BASIC DEFINITIONS

Charge

No one knows what charge really is anymore than anyone knows what gravity is. Both are models, constructions, fabrications if you like, to describe and represent something that can be measured in the real world, specifically a force. Gravity is the name for a force between masses that we can feel and measure. Early workers observed that bodies in "certain electrical condition" also exerted forces on one another that they could measure, and they invented charge to explain their observations. Amazingly, only three simple postulates or assumptions, plus some experimental observations, are necessary to explain all electrical phenomena. Everything: currents, electronics, radio waves, and light. Not many things are so simple, so it is worth stating the three postulates clearly.

Charge exists.

We just invent the name to represent the source of the physical force that can be observed. The assumption is that the more charge something has, the more force will be exerted. Charge is measured in units of Coulombs, abbreviated C. The unit was named to honor Charles Augustin Coulomb (1736-1806) the French aristocrat and engineer who first measured the force between charged objects using a sensitive torsion balance he invented. Coulomb lived in a time of political unrest and new ideas, the age of Voltaire and Rousseau. Fortunately, Coulomb completed most of his work before the revolution and prudently left Paris with the storming of the Bastille.

Charge comes in two styles.

We call the two styles positive charge, $+$, and (you guessed it) negative charge, $-$. Charge also comes in lumps of $1.6\; \times 10-19C$, which is about two ten-million-trillionths of a Coulomb. The discrete nature of charge is not important for this discussion, but it does serve to indicate that a Coulomb is a LOT of charge.

Charge is conserved.

You cannot create it and you cannot annihilate it. You can, however, neutralize it. Early workers observed experimentally that if they took equal amounts of positive and negative charge and combined them on some object, then that object neither exerted nor responded to electrical forces; effectively it had zero net charge. This experiment suggests that it might be possible to take uncharged, or neutral, material and to separate somehow the latent positive and negative charges. If you have ever rubbed a balloon on wool to make it stick to the wall, you have separated charges using mechanical action.

Those are the three postulates. Now we will present some of the experimental findings that both led to them and amplify their significance.

Voltage

First we return to the basic assumption that forces are the result of charges. Specifically, bodies with opposite charges attract, they exert a force on each other pulling them together. The magnitude of the force is proportional to the product of the charge on each mass. This is just like gravity, where we use the term "mass" to represent the quality of bodies that results in the attractive force that pulls them together

Figure: Opposite charges exert an attractive force on each other, just like two masses attract. External force is required to hold them apart, and work is required to move them farther apart.

Electrical force, like gravity, also depends inversely on the distance squared between the two bodies; short separation means big forces. Thus it takes an opposing force to keep two charges of opposite sign apart, just like it takes force to keep an apple from falling to earth. It also takes work and the expenditure of energy to pull positive and negative charges apart, just like it takes work to raise a big mass against gravity, or to stretch a spring. This stored or potential energy can be recovered and put to work to do some useful task. A falling mass can raise a bucket of water; a retracting spring can pull a door shut or run a clock. It requires some imagination to devise ways one might hook on to charges of opposite sign to get some useful work done, but it should be possible.

The potential that separated opposite charges have for doing work if they are released to fly together is called voltage, measured in units of volts (V). (Sadly, the unit volt is not named for Voltaire, but rather for Volta, an Italian scientist.) The greater the amount of charge and the greater the physical separation, the greater the voltage or stored energy. The greater the voltage, the greater the force that is driving the charges together. Voltage is always measured between two points, in this case, the positive and negative charges. If you want to compare the voltage of several charged bodies, the relative force driving the various charges, it makes sense to keep one point constant for the measurements. Traditionally, that common point is called "ground."

Early workers, like Coulomb, also observed that two bodies with charges of the same type, either both positive or both negative, repelled each other. They experience a force pushing

Figure: Like charges exert a repulsive force on each other. External force is required to hold them together, and work is required to push them closer.

them apart, and an opposing force is necessary to hold them together, like holding a compressed spring. Work can potentially be done by letting the charges fly apart, just like releasing the spring. Our analogy with gravity must end here: no one has observed negative mass, negative gravity, or uncharged bodies flying apart unaided. Too bad, it would be a great way to launch a space probe. The voltage between two separated like charges is negative; they have already done their work by running apart, and it will take external energy and work to force them back together.

So how do you tell if a particular bunch of charge is positive or negative? You can't in isolation. Even with two charges, you can only tell if they are the same (they repel) or opposite (they attract). The names are relative; someone has to define which one is "positive." Similarly, the voltage between two points $A$ and $B$, $V$_AB , is relative. If $V$_AB is positive you know the two points are oppositely charged, but you cannot tell if point $A$ has positive charge and point $B$ negative, or visa versa. However, if you make a second measurement between $A$ and another point $C$, you can at least tell if $B$ and $C$ have the same charge by the relative sign of the two voltages, $V$_AB and $V$_AC to your common point $A$. You can even determine the voltage between $B$ and $C$ without measuring it: $V$_BC = V_AC - V_AB . This is the advantage of defining a common point, like $A$, as ground and making all voltage measurements with respect to it. If one further defines the charge at point $A$ to be negative charge, then a positive $V$_AB means point $B$ is positively charged, by definition. The names and the signs are all relative, and sometimes confusing if one forgets what the reference or ground point is.

Current

Charge is mobile and can flow freely in certain materials, called conductors. Metals and a few other elements and compounds are conductors. Materials that charge cannot flow through are called insulators. Air, glass, most plastics, and rubber are insulators, for example. And then there are some materials called semiconductors, that, historically, seemed to be good conductors sometimes but much less so other times. Silicon and germanium are two such materials. Today, we know that the difference in electrical behavior of different samples of these materials is due to extremely small amounts of impurities of different kinds, which could not be measured earlier. This recognition, and the ability to precisely control the "impurities" has led to the massive semiconductor electronics industry and the near-magical devices it produces, including those on your RoboBoard. We will discuss semiconductor devices later; now let us return to conductors and charges.

Imagine two oppositely charged bodies, say metal spheres, that are being held apart, as in Fig. 4.3.

Figure 4.3: Two spheres with opposite charges are connected by a conductor, allowing charge to flow.

There is a force between them, the potential for work, and thus a voltage. Now we connect a conductor between them, a metal wire. On the positively charged sphere, positive charges rush along the wire to the other sphere, repelled by the nearby similar charges and attracted to the distant opposite charges. The same thing occurs on the other sphere and negative charge flows out on the wire. Positive and negative charges combine to neutralize each other, and the flow continues until there are no charge differences between any points of the entire connected system. There may be a net residual charge if the amounts of original positive and negative charge were not equal, but that charge will be distributed evenly so all the forces are balanced. If they were not, more charge would flow. The charge flow is driven by voltage or potential differences. After things have quieted down, there is no voltage difference between any two points of the system and no potential for work. All the work has been done by the moving charges heating up the wire.

The flow of charge is called electrical current. Current is measured in amperes (a), amps for short (named after another French scientist who worked mostly with magnetic effects). An ampere is defined as a flow of one Coulomb of charge in one second past some point. While a Coulomb is a lot of charge to have in one place, an ampere is a common amount of current; about one ampere flows through a 100 watt incandescent light bulb, and a stove burner or a large motor would require ten or more amperes. On the other hand low power digital circuits use only a fraction of an ampere, and so we often use units of $1/1000$ of an ampere, a milliamp, abbreviated as ma, and even $1/1000$ of a milliamp, or a microamp, $\mu a$. The currents on the RoboBoard are generally in the milliamp range, except for the motors, which can require a full ampere under heavy load. Current has a direction, and we define a positive current from point $A$ to $B$ as the flow of positive charges in the same direction. Negative charges can flow as well, in fact, most current is actually the result of negative charges moving. Negative charges flowing from $A$ to $B$ would be a negative current, but, and here is the tricky part, negative charges flowing from $B$ to $A$ would represent a positive current from $A$ to $B$. The net effect is the same: positive charges flowing to neutralize negative charge or negative charges flowing to neutralize positive charge; in both cases the voltage is reduced and by the same amount.

Batteries

Charges can be separated by several means to produce a voltage. A battery uses a chemical reaction to produce energy and separate opposite sign charges onto its two terminals. As the charge is drawn off by an external circuit, doing work and finally returning to the opposite terminal, more chemicals in the battery react to restore the charge difference and the voltage. The particular type of chemical reaction used determines the voltage of the battery, but for most commercial batteries the voltage is about 1.5 V per chemical section or cell. Batteries with higher voltages really contain multiple cells inside connected together in series. Now you know why there are 3 V, 6 V, 9 V, and 12 V batteries, but no 4 or 7 V batteries. The current a battery can supply depends on the speed of the chemical reaction supplying charge, which in turn often depends on the physical size of the cell and the surface area of the electrodes. The size of a battery also limits the amount of chemical reactants stored. During use, the chemical reactants are depleted and eventually the voltage drops and the current stops. Even with no current flow, the chemical reaction proceeds at a very slow rate (and there is some internal current flow), so a battery has a finite storage or shelf life, about a year or two in most cases. In some types of batteries, like the ones we use for the robot, the chemical reaction is reversible: applying an external voltage and forcing a current through the battery, which requires work, reverses the chemical reaction and restores most, but not all, the chemical reactants. This cycle can be repeated many times. Batteries are specified in terms of their terminal voltage, the maximum current they can deliver, and the total current capacity in ampere-hours.

You should handle batteries carefully, especially the ones we use in this course. Chemicals are a very efficient and compact way of storing energy. Just consider the power of gasoline or explosives, or the fact that you can play soccer for several hours powered only by a slice of cold pizza for breakfast. Never connect the terminals of a battery together with a wire or other good conductor. The battery we use for the RoboBoard is similar to the battery in cars, which uses lead and sulphuric acid as reactants. Such batteries can deliver very large currents through a short circuit, hundreds of amperes. The large current will heat the wire and possibly burn you; the resulting rapid internal chemical reactions also produce heat and the battery can explode, spreading nasty, reactive chemicals about. Charging these batteries with too large a current can have the same effect. Double check the circuit and instructions before connecting a battery to any circuit.

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