Power in electric
circuits
In addition to voltage and current, there is
another measure of free electron activity in a circuit:
power. First, we need to understand just what power is
before we analyze it in any circuits.
Power is a measure of how much work can be
performed in a given amount of time. Work is
generally defined in terms of the lifting of a weight
against the pull of gravity. The heavier the weight and/or
the higher it is lifted, the more work has been done.
Power is a measure of how rapidly a standard amount of
work is done.
For American automobiles, engine power is
rated in a unit called "horsepower," invented initially as a
way for steam engine manufacturers to quantify the working
ability of their machines in terms of the most common power
source of their day: horses. One horsepower is defined in
British units as 550 ft-lbs of work per second of time. The
power of a car's engine won't indicate how tall of a hill it
can climb or how much weight it can tow, but it will
indicate how fast it can climb a specific hill or tow
a specific weight.
The power of a mechanical engine is a
function of both the engine's speed and it's torque provided
at the output shaft. Speed of an engine's output shaft is
measured in revolutions per minute, or RPM. Torque is the
amount of twisting force produced by the engine, and it is
usually measured in pound-feet, or lb-ft (not to be confused
with foot-pounds or ft-lbs, which is the unit for work).
Neither speed nor torque alone is a measure of an engine's
power.
A 100 horsepower diesel tractor engine will
turn relatively slowly, but provide great amounts of torque.
A 100 horsepower motorcycle engine will turn very fast, but
provide relatively little torque. Both will produce 100
horsepower, but at different speeds and different torques.
The equation for shaft horsepower is simple:
Notice how there are only two variable terms
on the right-hand side of the equation, S and T. All the
other terms on that side are constant: 2, pi, and 33,000 are
all constants (they do not change in value). The horsepower
varies only with changes in speed and torque, nothing else.
We can re-write the equation to show this relationship:
Because the unit of the "horsepower" doesn't
coincide exactly with speed in revolutions per minute
multiplied by torque in pound-feet, we can't say that
horsepower equals ST. However, they are
proportional to one another. As the mathematical product
of ST changes, the value for horsepower will change by the
same proportion.
In electric circuits, power is a function of
both voltage and current. Not surprisingly, this
relationship bears striking resemblance to the
"proportional" horsepower formula above:
In this case, however, power (P) is exactly
equal to current (I) multiplied by voltage (E), rather than
merely being proportional to IE. When using this formula,
the unit of measurement for power is the watt,
abbreviated with the letter "W."
It must be understood that neither voltage
nor current by themselves constitute power. Rather, power is
the combination of both voltage and current in a
circuit. Remember that voltage is the specific work (or
potential energy) per unit charge, while current is the rate
at which electric charges move through a conductor. Voltage
(specific work) is analogous to the work done in lifting a
weight against the pull of gravity. Current (rate) is
analogous to the speed at which that weight is lifted.
Together as a product (multiplication), voltage (work) and
current (rate) constitute power.
Just as in the case of the diesel tractor
engine and the motorcycle engine, a circuit with high
voltage and low current may be dissipating the same amount
of power as a circuit with low voltage and high current.
Neither the amount of voltage alone nor the amount of
current alone indicates the amount of power in an electric
circuit.
In an open circuit, where voltage is present
between the terminals of the source and there is zero
current, there is zero power dissipated, no matter
how great that voltage may be. Since P=IE and I=0 and
anything multiplied by zero is zero, the power dissipated in
any open circuit must be zero. Likewise, if we were to have
a short circuit constructed of a loop of superconducting
wire (absolutely zero resistance), we could have a condition
of current in the loop with zero voltage, and likewise no
power would be dissipated. Since P=IE and E=0 and anything
multiplied by zero is zero, the power dissipated in a
superconducting loop must be zero. (We'll be exploring the
topic of superconductivity in a later chapter).
Whether we measure power in the unit of
"horsepower" or the unit of "watt," we're still talking
about the same thing: how much work can be done in a given
amount of time. The two units are not numerically equal, but
they express the same kind of thing. In fact, European
automobile manufacturers typically advertise their engine
power in terms of kilowatts (kW), or thousands of watts,
instead of horsepower! These two units of power are related
to each other by a simple conversion formula:
So, our 100 horsepower diesel and motorcycle
engines could also be rated as "74570 watt" engines, or more
properly, as "74.57 kilowatt" engines. In European
engineering specifications, this rating would be the norm
rather than the exception.
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REVIEW:
-
Power is the measure of how much work can
be done in a given amount of time.
-
Mechanical power is commonly measured (in
America) in "horsepower."
-
Electrical power is almost always measured
in "watts," and it can be calculated by the formula P =
IE.
-
Electrical power is a product of both
voltage and current, not either one separately.
-
Horsepower and watts are merely two
different units for describing the same kind of physical
measurement, with 1 horsepower equaling 745.7 watts.
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