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Basic Concepts of DC Electricity

Objective: To introduce students to basic concepts of DC Electricity

Vocabulary

The Atom

Atoms, the fundamental building blocks of matter, are made of three kinds of particles:

The figure above shows a particularly simple atom (an "isotope" of hydrogen, called deuterium, which just happens to have one particle of each type). All atoms except hydrogen atoms have more than one electron, proton, and usually one or more neutrons. 

Electron's orbit around the nucleus, which lies at the center and contains the protons and neutrons. 

The electron stays in orbit because it is negatively charged, and is therefore attracted to the positively charged proton in the nucleus. This is an example of the Law of electrical charges:

Like charges repel, opposite charges attract.

Most atoms, when in their normal state as components of matter, have the same number of electrons as protons, so that the total, or net charge of the atom is zero. That is, the atom is neutral. The number of protons (which is equal to the number of electrons if the atom is neutral) is called the atomic number of the atom, and this determines what element (hydrogen, helium, iron, etc), that the atom is classified as.

Ions are atoms to which some electrons have been added or taken away, so that the atom has a net charge (positive if electrons have been removed, negative if electrons have been added). Ions that have opposite net charges attract, and those with net charges of the same sign repel.

Atoms of the same atomic number can have different numbers of neutrons. These are the different isotopes of an element. Hydrogen has three isotopes: no neutrons - called "protium" (this is the hydrogen isotope most commonly found), one neutron - called deuterium, and two neutrons - called tritium. 

Although he didn't know about electrons and protons, the designations of positive and negative were made by Benjamin Franklin over two hundred years ago! Later on people realized they corresponded to the charges of protons and electrons, respectively.

What is Electricity?

In some materials, particularly metals, the electrons farthest from the nucleus are not bound to a particular atom - they can move freely from one atom to another. Electricity is the flow of these free electrons in a wire:

 

Such a flow of electrons is called a current.

What makes these free electrons move? Suppose we put something that has a net positive charge at the one end of the wire (say, at the right end of the wire pictured above). Let's also suppose that we put something with a net negative charge at the other end (the left end in the wire above). Then the electrons in the wire will be attracted to the positive end and repelled by the negative end. Hence, they will flow from left to right. That's electricity! 

Batteries

Batteries are devices which can do exactly what is described just above - make a current flow by creating a positive charge at one end of a wire and a negative charge at the other. A battery has two terminals (wire contacts), called positive and negative, corresponding to the net charges created at the terminals. The symbol for a battery is the following:

When a wire is connected across these terminals, forming a closed circuit, the positive and negative charges created by the battery cause a current to flow:

Note that the electrons flow from the negative terminal to the positive terminal. Eventually, when enough electrons have flowed, the battery will become drained, and the current will cease.

Even though the electrons flow from the negative to the positive terminals, it is conventional to say that the current flows from positive to negative:

Why is this? This is simply because people can't see electrons, and so they guessed wrong when the settled on a convention. But this is not really a problem, because even today we still don't see electrons in most applications, so it doesn't really matter for most purposes which direction the electrons actually go.

Measuring Current

How do we measure current? Current is measured by literally counting the number of electrons that pass a given point in the wire. Any point will do - it doesn't matter which one because the current will be the same in each point of the wire, unless the wire branches off into a more complicated circuit.  

Because there are billions of billions (much more than billions and billions! Carl Sagan would be impressed!) of electrons in even a very little piece of wire, we need to have a unit of measurement that will make it easy to count so many. 

The basic unit for counting electrons (that is, charge) is the "coulomb" (pronounced "cool lum"):

1 coulomb = 1.6 x 1019 electrons = 16,000,000,000,000,000,000

= 16 billion billion electrons!

To measure current, we pick one point along the wire and count the electrons that go by, like watching things go by on an assembly line. If 1 coulomb of electrons go by each second, then we say that the current is 1 "ampere" (pronounced "am - peer"), or 1 amp for short. If 2 coulomb's per second goes by, we say the current is 2 amps, and so on:

1 ampere = 1 coulomb per second

It is traditional to represent the current with the symbol I, as in I = 1 amperes, or I = 15 amperes, etc.

Measuring Voltage

Some batteries try to push electrons through the wire more strongly than others. How strongly the battery pushes is a measure of its voltage, symbolized with the letter V (as in the diagrams above). You can think of voltage like pressure: the higher the voltage, the higher the pressure is to push electrons through the wire. The lower the voltage, the lower the pressure.

Voltage is measured in volts. For example, common voltages for batteries are 1.5 volts, 6 volts, 9 volts, and 12 volts. Car batteries are typically 12 volts. An electrical outlet in the United States has a voltage of 110 volts (pretty high!). 

The voltage of a battery is related to the amount of energy that the battery can deliver. A voltage of V = 1 volt means that the battery will deliver 1 "Joule" of energy for each coulomb of charge that flows through the circuit. A voltage of V = 2 means that the battery will deliver 2 Joules of energy for each coulomb. A Joule is the basic unit of energy in the metric International system of units - its about the amount of energy it takes to lift two pounds 9 inches. How high the voltage of the battery is depends in detail on the internal construction of the battery, which is an "electro-chemical" energy storage device.

Measuring Resistance

How are amperes (current) and voltage (electrical pressure), related to one another? For a given voltage, some wires let more current flow than others. A wire that doesn't let very much current flow is said to have high resistance. Resistance is symbolized with the letter R.  

To simplify matters, we usually assume that the wire itself is an ideal wire with no resistance, and we represent the resistance as a localized component of the circuit symbolized with a broken line:

In fact the resistor now can represent the sum total of the wire's resistance, including that contributed by any additional components in the circuit that have resistance. There are devices call "resistors" whose function is simply to provide additional resistance.

The resistance is related to how much the current I we get from a given applied voltage V by "Ohm's Law" in the following way:

Ohm's Law: I = V / R

If I is measured in amperes, and V in volts, then we say that R has units of "ohms" (pronounced "olms"). More specifically, if we have a 1 volt battery, and a wire with a resistance of 1 ohm, then the current that results when the wire is placed across the battery's terminals is given by 

I = V / R = 1 volt / 1 ohm = 1 ampere.

Likewise, if we have a 2 volt battery, and a wire with a resistance of 3 ohms, then the current that results when the wire is placed across the battery's terminals is given by 

I = V / R = 2 volt / 3 ohm = 2/3 amperes.

Thus, knowing the voltage and the resistance, we can now predict the current. Likewise, we can also no turn the problem around, and say, calculate the resistance by measuring the voltage and current with a voltmeter (voltmeters are capable of measuring both voltage and current - but not generally at the same time!).  

Measuring Power in Watts

What happens to the energy delivered to the wire? For the case of a simple piece of wire plus some additional devices with are purely resistive, the energy is completely converted into heat energy in the wire (as shown in the figure above), which escapes into space.

As discussed above, the voltage of a battery is related to the amount of energy that the battery can deliver. A voltage of V = 1 volt means that the battery will deliver 1 Joule of energy for each coulomb of charge that flows through the circuit, a voltage of V = 2 yields two Joules per coulomb, and so forth. 

In many practical applications, we want to know the rate at which energy is delivered, not how much energy is delivered per coulomb of charge. For example, you might need to insure that a circuit you design will deliver 2 joules per second to make a toy car go fast enough. 

The rate at which energy is delivered is called power. Power is thus defined:

Power = Energy / Time.

In the metric International units, the unit of power corresponding to 1 joule per second is called a watt:

1 watt = 1 joule per second.

Because the voltage V tells us the number of joules per coulomb, and the current I tells us the number of coulombs per second, all we have to do to get the current is to multiply them:

Power = number of watts = number of joules/second 

= joules/coulomb x coulombs/second = I V, 

or 

Power Formula: P = I V

Thus, suppose we had a circuit with a battery voltage of 2 volts and a current of 3 amps. Then the power delivered to the resistor would be

P = I V = (3 amps) (2 volts) = 6 watts.

You are now ready to start doing some simple projects with electricity!

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