnet in it. ii) There is potential difference developed between the wing-tips of an aircraft when it is flying horizontally in air. iii) The pointer of a moving-coil meter stops at the final steady value as soon as it reaches that value and shows no further oscillation. [7] Essay 00-3a Transformer 3. a) i) Give TWO necessary conditions under which the relation Vs : V p N s : N p holds for a transformer. ii) State and explain TWO designs for a transformer to achieve high efficiency. iii) The figure below shows a practical transformer with a light bulb connected across the secondary coil. If an identical light bulb is connected in parallel with the first one, describe what would happen to the secondary current, the secondary voltage, the back e.m.f. in the primary coil and the primary current. [6] Essay 01-4c Induced emf c) A metal rod PQ of length l is moved with constant velocity v across a uniform magnetic field of flux density B as shown. A potential difference of magnitude Blv is developed across PQ. i) By considering the force(s) acting on an electron in the rod, explain how the potential difference is developed and why it remains constant. ii) Show that the result is consistent with the law of electromagnetic induction. iii) What would the situation be if the rod is moved with acceleration? Explain briefly. [7] Essay 02-4b Generator b) A rectangular coil of N turns, each of area A, is placed with its plane perpendicular to a uniform magnetic field of flux density B as shown. At time t = 0 s, the coil is rotated in a clockwise direction with a uniform angular speed . i) Derive an expression for the variation of the induced e.m.f. in the coil with time. Sketch a graph to show its variation within one cycle and indicate when the plane of the coil is parallel to the magnetic field. ii) In an actual a.c. generator the coil is wound around a soft iron cylinder, which is laminated. State and explain TWO advantages of such a design. [7] Essay 03-4a Self induction 4. a) Explain why sparking would occur between the switch contacts if the current in a coil is interrupted when the circuit breaks but not when it is closed. Explain the energy change when the circuit breaks and how sparking can be prevented by adding a capacitor to the circuit. (5 marks)