We will encounter two different but related ways of describing "electricity" in this course: electric power and electric energy. While they are related, they mean very different things.

**Energy** is defined as the ability to do useful work, like illuminating a room or moving a car. Energy inherently has a quantity component (how much light do we need for the room or how big was the car) and a time component (how long did we keep the room lit or how long did we keep the car going). So "energy" is a quantity, like a barrel of oil. We use lots of different physical units to measure energy. Two of the most common are:

- The
*British Thermal Unit (BTU)*is the amount of energy required to heat one pound of water by one degree Fahrenheit. This is the "English" measure of energy, and is one that we'll encounter very often. If you have taken other energy-related courses, you might recognize the BTU as being one of the major ways of measuring quantities of natural gas, oil or coal. - The
*Joule*is the SI for energy, and is equal to the work done by a force of one newton, applied for one meter.

**Power** is the rate at which that useful work is done, so it describes a quantity of energy that is used over some time period. The standard unit for power is the Watt, which is equal to one Joule per second. So, when you see a 60 Watt light bulb in your house, what that means is that the light bulb draws electricity from the grid at a *rate* of 60 Watts, or 60 Joules per second.

Electric power as we think of it is really the product of two components:

- Current (I): The flow of electrons through some conducting medium (e.g. copper wire); measured in Amperes (A), or "Amps" for short. You can think of current as being roughly equivalent to the number of droplets of liquid flowing through a pipe or a hose.
- Voltage (V): A measure of electric potential between two terminals. Voltage is not a "natural" measure; it is equal to the ratio of power over current (we'll come back to this later in the lesson). You can think of voltage as being roughly equivalent to pressure in a pipe or a hose. If the pressure difference between the two ends of the pipe is large, then liquid will flow through the pipe at a fast rate. If the pressure difference is small, then liquid will flow through the pipe at a slow rate. If the pressure difference is exactly zero, then no water flows at all.
- Thus, power as we think of it is really:

$$\begin{array}{l}\text{Power=Voltage}\times \text{Current}\\ \text{=Volts}\times \text{Amps}\\ \text{=Watts}\end{array}$$

The difference between electric power and electric energy is thus that "electric power," measured in Watts, describes the rate of flow of electricity. Devices that are powered by electricity, like a light bulb or toaster, usually have their draw from the electric grid described in Watts. The capacity of a power plant to produce electricity is also usually described in Watts. Finally, we often describe the flow of electricity along transmission lines in units of Watts. Thus, the capacity of a power plant corresponds to its maximum instantaneous rate of electricity production.

Electric energy, on the other hand, describes the total amount of power that is used over some time period. The typical unit for electric energy is the Watt-hour (abbreviated "Wh"). For example, if you leave that 60 watt light bulb on for one hour, it will have drawn 60 Watts of "electric power" from the power grid each and every second for that hour. Over the course of that hour, it would have used 60 Watts 1 hour = 60 Watt-hours of "electric energy."

Now is a good time to remind you of the standard metric units for factors of 1,000. We will use these constantly throughout the course.

- One kilowatt (kW), or one kilowatt-hour (kWh) is one thousand Watts or Watt-hours.
- One megawatt (MW), or one megawatt-hour (MWh) is one thousand kW or kWh (one million W or Wh).
- One gigawatt (GW), or one gigawatt-hour (GWh) is one thousand MW or MWh (one billion W or Wh).

Let's go through some examples of converting between electric power and electric energy.

Example #1 (this one is easy):

- A generator produces 500 MW of power continuously for three hours.
- Total electric energy output for this power generator during this 3-hour period would be:

$$\text{500MW}\times \text{3h=1,500MWh(over3hours)}$$

Drawing a picture may help with these kinds of problems. If the plant produces 500 MW for three hours, then if we plot its production over time we would get a straight line for 500 MW for three hours. The level of that line is the "electric power production" of the plant. The total area under the line is the "electric energy production" of the plant over those three hours.

Example #2 (this one is not hard but may be confusing):

- A generator produces 500 MW of power continuously for one hour. During that hour, the generator has produced 500 MW-hours (MWh) of electric energy.

Students often get confused as to whether they should use MW or MWh in an example like this one. After all, it's 500 either way, right? Yes, the number is the same, but the interpretation is totally different. 500 MW is the rate at which the power plant is producing electricity. 500 MWh is the total amount of electric energy that it produces during that hour.

This confusion arises because the "hour" has become the standard unit of time in measuring electric energy. The use of the word "hour" here can be very very misleading, but just convince yourself that the "hour" in MWh is a code word for a quantity (like a barrel of oil) and does not really have anything to do with time.

Example #3 (this one is a bit harder):

- During one hour, a generator produces 100 MW for 20 minutes, 500 MW for 20 minutes, and 300 MW for 20 minutes. How much energy (in MWh) has it produced in that hour?
- Here is how to think about this problem: the plant produced 100 MW of electric power for 1/3 of an hour, 500 MW for 1/3 of an hour and 300 MW for 1/3 of an hour.
- So the answer is:

$$\text{100}\times \text{}\left(1/3\right)\text{}+\text{}500\text{}\times \text{}\left(1/3\right)\text{+300}\times \text{}\left(1/3\right)\text{=300MWh}$$

Drawing a picture of this one may be helpful.