12.2 ALTERNATING CURRENT 12.3 TRANSMISSION OF ELECTRICAL POWER HW/Study Packet

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1 12.2 ALTERNATING CURRENT 12.3 TRANSMISSION OF ELECTRICAL POWER HW/Study Packet Required: READ Tsokos, pp Hamper pp HL Supplemental: Cutnell and Johnson, pp Giancoli, pp REMEMBER TO. Work through all of the example problems in the texts as you are reading them Refer to the IB Physics Guide for details on what you need to know about this topic Refer to the Study Guides for suggested exercises to do each night First try to do these problems using only what is provided to you from the IB Data Booklet Refer to the solutions/key ONLY after you have attempted the problems to the best of your ability UNIT OUTLINE I. ROTATING COILS IN MAGNETIC FIELDS A. ALTERNATING CURRENT B. AC CIRCUITS AND GENERATORS C. ROOT MEAN SQUARED AND PEAK QUANTITIES D. TRANSFORMERS II. TRANSMISSION OF ELECTRICAL POWER A. HOW TRANSFORMERS ARE USED IN POWER TRANSMISSION B. LIVING AND WORKING NEAR TRANSMISSION LINES FROM THE IB DATA BOOKLET WHAT YOU SHOULD BE ABLE TO DO AT THE END OF THIS TOPIC Recognize how the induced emf in a uniformly rotating coil within a B-field is sinusoidal. Explain how AC generators work and why they are important. Know how a transformer works and describe the operation of an ideal transformer. Explain the use of step-up and step-down transformers in power transmission and know how to use the transformer equation!! =!!.!!!! Outline the reasons for power losses in transmission lines and transformers. Understand what is meant by peak and rms current ( I!"# =!! ) and how they are related.! Understand what is meant by peak and rms voltage ( ε!"# =!! ) and how they are related.! Calculate the average power in simple AC circuits ( P!!!! = ε!!"#i!"# ) and solve AC circuits. Discuss how EM fields induce currents in the human body, and their possible risks. 1

2 HOMEWORK PROBLEMS: 1. The coil of an AC generator rotates at a frequency of 60.0 Hz and develops an rms voltage of 120 V. The coil has an area of A = 3.0 x 10-3 m 2 and consists of N = 500 turns. Find the magnitude of the B-field in which the coil rotates. [0.30 T] 2. The graph shows a plot of the output emf of a generator as a function of time t. The coil of this device has a cross-sectional area per turn of m 2 and contains 150 turns. Determine: a) the frequency of the generator. [2.4 Hz] b) the angular speed of the coil. [15 rad s -1 ] c) the magnitude of the B-field. [0.62 T] 3. An oscilloscope is used to measure the voltage wave form across a 500 Ω resistor in an AC circuit. The wave form is shown in the diagram. The time base of the oscilloscope is set to 5.0 ms per division, and its y-gain is set at 0.5 V/cm. Determine: a) the time period and the frequency of the oscillating ε. [20 ms, 50 Hz] b) the peak voltage and the rms voltage. [0.75 V, 0.53 V] c) the rms current through the resistor [0.001A] d) the mean power dissipated in the resistor. [ W] 2

3 4. A lamp is lit by a sinusoidal AC supply with a peak emf of 15.0 V. What DC supply would be required to light an identical bulb to the same brightness? [10.6 V] 5. The emf produced by a generator has the form ε(t) = 5sin(200π)t. Determine: a) the peak emf. [5 V] b) the rms emf [3.5 V] c) the frequency of the emf [100 Hz] d) What peak current will the generator supply when connected to a 10Ω resistor? [0.5 A] e) What is the power dissipated in this resistor? [1.2 W] 6. When a coil is rotated in a uniform magnetic field at a certain frequency, the variation with time t of the induced emf ε is as shown below. The frequency of rotation of the coil is reduced to ½ of its initial value. Sketch a graph of ε(t) vs. t. E 0 0 t 3

4 7. A coil rotates at a constant rate in a uniform magnetic field. The angle of rotation of the coil from its starting position is θ. The variation with angle θ of the emf ε generated in the coil is shown. Sketch a graph showing the variation with θ from the starting position of the emf ε when the rate of rotation of the coil is doubled. E / degree 8. The graph shows the variation with time of electromotive force (emf) for a generator. a) Calculate the rms value of the emf of the generator. [990 V] b) The speed of rotation of the generator is halved with no other changes being made. On the graph, sketch the variation of emf with time. 9. The element of an electric kettle for use with an AC supply is rated as 2400 W. a) What is the rms current through the element when it is used in the UK (240 V)? [10 A] b) What is the maximum current through the element under these conditions? [14 A] c) What is the resistance of the element? [24 Ω] 4

5 10. A step-down transformer inside a stereo receiver has 330 turns in the primary coil and 25 turns in the secondary coil. The plug connects the primary coil to a 120-V wall socket, and there is a current of 0.83 A in the primary coil while the receiver is turned on. Connected to the secondary coil are the transistor circuits of the receiver. Find a) the voltage across the secondary coil [9.1 V] b) the current in the secondary coil [11 A] c) the average electric power delivered to the transistor circuits [1.0 x 10 2 W] 11. A transformer in a radio reduces 120 V AC to 9.0 V AC. The secondary coil contains 30 turns and the radio draws a current of 400 ma. Calculate: a) The number of turns in the primary coil [400 turns] b) The current in the primary [0.030 A] c) The power transformed [3.6 W] 12. An average of 120 kw of electric power is sent to a small town from a power plant 10 km away. The transmission lines have a total resistance of 0.40 Ω. Calculate the power loss if the power is transmitted at: a) 240 V [100 kw] b) V [10W] 5