Dan is the proud owner of a pet love bird named Felix. One day while
Dan was cleaning Felix's cage, Felix flew out an open window. Looking out
the window, Dan saw Felix perched on a high tension power line just outside
Dan's window. In this problem, we will investigate how Felix is able to
rest on such a wire without injury, Dan's ill fated attempt to retrieve
Felix, and perhaps gain some insight into why high tension power cables
are generally far away from high rise apartment buildings.
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- Before we can consider the effects it might have, we must consider
the high tension power line itself. Such wires are frequently constructed
by twisting copper wires together into a large flexible bundle. Consider
such a cable with a diameter of 4 cm. If this cable is 10 km long, what
is its resistance?
- High tension power lines connect the transformers at a power plant
to the transformers at a substation where the voltage is stepped down for
household use. The impedance of the transformer at the substation will
vary greatly depending on the energy requirement it must meet. Suppose
that the transformer connected to the line where Felix is perched has an
impedance of 100,000 Ohms. If the root means squared voltage across the
transformer is to be 25,000 V, what must the root means squared voltage
across the transformer and the power line be?
- What is the root mean squared current though the power line?
- Estimate the distance between Felix's feet.
- What is the voltage drop in the power line across this distance?
- If Felix's legs have a resistance per centimeter of about 1 MOhm, estimate
the resistance from foot to foot.
- From the above information, calculate the current through Felix's legs.
- Assume that birds' sensitivity to electricity is similar to humans
and determine if Felix can feel the current through his legs.
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Part 2: Noticing Felix on the power cable, Dan decided to retrieve him.
In order to do this, Dan stepped out onto the window sill to call to Felix.
Once on the sill Dan began to slip and in order to avoid plunging to his
death he jumped to cable where he found himself hanging without hope of
returning to the window sill. Felix, disturbed by the commotion flew back
into the apartment.
- Estimate the distance between Dan's hands, and calculate the voltage
drop in the cable across this distance.
- The resistance from hand to hand on a person is about 400 Ohms. What
is the strength of the current through Dan?
- According to the table, is this current dangerous?
Part 3: Unable to return to the window, and too high in the air to jump
to the ground, Dan made his way to the nearest support tower. This tower
was unfortunately for Dan made of metal and grounded. As Dan reached for
the tower with his foot, he created a link between the grounded tower and
the high voltage cable. Current surged through this low resistance path
to ground, killing our unfortunate hero.
- Assuming that Dan's apartment is near the substation, what was the
root mean squared voltage across Dan's body?
- If the resistance from Dan's hand to his foot is about 500 Ohms, what
was the current through his body?
- This value should be off the chart for listed effects. To get an idea
for what type of effect it might have, calculate the power dissipated though
Dan.
Part 4: From the above story, it should be clear why in the real world,
great care is taken to keep high voltage power lines out of reach. As a
final exercise we will examine how Dan might have forced Felix off his
perch while sparing his own life.
- While the best solution may have been to leave the window open and
put some of Felix's favorite food on the sill, let's examine what would
have happened if Dan had reached out with a long plastic rod. Plastics
generally have resistivities on the order of 1012 Ohm m. If
Dan had a pole of such material with a diameter of 3 cm, and a length of
3m, what would be the resistance though that pole?
- How much current would flow across this pole if a 25,000 V potential
difference were placed across its ends? Would this be safe?
- Is it possible for this pole to act as a capacitor and transmit the
current in this fashion?
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.
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Work supported in part by NSF grant DUE-9455561 |
To contribute problems to this site, send them to redish@quark.umd.edu.
