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Physics 100 – Spring 2015
Enrichment Exercise #EE – 4
Due April 13, 2015
Please PRINT CLEARLY your name: _________________________________________
[Reminder: Please submit your responses at the start of class on the table provided (just inside
the door). Note that anything sue but received one lecture session late is eligible for 50% credit,
after that, no credit is available. Take these Enrichment Exercises as they are intended: an
opportunity to deepen or broaden your understanding of several aspects of the course. Please do
your own work, but you are free to discuss things with others in the class. ]
In this Enrichment Exercise we will explore some additional aspects of electricity and power
transmission. In particular, we will take a look at the major reason why electric power
distribution takes place at very high voltage. To do this effectively, we will do some calculations
that will make very clear why there are those “high tension” towers with wires high above the
ground decorating the landscape, towers that allow the distribution of electricity. We will also
cover another point and that is has to do with how the electricity you use in your house ends up
at 120 volts. Our story will be a partial story, of necessity, but it will contain the essence of the
subject with enough detail that you will work out to make clear why things are as they are.
In class we discussed the fact that in modern societies the electricity that is generated and
transmitted is ac electricity, where ac stands for alternating current. That is, rather than being
steady in a given situation (like would be the case for a dc situation such as with a battery and
bulb in a flashlight) the voltage oscillates and so does the current. We will begin with a reminder
about transformers, a bit of quick review of what was mentioned in class.
Transformers: One of the things we mentioned in class is that it is possible to change the voltage
and current by use of a transformer in the ac situation. Such devices typically should be thought
of as not changing the power available, but changing from high voltage and low current (in the
lines on one side of the transformer) to low voltage and high current (in the lines on the other
side of the transformer) with the power (in the ideal case), i.e., the product of voltage times
current, remaining the same. The transformer works because of the trapped magnetic field. For
more than you might want know about transformers, you might want to take a look at
http://en.wikipedia.org/wiki/Transformer. In the contents list on that web page if you click
section 1.1 you will be reminded that a simple transformer can be made by using turns of wire
and the ratio of the turns of wire on the two sides of the transformer is equal to the ratio of
voltages on the two sides: Vin/Vout = Nin/Nout. The power entering a transformer is IinVin and
this is equal to the power leaving the transformer IoutVout. So, by varying the ratio of the turns
of wire, one can produce any output voltage for a given input voltage, with a corresponding
change in the output current. If the voltage is increased by the transformer, the current is
decreased (because the power remains the same). This image is from the web site cited just
above. It shows different turns of wire in a traditional transformer design. The two sides of the
transformer are traditionally given names: primary for the input side, secondary for the output
side.
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You may know that you can purchase low voltage ac lights for use under the counters in your
kitchen. If the lights require 20 volts and 2 amps, and your house is wired with 120 volts, a
transformer will be necessary to lower the voltage. (1) If the 120 volts side of the transformer
is the input side (primary) for the electricity, what current will the 120 volt line supply
when a low voltage lamp of the type mentioned above is lit when attached to the output
(secondary) side of the transformer? If you have any trouble with this question, you may want
to take a look at the first part of this web site:
www.naterecording.com/transformerturns.pdf
Resistance in wires: In class we learned that different materials resist the flow of electric current
by different amounts. So, we have good conductors (e.g. copper) and we have good insulators
(e.g. most plastics). But, the electrical resistance of copper, while small, is not zero. The
electrical resistance that a wire provides is determined by the material, but also by the geometry.
If we imagine that a wire is just a long small diameter cylinder (like a long round pencil), then
the electrical resistance is given by R = ρL/A where ρ is called the resistivity and is tabulated for
each material, L is the length of the wire and A is the cross sectional area of the wire (i.e. the
area of the circle for a round wire). The bigger the area, the less resistance the wire presents to a
current. Now, the resistivity of copper is small, 1.7 x 10-8 Ωm; yes, the unit is the Ωm. A typical
copper wire that is used for electrical transmission (not what you have in your lamp cord) has a
diameter of about 0.64 cm (roughly ¼ inch). (2) What is the electrical resistance in Ohms for
a one kilometer length of this copper wire?
A typical reasonably-sized private residence has electrical service rated at 100 amps or 200
amps, at 120 volts depending on the house. So, if we take 200 amps, then the power that is
designed to be able to be delivered to the house is Power = (current)(source voltage) =
(200)(120) = 24,000 watts. For a 100 amp house it would be 12,000 watts. Typically someone
living in the house would not use this total power, because everything that uses electricity in the
house may not be operating at the same time, but this is what can be safely delivered. [The
heating elements on a stove are each several thousand watts, you have 100 watt bulbs, your
hairdryer is 1200 watts, you may have an electric clothes dryer, etc., etc.].
So, now suppose that we have a little village of 100 houses, and each has been provided with 200
amp service at 120 volts. (3) What is the total power that might (in the worst case) have to
be delivered to the entire village of 100 houses? Suppose that there is a small hydroelectric
generating station located some distance from the little village and there is the plan to deliver this
amount of power to the village directly using a voltage of 120 volts. (4) How much power will
be lost in each kilometer of a copper transmission wire if this is the case? (5) If the
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generating station is 10 km from the little village, what will be the total power loss due to
transmission at 120 volts? Your answer should tell you that if you were running the power
distribution, you might think that this would be pretty inefficient and there ought to be a better
way.
Your answer to questions 3-5 should have told you that there would be substantial transmission
losses compared to the needs of the village if the transmission were done at 120 volts. But, we
know that transformers (let’s say ideal transformers) are able to cause a shift from high current,
low voltage to low current, high voltage. Let us take a look at what this might mean for our
transmission problem for our little village. In (3) you computed the power that might have to be
delivered to the little village in the worst case. In (4) and (5) you computed the consequences of
doing that transmission at 120 volts. Here next we will take a look at what would happen if we
used a transformer at the power plant to increase the transmission voltage (and we would need a
transformer used in the opposite sense to decrease the voltage from the transmission line back to
120 volts for use in the homes). So, (6) if we imagine using a transformer at the power plant
to increase the voltage of transmission to 100,000 volts, what current will flow in the
transmission line if the little village is using electricity at the design maximum current?
At this value of the current in the transmission line that you just found, (7) how much power
will be lost in each kilometer of copper transmission wire? (8) If the generating station is
located 10 km from the little village, what will be the total power loss due to the
transmission at 100,000 volts? You should have found a much smaller number for this answer
to question (7) than you did for question (5). This shows you the huge advantage of transmitting
electricity at high voltage. The invention of the transformer and the use of ac approaches makes
this sort of thing relatively easy to accomplish. The larger the city that has to be supplied, the
greater the total current needed and thus the more benefit of going to ever higher voltages. As
we noted in class, the transmission lines that cross the landscape on those tall “high tension”
towers can operate at voltages as high as 500,000 volts. This, of course, has required substantial
technology development in transformers.
As a final comment and question, birds can happily sit on those high voltage lines (as much as
500,000 volts) that cross the landscape without any harm at all (see the picture below). But,
people are sternly warned to never climb the towers and approach the wires. (9) Say in (in 50 –
75 words) words as clearly as you can why it is that a bird can perch on one of those wires
without any harm at all? This you should be able to do with some careful thought based on
what you know from our two lectures about electricity. If not, you can try a web browse and if
you rely on a web site, list the URL for that site at the end of what you have written, but be sure
to explain why your response is correct. Note: the answer is NOT that these wires have
insulation on them. Transmission wires typically have no insulation (to save weight); they are
bare metal conductors.
Here is an image of a bird perched on a wire taken from
http://www.shutterstock.com/pic-70496686/stock-photo-a-starling-bird-perched-on-a-wire.html
(which says that it hosts royalty-free stock photographs)
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