Potential or Voltage

 Potential or Voltage

Because like charges repel and opposite charges attract, charge has a natural tendency to “spread out.” A local accumulation or deficit of electrons causes a certain “discomfort” or “tension” unless physically restricted, these charges will tend to move in such a way as to relieve the local imbalance. In rigorous physical terms, the discomfort level is expressed as a level of energy. This energy (strictly, electrical potential energy), said to be “held” or “possessed” by a charge, is analogous to the mechanical potential energy possessed by a massive object when it is elevated above the ground: we might say that, by virtue of its height, the object has an inherent potential to fall down. A state of lower energy—closer to the ground, or farther away from like charges—represents a more “comfortable” state, with a smaller potential fall.

The potential energy held by an object or charge in a particular location can be specified in two ways that are physically equivalent: first, it is the work that would be required in order to move the object or charge to that location. For example, it takes work to lift an object; it also takes work to bring an electron near an accumulation of more electrons. Alternatively, the potential energy is the work the object or charge would do in order to move from that location, through interacting with the objects in its way. For example, a weight suspended by a rubber band will stretch the rubber band in order to move downward with the pull of gravity (from higher to lower gravitational potential). A charge moving toward a more comfortable location might do work by producing heat in the wire through which it flows.

This notion of work is crucial because, as we will see later, it represents the physical basis of transferring and utilizing electrical energy. In order to make this “work” a useful and unambiguous measure, some proper definitions are necessary.

The first is to explicitly distinguish the contributions of charge and potential to the total amount of work or energy transferred. Clearly, the amount of work in either direction (higher or lower potential) depends on the amount of mass or charge involved. For example, a heavy weight would stretch a rubber band farther, or even break it. Similarly, a greater charge will do more work in order to move to a lower potential. On the other hand, we also wish to characterize the location proper, independent of the object or charge there. Thus, we establish the rigorous definition of the electric potential, which is synonymous with voltage (but more formal). The electric potential is the potential energy possessed by a charge at the location in question, relative to a reference location, divided by the amount of its charge. Casually speaking, we might say that the potential represents a measure of how comfortable or uncomfortable it would be for any charge to reside at that location. A potential or voltage can be positive or negative. A positive voltage implies that a positive charge would be repelled, whereas a negative charge would be attracted to the location; a negative voltage implies the opposite. Furthermore, we must be careful to specify the “reference” location: namely, the place where the object or charge was moved from or to. In the mechanical context, we specify the height above ground level. In electricity, we refer to an electrically neutral place, real or abstract, with zero or ground potential. Theoretically, one might imagine a place where no other charges are present to exert any forces; in practice, ground potential is any place where positive and negative charges are balanced and their influences cancel. When describing the potential at a single location, it is implicitly the potential difference between this and the neutral location.

However, potential can also be specified as a difference between two locations of which neither is neutral, like a difference in height. Because electric potential or voltage equals energy per charge, the units of voltage are equivalent to units of energy divided by units of charge. These units are volts (V). One volt is equivalent to one joule per coulomb, where the joule is a standard unit of work or energy. Note how the notion of a difference always remains implicit in the measurement of volts. A statement like “this wire is at a voltage of 100 volts” means “this wire is at a voltage of 100 volts relative to ground,” or “the voltage difference between the wire and the ground is 100 volts.” By contrast, if we say “the battery has a voltage of 1.5 volts,” we mean that “the voltage difference between the two terminals of the battery is 1.5 volts.” Note that the latter statement does not tell us the potential of either terminal in relation to ground, which depends on the type of battery and whether it is connected to other batteries. In equations, voltage is conventionally denoted by E, e, V, or v (in a rare and inelegant instance of using the same letter for both the symbol of the quantity and its unit of measurement).