Our previous exercise was all about electrical charge. However, engineers are generally not really interested in charge itself^{1}. We are mostly concerned with moving charges around, or energy transfer—we need to use electrical energy in order to perform useful work, like spinning a motor, or lighting a light bulb^{2}. It is awkward to deal with energy transfer directly in terms of charge, so we introduce a couple of parameters that relate more directly to electrical energy: current and voltage.
The first parameter which is commonly used to quantify the energy transfer associated with charge motion is the rate at which charge is passing a given point. This rate of the flow of charge is called current. Since the units of charge are coulombs, the units of current are coulombs per second, or amperes (1 ampere = 1 coulomb/second). Amperes are commonly referred to as amps. The abbreviation for amps is “A”.
Current is typically considered to be the motion of positive charges. As we saw in the section relative to charge and charge motion, however, charge motion usually results from the motion of negative charges (electrons). Luckily, it turns out that—from the standpoint of circuit analysis, anyway —we don't really need to worry about the physical process which results in a current; we just need to be consistent in our definitions. Therefore, we can consider a negative charge motion in one direction to be the same as a positive charge (with the same magnitude) moving in the opposite direction. Consequently, positive current corresponds to a motion of electrons in the opposite direction to the current. This is illustrated in Fig. 1; electrons are moving from right to left, but positive current is left to right.
Since current corresponds to a rate at which charge passes a given point, it has both a magnitude (the number of coulombs passing the point per second) and a direction. Current direction is specified in terms of a reference direction. The actual direction of current flow is not necessarily in the reference direction; the reference direction, in conjunction with a sign on the value of current, defines the actual current direction. On circuit diagrams, the reference current direction is indicated by an arrow— the arrow points in the assumed direction of positive current. If the current actually is in the reference direction, the sign on the current will be positive. If the current is in the opposite direction as the reference direction, the sign on the current will be negative. Figure 2 shows an example of defining current direction through a circuit element in terms of a reference direction and a sign on the current value.
We can, of course, change our reference direction (the reference direction is entirely arbitrary). Changing the reference direction simply changes the sign on the current, as shown in Fig. 3.
The second parameter used to characterize energy transfer is related to the force that must be applied to cause a charge to move. This concept is closely related to the fact that charges with the same sign will repel one another and charges with opposite signs will attract one another. As we saw in our section on electric fields, this force is best explained in terms of an electric field, so we will develop the concept of voltage in terms of electric fields. You may want to refresh your memory about electric fields at this point; a link to that section is provided here.
Suppose we have some charge, q_{1}, which is creating an electric field as shown in Fig. 4. If we place another charge (q, in Fig. 4) in this electric field, there will be a force applied to the charge. Since we are moving charges around, we want to see what happens when the charge q is moved from one point to another in this electric field. For example, if we originally place the charge q at some point “b”, as shown in Fig. 4, and then move the charge to point “a”, some work needs to be done^{3}. This work corresponds to the change in energy level of the charge. The overall idea is analogous to moving a mass in a gravitational field.
A gravitational field, such as earth's, causes the earth to “attract ” nearby masses. In the Fig. 5 to the right, we have a mass, m, that we are lifting from position “a” to position “b”. In the process of lifting this mass, we've exerted energy (or in other words, “done some work” since we've moved a force through some distance) to increase the potential energy of the mass. If we allow the mass to drop back to its original height, we can get work back out in exchange for reducing the mass's potential energy.
The work done in moving a charge from one point to another in an electric field (or, equivalently, the change in energy of the charge during this process) is called voltage. Since this process is similar to changing the potential energy of the mass in our above analogy, voltage is sometimes called an electric potential difference. Voltage is also sometimes called electromotive force, or emf, since the difference in energy levels between the points has the effect of a “force” which is available to move charges around.
In short, voltage is the energy (or work) required to move a one coulomb charge from one point in a circuit to another. It is always a difference between two different points in a circuit. Units of voltage are joules/coulomb, or volts (abbreviated V).
As with current, voltages are specified relative to a reference direction, called a polarity. The polarity is used to define which point in the circuit is at the higher energy level. As with currents, the polarity simply specifies a convention relative to which voltage values will be defined. The “+” sign indicates the point at which the voltage is assumed to be higher, and the “-” sign indicates the point with the assumed lower voltage. Figure 6 shows a typical reference polarity between two terminals of a circuit element.
As with reference current directions, the reference polarity does not tell you which point is actually at the higher voltage! The voltage itself can be either positive or negative—if the voltage is positive, it has the same polarity as the reference direction, and if the voltage is negative, the polarity is opposite to the reference direction. This is illustrated in Fig. 7. If we change both the polarity and the sign of the voltage, the voltages are identical, as shown in Fig. 8.
In any electrical circuit, our typical goal is to move charges around to perform some useful task. This involves both voltage differences and currents. We create voltage differences in the circuit, which provides energy differences (or electromotive forces) that move charges around, creating currents. The trick is to provide the voltages needed to get the right amount of current to go where we want it^{4}.
In Fig. 1 above, we are somehow causing electrons to move from right to left in the wire in order to create a current which moves from right to left through the wire. Conceptually, we cause this motion by applying a voltage difference between the two ends of the wire, as shown in Fig. 9. The negative voltage terminal is at the right of the wire, and the positive voltage is at the left of the wire—this creates an electromotive force (emf) which causes electron motion and, ultimately, a current flow from left to right in the wire. But how do we control the relationship between voltage and current in order to get the desired voltage and current? The answer is to choose or create an electrical component with the desired relationship between voltage and current.
Engineers describe the behavior of most electrical components in terms of the relationship between voltage and current for the component. This relationship is called the voltage-current characteristic, the i-v characteristic ^{5}, or the i-v curve^{6}.
An example of the use of voltage-current characteristics is the concept of resistance introduced in the section relative to charge and charge motion. In that section, we pointed out that materials resist the motion of charge to various degree; for example, conductors allow charges to move easily through them, while insulators don't.
This concept can be stated in terms of voltage and current: insulators require large voltage differences across them relative to the amount of current that flows through them, while conductors allow large amounts of current flow relative to the voltage difference across them.
In the extreme cases, a perfect conductor allows any amount of current to flow through it, with no voltage difference across it. Conversely, a perfect insulator doesn't allow any current to flow through it, regardless of the amount of voltage across it. We can plot these voltage-current relations, as shown below in Fig. 10.