A farmer reportedly stole electrical power by
strategically placing a large coil of wire beneath the high-voltage
transmission lines that crossed his field. For several years, the
farmer obtained free electricity to operate equipment for his farm,
until the power company finally discovered the theft. Eventually
the farmer was convicted of stealing power even though no physical
connections were made to the transmission lines. Use this
information and your knowledge of physics to answer the following
questions: (Each question is worth 2 points, except for #4, which
is worth 5 points, for a total of 25 points.)
1) Without examining the farmer's property, how
could the power company recognize that energy was being stolen?
2) What principle did the farmer utilize to steal electrical
power from the transmission lines?
3) How must the farmer have positioned and oriented the coil in
order to most effectively achieve his goal?
4) Assume that the lowest transmission line was10 m above the
ground and carried current alternating at 60 Hz with a maximum of 150 A
at 230 kV. If the coil was in the shape of a square 5 m on a side
and touching the ground, approximately how many turns (loops) of wire
were needed for the coil to produce a standard voltage of 120
V?
5) Why would the voltage in the coil vary depending on the time of
day? When would you expect it be largest and smallest?
6) What is the frequency of the current in the coil? What is the phase
angle between the voltage in the transmission line and the coil?
7) If the coil and all of the equipment connected to it had a total
impedance of 200 ohms, what is the maximum rate at which energy was
consumed?
8) Assuming a cost of $0.10/kW-h, what is the approximate value of the
energy stolen by the farmer over the period of one year?
9) Estimate the cost to make the coil, assuming that the farmer used
12-Gauge copper wire at a cost of $0.15/ft. Evaluate the
cost-effectiveness of the farmer's design and calculate the approximate
pay-back period for his investment.
10) What advice would you give to the farmer to maximize the efficiency
of his design?
11) What other insights can be learned from this problem?