Because energy has many forms, there are many ways to measure
it, and this has led to the definition of many units for it:
calories, therms, watt-hours, ergs, BTU, ... . We will use
the metric unit, which is called the Joule. One joule is roughly
the amount of energy it takes to lift an egg from the bottom of
the refrigerator to the top. It takes 84,000 J to turn 250 ml (1
cup) of room-temperature water into water that is about to boil. A
fresh flashlight battery contains 63,000 J.
Sometimes we are interested in the rate that energy is delivered
or converted into another form. For example, we use a certain
amount of energy every day to keep our house warm -- this is quite
different from getting one lump of energy for the house when you
build it. This new concept is power, which is the rate of
delivery or use of energy (amount of energy divided by the time
interval). Power can be measured in Kilowatts (1000 Joule/second)
or horsepower (3/4 Kilowatt). A stick of dynamite releases less
energy than burning a pint of gasoline, but the dynamite explosion
is a high power event because the time interval is small. For a car
to change its speed quickly, it must change its energy quickly,
which requires a high power engine (200 horsepower!). A bright
light bulb (200 Watts) is rapidly converting electrical energy into
heat and light -- 200 Joules in every second.
How electrical circuits deliver energy
We should distinguish carefully between the electrical potential
(measured in volts), electrical current (measured in amperes), and
power (measured in watts).
Since we can't see inside batteries and wires, we have to
visualize what is happening.
To understand the distinctions, think of a water mill. As water
goes through the mill, it leaves behind energy, but all the water
continues going. There has to be both a stream leading to the mill
and a stream to carry the water away, or the water mill will not
work. The flow rate of the water is the same in the arriving stream and
in the departing stream. What is different is that the water has
decreased in height -- it has given up gravitational potential
energy.
Power is the rate of delivery of energy -- the amount of
energy per second. The amount of power delivered to the mill is
determined by the rate that water flows through the mill, but it
also depends on the height difference at the mill.
In the same way, consider a light bulb. As electrical current
goes through the light bulb, it leaves behind energy, but all of
the current continues going. There has to be both a wire leading to
the light bulb and a wire to carry it away, or the light bulb will
not work. The current is the same in the two wires. What is
different is that the voltage is different on the two sides of the
light bulb. The electrical power delivered to the light bulb is
determined by both this voltage difference and by the current
through the light bulb.
The energy that is delivered to the light bulb comes from inside the
battery. This is another kind of potential energy -- energy that is stored,
until we want to use it. The quantity that corresponds to the height of the
water wheel is the voltage of the battery, which is sometimes called the
potential of the battery. It tells us how much energy the battery will
release for each unit of charge that moves through the circuit.
You may still want to object that electricity is unlike flowing
water, in that the electrical current has to return to the battery
or the power plant, while water just runs to the ocean. But this is
not after all so different: it is always true that outside the
battery the current moves to lower voltage, just as water always
flows down hill. Inside the battery, something happens that gets
the current back to 1.5 Volts. The corresponding part of the water
cycle is that the sun adds energy to the ocean, evaporating the
water, and lifting it to the tops of the mountains. We tend to
ignore this part of the water circuit because we can't see the
water vapor moving upwards, but it has to be there for the system
to work.
Voltage and power
A battery has a voltage whether it is in use or not, just as
a water tower provides pressure whether your faucet is open or not.
Only when
there is a current is the battery supplying power. The voltage and
current both play a role in determining how much power is supplied,
according to the relationship
Power (in watts) = voltage x current
Similarly, a high dam on a large river provides both pressure and flow
rate to produce high power.
Two fresh D cells in series give 3.2 V; when
connected to a standard flashlight bulb, the current is 0.33 A. The
power delivered is the product of these two numbers: 1.06 Watts.
This implies that a pair of alkaline D cells (which contain 126,000
J) could keep the bulb bright for 119,000 seconds (33 hours).
This relationship explains why electrical power is moved from
generating plant to the city using high voltage lines: a very large
amount of energy is transmitted every second, so the voltage must
be large (the alternative of using low voltage and a large current would require
thick wires to accomodate the large current, just as moving a lot of water requires large
pipes).
Ordinary household voltage ranges from 110 V to 120 V. It is the
equivalent of about 75 flashlight batteries in series.
