| Power & Energy |
An Introduction To Electrical Power And Energy
Why Do You Need To Know About Electrical Energy?
A power station is a place where other forms of energy - coal, gas, potential
energy in water and nuclear energy - are turned into electrical energy for
transmission to places that use electrical energy. Electrical engineering
is concerned with transmission and ultilization of two things - energy and
information. Here, in this lesson, we are going to focus on power and
energy. In this lesson you will want to learn the following.
Given an electrical circuit or device
Be able to compute instantaneous rate of energy use (power).
Be able to compute how much energy is used over a period of time.
Be able to compute how much energy is stored in an electrical storage device
like a battery or a capacitor.
What Is Electrical Power?
Electrical power is conceptually simple. Consider a device that has a
voltage across it and a current flowing through it. That situation is
shown in the diagram at the right.
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The
voltage
across the device is a measure of the energy - in joules - that a unit charge -
one couloumb - will dissipate when it flows through the device. If the
device is a resistor, then the energy will appear as heat energy in the
resistor. If the device is a battery, then the energy will be stored in
the battery.
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The
current
is the number of couloumbs that flows through the device in one second.j
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If each couloumb dissipates V
joules, and I couloumbs flows in one second, then the rate of energy dissipation
is the product, VI .
That's what power is - the rate at which energy is expended. The rest of
the story includes these points.
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It doesn't matter what the
electrical device is, the rate at which energy is delivered to the device is VI
as long as the voltage and current are defined as shown.
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The power can be negative.
If the device is a battery, then current - as defined in the figure - can easily
be negative if, for example, a resistor is attached to the battery. If the
power is negative, then the rate at which the device expends energy is negative.
That really means that it is delivering energy in that situation.
Power in Electrical Devices
A resistor is one device for which you can compute power dissipation.
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A symbol for a resistor is
shown below, along with a voltage, Vr, across the resistor and
a current, Ir, flowing through the resistor. 
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We can compute the power
delivered to the resistor. It's just the product of the voltage across the
resistor and the current through the resistor, VrIr . But there's more to the story.
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In a resistor, there is a
relationship between the voltage and the current, and we can use that knowledge
to get a different expression - one that will give more insight.
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We know that Vr
= Rir, so the power is just:
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Power into the resistor = VrIr
= (RIr)Ir
= R(Ir)2 . -
We can also use the expression
for the current Ir = Vr/R,
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Power into the resistor = VrIr
= Vr(Vr/R) = (Vr)2/R .
At different times, these two results - which are equivalent - can be used -
whichever is appropriate. Besides being a useful result tthese are also
illuminating results (And that's not a reference to the fact that a typical
light bulb is a resistor that dissipates power/energy.).
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The power dissipated by a
resistor is always positive. That means that it does not (and in fact it
could not) generate energy. It always dissipates energy - uses it up -
contributing to the heat death of the universe.
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We know the power is positive
because R is always positive (and it will always be for any resistor that
doesn't have hidden transistors) and because the square of the current has to be
a positive number.
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