Download Lesson Plan - GK-12 at Harvard University

JASON BELLORADO
[email protected]
GK-12 PROGRAM - HARVARD UNIVERSITY
PHYSICS FIRST! - HONORS OPTION
KILOWATT-HOURS
FEBRUARY 3, 2004
The Physics of Electricity:
All matter is made up of atoms, and atoms are made up of smaller particles,
called protons (which have positive charge), neutrons (which have neutral
charge), and electrons (which are negatively charged). Electrons orbit around
the center, or nucleus, of an atom, which is made up of neutrons and protons.
Some material, particularly metals, have certain electrons that are only
loosely attached to their atoms. They can easily be made to move from one
atom to another if an electric field is applied to them. When those electrons
move among the atoms of matter, a current of electricity is created.
This is what happens in a piece of wire when an electric field, or voltage, is
applied. The electrons pass from atom to atom, pushed by the electric field
and by each other (they repel each other because like charges repel), thus
creating the electrical current. The measure of how well something conducts
electricity is called its conductivity, and the reciprocal of conductivity is called
the resistance. Copper is used for many wires because it has a lower resistance
than many other metals and is easy to use and obtain. Most of the wires in your
house are made of copper, although some older homes still use aluminum
wiring.
The energy is really transferred by the chain of repulsive interactions
between the electrons down the wire, not by the transfer of electrons. This is
just like the way that water molecules can push on each other and transmit
pressure (or force) through a pipe carrying water. As the electrons move
through a "resistor" in the circuit, they interact with the atoms in the resistor
very strongly, causing the resistor to heat up - hence delivering energy in the
form of heat. Or, if the electrons are moving instead through the wound coils
of a motor, they instead create a magnetic field, which interacts with other
magnets in the motor, and hence turns the motor.
Electrical Units of Energy:
The "International System of Units" form the basis for the electrical units we
use. In such, both work and energy have the same unit, called the "Joule".
To understand the definition of a Joule, we first have to understand a
definition of the unit of force used in the International System of units, which
is called the "Newton". A Newton of force is defined to be the force that can
accelerate a mass of 1 kilogram (about 2.205 lbs), such that it picks up 1 meter
1
per second of velocity during each second that the force is exerted. Thus, after
one second, the 1 kilogram mass is going 1 meter per second, after two
seconds, 2 meters per second, and so on.
A Joule is also the amount of energy we expend as work if we exert a force
of 1 Newton of Force over a distance of one meter. Intuitively, 1 Joule is about
how much energy it takes to lift 1 lb about 9 inches.
When we talk about powering appliances in our home with electricity, we
are not usually interested in how much energy an appliance uses, but rather
the rate of energy use, or in other words, how much energy per unit time the
appliance draws. This quantity is called the "power":
Power = Energy / Time
(1)
In particular, for electrical power we use the "Watt":
1 Watt = 1 Joule / Second
(2)
Remember the definition of energy given in your physics class; “energy is
the ability to do work”. Charged particles (electrons) have the ability to do
work when a force (or voltage) is applied to them, causing a net flow of
electrical charge called a current. A current is defined as the rate of charge
flow, and is given by the equation:
Current (I) in Amperes
Current = Charge / Time
Charge (Q) in Coulombs
(3)
Time (t) in Seconds
We illustrate this in the following example:
Example 1: If a .2-Ampere current flows through a circuit for 1 minute, how
much charge has passed through the circuit?
Answer: Rearranging equation (3) above, we get the following equation for
charge:
Charge = Current *Time
Plugging in the given values we solve for charge as:
Charge = (.2 Amps) * (60 seconds)
= 1.2 Coulombs
2
Given that we apply a voltage (V) and produce a current (I), we can
calculate the power (P) as:
Power (P) in Watts
Power = Voltage * Current
Voltage (V) in Volts
(4)
Current (I) in Amperes
We illustrate this with the following 2 examples:
Example 2: If a 100-Watt light bulb is connected to a 240-Volt voltage source,
how much current will pass through it?
Answer: Rearranging equation (4) above, we solve for the current as:
Current = Power / Voltage
= 100 Watts / 240 Volts
= .42 Amperes
Example 3: If a 60-Watt light bulb is connected to a battery and a .5 Amp
current is observed, what is the resistance of the light bulb?
Answer: In order to determine the resistance of the light bulb, we first need to
know the voltage applied to it. For this, we rearrange equation (4) above as:
Voltage = Power / Current
= 60 Watts / .5 Amps
= 120 Volts
To determine the resistance from the current and voltage across the resistor,
we will use Ohm’s Law:
Voltage in Volts
Voltage = Current * Resistance
Current in Amperes
(5)
Resistance in Ohms
(You have seen Ohm’s Law in class by now and it should look familiar. If is
doesn’t, then memorize it because it is the most important equation in
electrical circuits).
Rearranging equation (5) we solve for the resistance as:
Resistance = Voltage / Current
= 120 Volts / .5 Amps
= 240 Ohms
3
It is important not to confuse power and energy, although they are closely
related. Just remember that power is the rate at which energy is delivered,
not an amount of energy itself. With simple algebra, can manipulate formula
(1) to solve for energy instead:
Energy = Power x Time
Power in Watts
Energy in Joules
(6)
Time in seconds
We know illustrate this point with an example:
Example 4: A 100-Watt light bulb is a device that, ideally, converts 100 joules
of electrical energy into 100-Joules of electromagnetic radiation (light) every
second (in reality, a light bulb converts some of the energy to light and some to
heat). If you leave a 100-Watt light on for one hour, that is, 3600 seconds, then
what is the total amount of energy (in Joules) used?
Answer: Using equation (6) above and the given information, we solve for the
energy used as:
Energy = Power x Time
= (100 Joules/Second) x (3600 Seconds)
= 360,000 Joules
Watts are a very convenient unit when working with appliances, for
example, for specifying the power of light bulbs. But there are also times when
you are interested in the total energy use, for example, when you are
calculating how much your utility bill is going to be. You can see that it is not
so convenient to work with Joules to specify total energy use in practical
situations, because you get such large numbers (like the 360,000 Joules figure
in Example 4). So, when it comes to working with total energy use (as opposed
to the power you need to run something), people like work with another unit,
called the "kilowatt-hour" (abbreviated kWh):
Definition: 1 kilowatt-hour = energy delivered by 1000 watts of power over a
period of one hour.
We can calculate the energy in kWh using equation (6), but we must have the
correct units, as:
Energy = Power * Time
Energy in kilowatt-hours
Power in kilowatts
(7)
Time in hours
4
Example 5: A typical hair dryer uses about 700 Watts of electrical energy. If
you run the dryer for 20 minutes, calculate the total energy used in both (a)
Joules and (b) kilowatt-hours.
Answer: Using equation (6) on the previous page, we can calculate the total
energy used. Remember that we need the time in seconds for this calculation,
so we first convert 20 minutes to seconds as:
Time (seconds) = Time (minutes) * 60 (seconds/minute)
Time (seconds) = 20 minutes * 60 seconds/minute
= 1200 seconds
We can then use equation (6) to determine the total energy used:
Energy = Power x Time
= (700 Joules/Second) x (1200 Seconds)
= 840,000 Joules
In kilowatt-hours we use equation (7), which requires that we have power in
kilowatts and time in hours. We make these conversions as follows:
Time (hours) = Time (minutes) * 1 (hours / 60 minutes)
= 20 minutes * 1 hours / 60 minutes
= 20 / 60 = 1/3 hours
Power (kilowatts) = Power (Watts) * 1 (kilowatt / 1000 Watts)
= 700 Watts * 1 kilowatt / 1000 Watts
= 700 / 1000 = .7 kilowatts
We, finally, calculate the energy in kilowatt-hours as:
Energy = Power * Time
= .7 Kilowatts * (1/3) hours
= .7/3 = .23 kWh
So you see that kilowatt-hours is a much better unit for large amounts of
energy.
5
When the power company charges you for electrical energy they charge you
by the number kilowatt-hours that you have used. The cost per kilowatt-hour
can range from $0.05 to $0.20 to even higher rates depending on a number of
factors. The area in which you live, the time of year, the cost of producing the
energy, the time of day you use the energy (energy is cheaper to buy at night),
and the demands of the customers all play a role in the amount you are
charged for electrical energy. We illustrate the cost of electrical energy with a
final example.
Example 6: In Example 5 we gave the situation of running a hair dryer for 20
minutes and showed that .23 kWh of electrical energy was used. If you are told
that the energy company charged you $0.03 to run the dryer, what are they
charging you per kilowatt-hour?
Answer: To find the rate per kWh, we just divide the total cost by the energy
used as:
Rate = Cost / Energy
(8)
= $0.03 / .23 kWh
= $0.13 per kWh
6