Units of Measurement

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Units of Measurement
Units are one of those things that, like
electricity itself, are almost too obvious. We
all use them every day, without thinking about
them. Units are used to describe the size or
duration of things Units give scale to the world
around us. To describe a rope as long has no
meaning. The rope that is short to me, might
seem long to you. To describe a rope as 10
meters long has a precise meaning, conveyed by
the use of the unit of length called the meter
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Units of Measurement
The meter is a basic unit of length. The second
is a basic unit of duration, or time. Combining
the two gives speed Suppose a runner runs 100
meters in 10 seconds. His speed is
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Units of Measurement
When performing a mathematical operation on
physical quantities, we can carry the units
through the operation as a sanity check. For
example, if when calculating speed, we divide
distance traveled (with units of length) by the
time required to travel the distance (units of
time)
The result has units of (length divided by time),
or length per unit time, which is the same as
units of speed. If the result does not have
units of speed, we did something wrong.
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Unit conversions
Previously, we calculated a speed of 10 m/sec.
Meters per second is a commonly used unit of
speed, but so is feet / sec. Suppose we want the
answer in ft./sec. rather than m/sec. How many
feet in one meter? 3.281
The meters in the numerator of the first quantity
cancel with the meters in the denominator of the
second, and were left with
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Unit conversions
But what if we really want the speed in miles per
hour? There are 5280 feet in one mile, and 3600
seconds in an hour, so
This time, the feet and seconds cancel, and were
left with
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Unit conversions
So 22.37 mph is the same as 10 meters per second,
and 2.237 mph is the same as 1 meter per second.
Thus, we can use
as a conversion factor for converting meters per
second to miles per hour. We can also use its
reciprocal,
for converting miles per hour to meters per
second.
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Unit conversions
Thus, 65 mph is the same as
Weve found conversion factors for converting
speed between the English and metric systems of
units. We can obtain conversion factors for any
physical quantity, and any two systems of units.
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Systems of Units
In the US, were all familiar with the English
system of units
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Systems of Units
Most of us are somewhat less familiar with the
metric system. There are actually two very
similar metric systems, the Meter-Kilogram-Second
(MKS) system for large physical quanities
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Systems of Units
And the Centimeter-Gram-Second (CGS) system,
which is more convenient for small physical
quanities
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Systems of Units
And there is the SI (Le Systeme International
dUnites), which is very similar to the MKS
system, and which we will use most of the time
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Per-Unit System of Measurement
We can know how large a quantity is in standard
units, and still not have an intuitive feel for
its size. For example, someone who isnt
familiar with horsepower might hear of a car
which has a 450 hp. engine and not have any idea
how powerful it is. However, if the average
passenger car has a 225 hp. engine, we could use
its power as the base for per-unit measurement.
The 450 hp. car a per-unit power of 2.0, so we
know its twice as powerful as the base care
(which we may know is the average car). This is
immediately impressive. Another example is the
relative effectiveness factor (also called
brisance) of explosives. The base explosive is
TNT, which has a relative effectiveness of 1.00.
C4s relative effectiveness is 1.34, commercial
dynamites is 0.80, and liquid nitroglycerine is
1.6. Thus, liquid nitro is 1.6 times as
effective (powerful) as TNT. Ka-boom!
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Per-Unit System of Measurement
Suppose we want to measure impedance on a
per-unit basis. Well use 50 Ohms as the base
(the characteristic impedance of commonly used
coaxial cable). An impedance of 150 Ohms on a
per-unit basis is
This per-unit system is often used in radio
systems, where 50 Ohms is a standard input and
output impedance. For power systems, we will
often want to have both a base Voltage (EB) and a
base power (PB)
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Per-Unit System of Measurement
For example, we may choose the base voltage and
base power as
But since power is the product of Voltage and
current, we can derive a base current
And because impedance is the ratio of Voltage to
current, the base impedance is