Hoover Dam has been supplying a portion of the southwest's electrical
power since 1935. A project completed in 1993 modernized the Dam's power
plant and greatly increased it's output to approximately 2000 Megawatts.
The object of this problem is to design a portion of this modernization
project. The task is to take the energy stored in the gravitational potential
energy of the water in Lake Mead, and make it available as electricity
for use in an industrial center in the vicinity of LA, nearly 300 miles
away.
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- At the base of the Dam's 726 foot tall wall, there are 17 generators.
These generators are powered by water that falls down 220 m shafts onto
turbines which turn the generators. What volume of water must fall in each
second in order to power one of the generators?
- This generator consists of a coil of wire with a radius of 1m which
is rotated by the turbine at a rate of 60 Hz. The coil is in a 0.1 T magnetic
field which induces an AC EMF in the coil. If this generator produces an
RMS voltage across its terminals of 16,500 V, how many turns of wire should
the coil have?
- The generator is attached to a transformer which steps up the voltage
for transmission. If the generator is producing its maximum power, what
is the impedance across the transformer?
- The power from this generator is to be transmitted to LA via a copper
cable that is 5cm in diameter. If this cable is to be 300 miles long, what
is the total resistance across this cable?
- In LA, the cable will connect to another transformer which will step
the voltage down to a level that the factories in the industrial center
can use. The power delivered by this transformer will be proportional to
the voltage drop across its primary coil. This means that in order to be
as efficient as possible, the impedance across the transformer must be
large compared to the resistance in the cable. What impedance must the
transformer have if the voltage drop across the cable is to be less then
the voltage drop across the cable and transformer combined by a factor
of 108?
- How much power is dissipated by the resistance in the cable?
- What is the minimal integer number of turns the transformer at the
Dam needs to have in each of its coils in order to accomplish this change
in voltage?
- For industrial use, it is convienient to have power available in voltages
greater than 120 V. For this reason, the standard voltage for industrial
use is 66,000 V. What is the minimal integer number of turns it needs to
have in each of its coils, in order to step the transmission voltage down
to this level?
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Work supported in part by NSF grant DUE-9455561 |
These problem 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 (AHA's) Problem sight is mentioned and the URL given.
To contribute problems to this site, send them to redish@quark.umd.edu.
