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PS06 Solution - 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2008 Problem Set 6 Solutions Problem 1: Short Questions (a) If charges flow very slowly through a metal, why does it not require several hours for light to come on when you throw a switch? Even though the average velocity of charges is very slow, when you connect a potential difference across a circuit (wire & light bulb), an electric field is established almost instantly (propagating near the speed of light) everywhere in the circuit, and the electrons begin to drift everywhere all at once. (b) What advantage does 120-V operation offer over 240 V? What are the disadvantages? Both 120-V and 240-V lines can deliver injurious or lethal shocks, but there is a somewhat better safety factor with the lower voltage. On the other hand, a 240-V device requires less current to operate at the same power, and hence generates less heating and loss (I 2 R) in wiring. (c) Why is it possible for a bird to stand on a high-voltage wire without getting electrocuted? The reason is because the potential on the entire wire is nearly uniform, and the potential difference between the bird’s feet is approximately zero. Thus, the amount of current flowing through the bird is negligible, since the resistance through the bird’s body between its feet is much greater than the resistance through the wire between the same two points. (d) If your car’s headlights are on when you start the ignition, why do they dim while the car is starting? The starter motor draws a significant amount of current from the battery while it is starting the car. This, coupled with the internal resistance of the battery, decreases the output voltage of the battery below its the nominal 12 V. This decrease in voltage decreases the current through (and brightness of) the headlights. (e) Suppose a person falling from a building on the way down grabs a high-voltage wire. If the wire supports him as he hangs from it, will he be electrocuted? If the wire then breaks, should he continue to hold onto the end of the wire as he falls?
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PS06 Solution - 2 Problem 1: Short Questions continued As long as he only grabs one wire and does not touch anything that is grounded, he will be safe. If the wire breaks, let go! If he continues to hold on to the wire, there will be a large—and rather lethal—potential difference between the wire and his feet when he hits the ground. (f) A series circuit consists of three identical lamps connected to a battery as shown in the figure below. When the switch S is closed, what happens to the brightness of the light bulbs? Explain your answer. Closing the switch makes the switch and the wires connected to it a zero-resistance branch. All of the current through A and B will go through the switch and lamp C goes out, with zero voltage across it. With less total resistance, the current in the battery becomes larger than before and lamps A and B get brighter.
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