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Voltage, Current, and Resistance
In order to talk meaningfully about electricity, and especially how we can use electricity, we need to be able to measure its fundamental properties. There are three primarily characteristics that describe the nature of electrical flows.
The first is voltage, usually abbreviated "V" and measured in volts (also abbreviated "V".) Voltage, also sometimes called potential difference or electromotive force (EMF), refers to the amount of potential energy the electrons have in an object or circuit. In some ways, you can think of this as the amount of "push" the electrons are making to try to get towards a positive charge. The more energy the electrons have, the stronger the voltage. If we draw an analogy to a waterfall, the voltage would represent the height of the waterfall: the higher it is, the more potential energy the water has by virtue of its distance from the bottom of the falls, and the more energy it will possess as it hits the bottom.
The second primary characteristic of electricity is current, usually abbreviated "I" ("C" is reserved for the principle of charge, the most fundamental building block of electricity.) Current is measured in amperes or amps, abbreviation "A". Current refers to how much electricity is flowing--how many electrons are moving through a circuit in a unit of time. If we think about our waterfall example, the current would represent how much water was going over the edge of the falls each second.
The third primary characteristic of electricity is resistance, normally abbreviated "R" and measured in ohms, abbreviated using the Greek letter omega (). Resistance refers to how much the material that is conducting electricity opposes the flow of electrons. The higher the resistance, the harder it is for the electrons to push through. In the waterfall analogy, resistance would refer to any obstacles that slowed down the flow of water over the edge of the falls. Perhaps there are many rocks in the river before the edge, to slow the water down. Or maybe a dam is being used to hold back most of the water and let only a small amount of it through.
These three characteristics are directly related through a mathematical principle known as Ohm's Law. Its usual formulation is:
meaning that the voltage of a circuit is equal to the current through the circuit times its resistance. Another way of stating Ohm's Law, that is often easier to understand, is:
which means that the current through a circuit is equal to the voltage divided by the resistance. This makes sense, if you think about our waterfall example: the higher the waterfall, the more water will want to rush through, but it can only do so to the extent that it is able to as a result of any opposing forces. If you tried to fit Niagara Falls through a garden hose, you'd only get so much water every second, no matter how high the falls, and no matter how much water was waiting to get through! And if you replace that hose with one that is of a larger diameter, you will get more water in the same amount of time.
Getting back to electrical circuits, what does resistance mean in practical terms? First, conductors have relatively low resistance; that's what makes them conductive. Insulators have high resistance. Let's consider a D-cell battery. This is a device that chemically creates a charge differential; one end of the battery is positively charged, and the other is negatively charged, so it has a voltage (typically 1.5V for alkaline cells). What prevents the electrons from jumping straight to the positive charge and neutralizing the battery? It is the conductor that separates them: the air itself. Air is one of the best insulators around. Now if you attach a wire from one terminal to the other, you have replaced the high resistance of the air with the low resistance of the wire, and you will get a very high current as a result through the wire. How high? Well, directly short-circuiting a battery in this manner can cause burns!
How can electricity cause burns? Some of the electrical energy is converted to heat. How much heat is created depends on the current through the circuit, and the resistance of the conductor. In fact, this is all that an incandescent lightbulb is: a closed circuit is made to the bulb. Inside the bulb is a filament made of a special material with a fairly high resistance. When electricity flows through it, some of it is converted to heat, which causes the filament to glow and, combined with the gases in the bulb, produce light. When you turn off the switch, you open the circuit by replacing part of the wire in the circuit with air, and the electrical flow stops.
There's one final thing to note about current: even though it is comprised of negatively-charge particles (electrons) moving towards a positive charge, by convention current is considered to be the opposite: positive charges moving towards a negative charge. I believe that this is the case because in the early days of research into electricity, scientists believed the positive charges are what moved in the circuit, and not the negative ones. It doesn't really matter too much actually, except that you will normally see, for example, battery voltages referred to as positive and not negative. All voltages are measured in reference to a common zero point, normally called ground potential because it is usually connected to the ground of the earth, directly or indirectly.