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1.4: Energy and Voltage

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    Energy is defined as the ability to do work. It is denoted by the letter \(W\). The basic unit is the joule although other units are sometimes used (for example, the calorie or the kilowatt-hour, kWh).


    Figure 2.4.1 : Defining voltage as work to move charge.

    If we were to move a charge from one point to another (for example, separating an electron from an atom), we would have to expend energy to do so. This is illustrated in Figure 2.4.1 . In this Figure, we would say that \(B\) has a higher electric potential than \(A\). In other words, there is a potential difference between \(B\) and \(A\). We refer to this change as voltage. It is denoted by the letter \(V\) (or sometimes \(E\)1) and has units of volts, in honor of Alessandro Volta. One volt is defined as one joule per coulomb.

    \[1 \text{ volt } \equiv 1 \text{ joule } / 1 \text{ coulomb } \label{2.3} \]

    As you might guess, the bigger the charge to be moved, the greater the energy required. Expressed as a formula,

    \[V = W / Q \label{2.4} \]


    \(V\) is the voltage in volts,

    \(W\) is the energy in joules,

    \(Q\) is the charge in coulombs.

    Unlike current, voltage always implies two points for measurement because it involves a difference. Often, one of the points is a common reference, such as earth ground or a circuit ground (i.e., chassis ground). Sometimes people will refer to a point in a circuit as having a certain voltage, as in “point \(X\) is 12 volts”. Although common in use, this is somewhat sloppy and not strictly correct. It is important to always remember that this value is relative to some reference point. As a general rule, a voltage will be denoted using the two points as subscripts, for example, \(V_{AB}\), that is, the voltage at point \(A\) relative to point \(B\). If only a single subscript is used, as in \(V_A\), then the second, or reference, point is assumed to be the system common or ground. In this case, we're referring to the voltage at point \(A\) relative to the system common point. Finally, by definition, \(V_{AB} = V_A − V_B\), as they have the same reference.

    Example 2.4.1

    100 joules are expended to move a 20 coulomb charge from point \(A\) to point \(B\). Determine the resulting voltage.

    \[V_{BA} = \frac{W}{Q} \nonumber \]

    \[V_{BA} = \frac{100 J}{20C} \nonumber \]

    \[V_{BA} = 5 V \nonumber \]

    Note that it is possible for a voltage to be negative. This simply means that the potential at the point of interest is less than that of the reference point. In Example 2.4.1 we discovered that point \(B\) is five volts above point \(A\). We could just as easily say that point \(A\) is five volts below point \(B\), or \(V_{AB} = −5\) V. Further, we can state the difference in terms of the individual ground-referenced voltages, or \(V_{BA} = V_B − V_A\).

    Static Electricity and ESD

    While it is obviously true that higher voltages imply higher associated energies (charge being held constant), it is not true that a particularly high voltage is necessarily lethal. This is because a very high voltage can be achieved by moving a small charge with only modest energy input. A good example of this is static electricity, so called because it is not associated with a moving current.

    Static electricity is commonly generated through the triboelectric effect which involves the transfer of electrons from one material to another via physical contact such as rubbing or scraping. If said materials are good electrical insulators, charges will remain on the materials and can build to very high levels, creating a large voltage. Many plastics, such as polystyrene and polyester, are good candidates. The effect can be noticed with certain fabrics, especially under low humidity. For example, removing a polyester fleece pullover or jacket can elicit a certain crackling sound. The sliding of the fleece builds up the charge and eventually the voltage will be become so large that it will arc through the air to surrounding objects which have a lower voltage. This happens quickly over many parts of the garment, each crackle being an individual arc. In fact, if tried in darkness, it is possible to see a cascade of small sparks. This is the same phenomenon that causes a spark when you touch a car after sliding off the seat on a cold and dry winter's day, or a small shock when you touch an object (or another person) after walking across a carpet in a dry library.


    Figure 2.4.2 : Triboelectric effect and static electricity: Cat fur meets polystyrene.

    Anyone who has opened a box filled with polystyrene packing peanuts can attest to the troublesome nature of the triboelectric effect, as the very light peanuts can easily adhere to other objects due to the electric charge generated through their displacement. No amount of manic brushing or throwing of the pieces will reduce the effect and may, in fact, make it worse. A simple solution in some instances is to spray a fine mist of water on the packing peanuts as the water will provide a conduction path, draining off the charges. Of course, this will not be appropriate in all situations, particularly in the one shown in Figure 2.4.2 . In the prior examples, the static voltage may be on the order of a few thousand volts but the associated energy may be just a few microjoules. In spite of the high voltage, this is not enough to kill someone. On the other hand, the same voltage achieved with a much higher charge and energy could be lethal.

    Beyond its simple inconvenience and inadvertent feline entertainment capabilities, high static potential can damage sensitive electronic devices. Care must be taken to prevent the accidental buildup of damaging charges. In the electronics industry this is commonly referred to as ESD, or electrostatic discharge. Steps to reduce ESD include humidity control and the use of conductive devices such as resistive wrist straps for technicians to continually bleed off the charges, thus preventing the creation of a high static potential.

    The Height Analogy

    Just as the flow of water can be seen as an analogy for electrical current, a serviceable analogy for voltage involves pressure or height. Indeed, sometimes voltage is referred to as “electrical pressure”. The height analogy ties together the concepts of voltage and energy. In this analogy, height corresponds to voltage and mass corresponds to charge.

    To begin, we note that there are two kinds of energy: kinetic energy, or energy of motion; and potential energy, or energy by virtue of position. Potential energy is the product of mass, gravity and height, or \(w = mgh\). Keeping gravity equal, we see that the more mass something has or the higher up it is, the greater its potential energy. We might think of potential energy as the object's potential to inflict damage when released.


    Figure 2.4.3 : Understanding voltage: David Hume does a header.

    To illustrate, we shall call upon 18th century Scottish philosopher and noted soccer fan2, David Hume. If a soccer ball is held stationary over Mr. Hume's head, as shown in Figure 2.4.3 , the ball has energy by virtue of its position. Releasing the ball from the position shown will scarcely bother Mr. Hume as there is little energy associated with this position relative to the top of his noggin. In fact, he would be hard pressed to head the ball to another player. If, on the other hand, the ball were held considerably higher, its potential energy would be much greater. Therefore, the impact on Mr. Hume's head would be increased dramatically and he would have little difficulty heading the ball down field (i.e., the transformation of potential energy into kinetic energy), although the chances of him gaining a concussion are greatly increased.

    Thus, we note that the height of the ball gives us some insight into its potential energy, although these terms are not synonymous. That is to say, if, instead of a soccer ball, we had used a ping-pong ball, even when dropped from an extreme height, the chances of a concussion are non-existent3. On the other hand, if the ball had been replaced with one made of solid iron, a drop from even a modest height could render our most excellent philosopher seriously dead. So it is with voltage. If the charge associated with the voltage is small, even a relatively high voltage will not be lethal (as in the case of simple static electricity on clothing), however, if associated with a sufficiently large charge, a much lower voltage can be deadly


    1\(E\) is used for voltage sources such as batteries. It is short for EMF, or electromotive force.

    2Hume, author of An Enquiry Concerning Human Understanding, died in 1776. The modern game of soccer was established in 1863. Let's not let that deter our own inquiry.

    3The construction of the referred sentence owes a certain debt to the writing style of Mr. Hume.

    This page titled 1.4: Energy and Voltage is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by James M. Fiore.

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