Elliot M. Rothkopf, College of Staten Island / CUNY
When students are first presented with the concept of electrical charge, they can get a ``feel'' for the force of attraction using the force of gravity as a model. Throw a book up in the air and ask the class, ``Why does it fall down?.'' They will reply that it is due to ``gravity.'' What is ``gravity?'' - a force of attraction between ``unlike'' charges and between the ``opposite'' poles of magnets. From the forces of attraction between ``unlike'' charges and ``opposite'' magnetic poles, one can then discuss the forces of repulsion experienced by ``like'' charges and ``similar'' magnetic poles. It is a good idea to demonstrate the forces of attraction and repulsion with magnets even though the students know how magnets behave because ``seeing'' gives even more reinforcement to the learning.
This paper will discuss other analogies for physical quantities such as work, voltage, current, and resistance as well as analogies for series and parallel connections, and Kirchhoff's current and voltage laws. Suggestions will be given as to how to enliven the presentation of the material to enhance the learning experience.
Many college professors have found that a good percentage of today's students are poorer learners than their predecessors. The days when an engineering or technology professor could simply present an equation, say ``This is the relationship,'' and then go on to the next topic or equation are gone. Even thirty years ago, it was a poor way to teach. Today, it cannot be done at all. There are many sociological theories to explain this phenomenon. However, the topic of this paper is not why this occurs, but what to do about it. The solution is to teach the topic by connecting it with the students' own lives [1,2]. The material must be taught in an active way to keep the students' interest [3]. To motivate and aid students in understanding a concept, it is very effective to use analogies of that concept [4] or mental models [5] in explaining it. This should be accomplished with active teaching wherever possible.
When students are first presented with the concept of electric charge, they can get a ``feel'' for the force of attraction using the force of gravity as a model. Throw a book up in the air and ask the class, ``Why does it fall down?.'' They will reply that it is due to ``gravity.'' What is ``gravity?'' - a force of attraction between two masses. Once that concept becomes clear, it then can be related to the forces of attraction between ``unlike'' charges and between the ``opposite'' poles of magnets. From the forces of attraction between ``unlike'' charges and ``opposite'' magnetic poles, one can then discuss the forces of repulsion experienced by ``like'' charges and ``similar'' magnetic poles. It is a good idea to demonstrate the forces of attraction and repulsion with magnets even though the students know how magnets behave because ``seeing'' gives even more reinforcement to the learning.
Now the concept of ``work'' must be explained. Pick a book up from the level of the desk to a level one foot above the desk. Was work done? Yes it was because the instructor exerted energy of the muscles to fight gravity by raising the book one foot. This book at a height of one foot above the desk possesses potential energy since on the return ``fall'' of one foot it could accomplish some mechanical work. The water of Lake Erie on top of Niagara Falls also possesses some potential energy since it can turn water wheels (turbines) producing mechanical work. This mechanical energy produces electricity. An analogy similar to this is given in Walls and Johnstone [6].
Examine a spring in its normal uncompressed state. It requires work to compress the spring. When the spring is released, it returns to its original position accomplishing work in the process if it is connected to a proper mechanical device. Now consider a box containing positive and negative charges in a neutral solution called an electrolyte. Work is required to separate the positive and negative charges so that all positive charges are at one terminal and all negative charges are at the other terminal. This is done in a battery by chemical means. Neutral electrolyte separates into electrons on one terminal and excess positive ions on the other. Chemical work was expended to separate the neutral molecules. Work can be accomplished when these charges are made to flow through a wire to reunite. The work per unit charge is characteristic of the chemical reaction of the battery and is called the voltage. Since the chemical work of separation can be reversed by the electrical force of repulsion pushing the negative charges away from the negative terminal and by the force of attraction pulling the electrons toward the positive battery terminal, through a wire attached between the terminals, producing work by means of the flow of electrons, this work of separation represents a potential energy. Thus, when we speak of voltage across two terminals, we can also refer to the potential difference (per unit charge) between the terminals. The third name for voltage, electromotive force or emf, is also appropriate since the voltage provides the pushing force to move electrons through the circuit joining the two voltage terminals.
A useful analogy for voltage is height [7]. A difference in voltage between two points can be represented by a difference in height between those points. Just as matter tends to fall from a higher elevation to a lower elevation, so too does current flow through a circuit from a higher voltage to a lower voltage. Differences in potential with respect to ground can be represented as floors of a skyscraper. Some 10 volts above ground is equivalent to the tenth floor while 3 volts below ground is equivalent to the level of the third sub-basement. The elevator must travel 13 floors to travel from one to the other.
There is no current flow through a resistor when both ends of the resistor are connected to points at the same potential. Imagine that two large apartment houses are located facing each other across a common street with a plank placed from the 10th floor window of the first building over the street to the 10th floor window of the second building. A marble placed on that plank will not roll across the plank. If that plank were placed through the 9th floor window of one of the buildings, the marble will roll down from the 10th floor to the 9th floor. The difference in potential is crucial for current flow-not the value of the potential to ground of the end points. This analogy is shown in Figure 1 and is especially useful in describing the operation of the wheatstone bridge.
Kirchhoff's Voltage Law, KVL, can be illustrated by considering the situation of a mountain climber located half-way up a mountain. If that person walks around the mountain and returns to his/her original starting point by any pathway and if all upward vertical distances are considered as positive and all downward vertical distance are considered as negative, the sum of all the vertical motion over the trip equals zero. Isn't that obvious? That's analogous to Kirchhoff's Voltage Law. Similarly, the sum of the voltage drops and rises around any closed loop equals zero. The analogy is shown in Figure 2.
Current can be represented as a flow of mass-balls called electrons or marbles or liquid flow-moving across a fixed position in a unit of time. Thus, Kirchhoff's Current Law can be illustrated by a series of pipe connections in the home as is shown in Figure 3.
One can also show in an analogy to a river bed that although the dimensions of a river may change from an upstream position to a downstream position, the mass flow across any lateral fixed position must be constant in, say, gallons per minute. Why? If a downpour occurs upstream and the river's flow there increases from 10,000 gallons per minute to 20,000 gallons per minute, it must increase to that same value downstream. If the river bed downstream cannot accommodate such a large flow, the water overflows the banks and we have a ``flood.'' The water must go somewhere. Thus, the current flow in a series circuit is constant and does not change through different series resistors.
An analogy to current flow through a resistor is traffic flow on a road or highway. A low resistance path can be represented as a wide, multilane, well paved highway. A single lane, narrow road is a higher resistance path. This represents the area factor, A, in the resistance equation,
The quality of the road surface, paved, dirt, or fall of pot holes represents
, the resistivity of the pathway. The length of the road represent the
length, l, of the resistive wire. A driver would choose the path of least
resistance, the widest, shortest, and best paved road to travel from city
A to city B given a number of alternative pathways. As traffic between
the two cities increase, some drivers decide to forgo highway driving and
take a path of higher resistance with less traffic. The flow will work
out so that the number of cars per pathway multiplied by the resistance
of each pathway are equal for all roads. This represents Ohm's law for
parallel paths,
where
is the source voltage. The source voltage for this analogy
is the desire of the motorist to travel to City B from City A at this time.
Every driver that makes the trip has the motivation to do so. Thus, driver-motive-force
is akin to electro-motive-force.
Capacitors may be introduced to students by drawing a bucket on the blackboard with a label ``one gallon'' on it. Then ask, ``what is the capacity of the bucket?'' Once the concept of capacity is clear, a parallel plate capacitor connected to a voltage source is drawn. The electrons on the negative side of the battery need some ``breathing'' room being squashed together so tightly on the battery. When the circuit switch closes, an uncharged capacitor with a large plate open area becomes available for these electron to migrate to. They tend to spread out on the negative plate of the capacitor until the force created by these negative charges becomes large enough to repel further electrons from migrating to the plate. A similar phenomenon occurs on the positive plate as electrons migrate from the plate to unite with positive charges on the battery leaving the positive plate with an equal amount of positive charge. This is the capacity of the plates at a given voltage. If the voltage of the source is increased, more electrons will now be driven from the battery to the negative plate and from the positive plate to the battery. The amount of charge on the plates will increase. The amount of charge that the plates can handle is
This is not analogous to a bucket containing water, an incompressible fluid but rather to a gas cylinder whose capacity is a function of pressure. However, few students have any experience with gas cylinders. The bucket analogy is sufficient to clarify the concept of ``capacity'' at a fixed voltage.
Analogies for various electric phenomena have been presented. There are analogies for nearly all physical phenomena that can help the student connect his/her life experiences with the concept(s) to be taught. The instructor must present these analogies by demonstration (as by dropping a book from a height) or illustration with sketches on the blackboard. It is most important that the student's interest and imagination be aroused for a successful learning experience. Get the students involved physically and emotionally, let the students ``see'' the phenomena being taught, or, at least, on analogy of it, and they will learn!
Dr. Rothkopf is Associate Professor, Engineering Technologies, College of Staten Island/ CUNY, Staten Island, NY. Dr. Rothkopf earned his Ph.D. in physics at the Hebrew University of Jerusalem and his M.S.E.E. and B.E.E. in electrical engineering at Polytechnic University and City College of New York, respectively.
Dr. Rothkopf has been teaching electrical engineering technology for nearly twenty-five years. His research interests focus on electrical instruments and student motivation and retention. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE) and is a member of the American Society for Engineering Education (ASEE), Eta Kappa Nu, and the New York State Engineering Technology Association (NYSETA).the learning experience.
