An
Introduction To Electrical Power And Energy
Why
Do You Need To Know About Electrical Energy?
What
Is Electrical Power?
Power
and Energy In Electrical Devices
Resistors
Batteries
Problems
You are at: Basic Concepts
 Quantities  Power & Energy
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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.

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.
(Click here to go to the lesson on
voltage if you want to review.) 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.

The current
is the number of couloumbs that flows through the device in one second.j
(Click here to go to the lesson on
current if you want to review.)

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.

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.

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.

A symbol for a resistor
is shown below, along with a voltage, V_{r}, across the
resistor and a current, I_{r}, flowing through the resistor.

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, V_{r}I_{r}.
But there's more to the
story.

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.

We know that V_{r}
= Ri_{r}, so the power is just:

Power into the resistor
= V_{r}I_{r} = (RI_{r})I_{r}
= R(I_{r})^{2}.

We can also use the expression
for the current I_{r} = V_{r}/R,

Power into the resistor
= V_{r}I_{r} = V_{r}(V_{r}/R)
= (V_{r})^{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.).

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.

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.
Problems
P1. You
have a 1KW
resistor, and there is 25 volts across the resistor. Determine the
power (in watts) that the resistor dissipates.
P2. You
have a 25 watt light bulb that operates with 12.6 volts across it.
Determine the resistance of the light bulb.
Power
In Batteries
Batteries are ubiquitous components. They are in TV remotes, cell
phones and things like that. But, batteries also appear in places
you don't expect them to be. For example, you can turn this computer
off. When you turn it back on it remembers things and recalculates
things like the time. Now, you expect that for things that can be
stored on a hard drive. You don't expect it for the time.
When you turn this computer off and later turn it back on it will have
the right date and time. How does it do that? If you think
about it (and don't do that for too long!) you have to believe that there
is a battery somewhere inside the computer and that when you turn the computer
off that battery runs some sort of little clock hidden inside the computer.
You can't see the clock and you wouldn't even know it's there, but you
can probably see the time now on the task bar of this computer  and it's
probably close to being right!
Batteries are used to solve many problems.

They are used to provide
power to run things like computer clocks that need to keep running even
in the absence of AC power.

They are used to store
energy for things like starting a car. When you run the car you generate
energy (from the gasoline) and store it in the car battery. Then
there is energy there when you need it to get the car going again.

They are used for low
power devices to make them portable. That includes things like cell
phones, TV remotes and calculators.
You use batteries  whether you want to or not, and whether you know it
or not! You need to be able to compute some of the quantities involved.
Here is a simple circuit where a resistor is connected to a battery.
We know some salient facts about this circuit.

There is energy stored
in the battery and the battery delivers stored energy to the resistor.

The resistor dissipates
energy, and what happens physically is that the electrical energy that
is delivered to the resistor gets turned into heat energy and the resistor
becomes warmer.
Now, we need to look at a circuit diagram for this situation. That
circuit diagram is shown to the right of the picture below.

In the diagram, we have
defined a battery voltage, V_{b},
and a current, I_{r}.

Notice that we have used
a natural definition for the current polarity. We have the arrow
pointing out of the battery and into the resistor. We do that because
we know that positive charge actually flows from the battery terminal through
the resistor.

That definition of current
polarity raises questions about calculation of power to/from the battery.
Let us consider the power flow into the battery.
Power flow into the
battery or any other device  is the product, VI, when

V
is the voltage across the device, and

I
is the current flowing into the device.

Remember, for our polarity
conventions here, the current arrow points into the terminal of the device
that is labelled "+" for the voltage definition.
We have reproduced the diagram from above here to emphasize how the voltage
and current polarities are defined. Notice that the current arrow
in our earlier definition points toward the "+" sign on the device.
In the batteryresistor circuit below, the current arrow is directed out
of the positive ("+") terminal of the battery. That means the power
delivered to the battery must be computed by (note the minus sign!):
P =  VI
What does this mean?
Let's look at a numerical example. Let's assume the battery voltage
is 12 volts and the resistor is 24 ohms. That means the current is
0.5 amps, i.e.:
I_{r} = 12v/24W
= 0.5a
In other words, the
power flowing into the battery is:
P =  V_{b}
I_{r} =  12 * 0.5 =  6w

The power flowing into
the battery is negative!

The power flowing out
of the battery is positive!

And, it makes sense because
we know the battery supplies power.
How much energy is stored
in a battery?

Batteries are often rated
in amperehours (or milliamperehours) and an amperehour is really
a unit of charge.

As a battery is used it
discharges  charge flows from the battery  but it tends to hold a constant
voltage. This is different than the internal resistance of the battery.
What we are saying here is that as time goes on  for the same current
drawn from the battery  the voltage stays about the same. There
may be a slight dropoff but it is not very large.

Thus, if we have a 12.6
v battery, it will have something close to 12.6v until it gets close to
being discharged.

Let's say we have a 12.6v
battery rated at 70 amperehours.

Assuming it can deliver
1 ampere for 70 hours, then it will be delivering

Power = 12.6v x 1.0 amp
= 12.6 watts for 70 hours.

That works out to 12.6
x 70 = 882 watt hours or .882 kwhr.  and remember you pay the

electric company
by the kilowatthour!

In joules we have 882
whr x 3600sec/hr = 3,175,200 joules.
That might sound like a lot, but an interested student might want to compare
that amount of energy with the energy stored in a gallon of gasoline.
Problems
Power/Energy
Problem Basic6P01
Power/Energy
Problem Basic6P02  Grandfather Clock
Power/Energy
Problem Basic6P03  Town Power
Power/Energy
Problem Basic6P04  Light Bulb
Power/Energy
Problem Basic6P05
Power/Energy
Problem Basic6P06  Resistor
Power/Energy
Problem Basic6P07  Which resistor is warmer?
Power/Energy
Problem Basic6P08  AC Power
Links to Other Lessons
on Basic Electrical Engineering Topics
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your comments on these lessons.