Alternative Homework Assignment: Electrical Safety

Chris was ironing clothes when his roommate Mike turned on a fan in the room. Suddenly the lights went out. Realizing they had blown a fuse, they went to the basement to replace it. As the removed the burned out fuse, Chris noticed some dirt in the treads of the fuse box. Without thinking, he reached to brush it away with a finger. Chris quickly pulled his finger away as he received an extremely painful shock. In the following problem we will consider what caused the fuse to blow, how strong the shock Chris received was, and what fortunate happenstance saved his life.

Picture Courtesy of Michael Bath

1. A standard household fuse allows a current of up to 15 A before it breaks. With a standard household voltage of 120 V, what is the maximum power that can be delivered though such a fuse?
2. If the room was lit by three 100 W light bulbs and the iron uses 1100 W, what is the minimum power used by the fan?
3. Use the table provided to estimate the strength of the current that passed through Chris.
4. The resistance from hand to foot on an average person is about 500 Ohms. Assuming that Chris had an unusually high resistance it may have been 600 Ohms. Use this to estimate the amount of current that might have passed though Chris? What effect would this have had?
5. What may have helped Chris is that he was wearing rubber soled shoes. The resistivity of rubber is approximately 10¹³ Ohm m. Estimate the resistance across the soles of Chris' shoes.
6. Calculate the current that should pass through Chris with this resistance value. Does this value explain the shock he received?
7. Since rubber is such a good insulator, Chris' foot and the floor may have behaved as the two plates of a parallel capacitor instead of a resistor. Based on your estimate of the current that passed through Chris, estimate the impedance of the foot/floor capacitor.
8. Household electricity alternates at a frequency of 60 Hz. At this frequency, what value of capacitance corresponds to the impedance value calculated above?
9. Considering that rubber has a dielectric constant of approximately 3, is this a reasonable value for the capacitance?
   

Work supported in part by NSF grant DUE-9455561

These problems written and collected by K. Vick, E. Redish, and P. Cooney. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity-Based Physics (ABP) Alternative Homework Assignments are mentioned and the source cited.