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# Ohm and Ohm’s Law

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Ohm’s law is a law of physics. It states that in an electrical conductor the ratio of potential difference (voltage) to current is constant. For example, if the terminals of an electric battery are connected to an electric lamp and the voltage output of the battery is then decreased by 20 percent, the amount of current flowing through the lamp will also be reduced by 20 percent.

Ohm’s law was derived experimentally by German physicist Georg Simon Ohm in 1826. It is expressed by the following equation:

V=I x R

In this equation V represents the potential difference between one end of the conductor and the other (that is, the voltage applied to the conductor); and R is called the resistance of the conductor. If V is given in volts and I is given in amperes, R will be in ohms (Crandall, 2004).

The law offers a simple method of calculating the voltage, current, or resistance in a conductor when two of these three quantities are known. For example, if the direct-current voltage applied to an electric light bulb is 120 volts and the filament in the bulb has a resistance of 240 ohms, the current flowing through the filament is

I = V = 120 volts = 0.5 ampere

R     240 ohms

Ohm’s Law is valid for metallic conductors (for example, copper and tungsten) in is relatively low. High currents will heat a metallic conductor and cause its resistance to change, so that the ratio of voltage to current in the conductor will also change. Ohm’s Law holds for a complete direct-current circuit as well as for any part of the circuit, provided that I is the total current flowing between the points across which the voltage, V, is measured (Leroy, 2003).

In alternating-current circuits, Ohm’s Law seldom is valid because the current flow is affected not only by resistance but also by factors known as inductance and capacitance.

Moreover, the equation called Ohm’s law is not one of the fundamental principles of physics, as are Newton’s laws of motion and the conservation-of-energy principle. Yet Ohm’s law has been considered important enough to be included in the physics curriculum of students for more than one hundred years. When Ohm presented his idea, it was received with scorn.

Ohm, at the age of 38, has served for ten years as a poorly paid mathematics and science teacher at the Jesuit College of Cologne. To qualify for a university position, he was required to produce some kind of scientific masterpiece, the value of which would bring recognition and university job offers. After many years of experimenting with electricity, during which time he published numerous short papers, Ohm produced a 250-page manuscript entitled Mathematical Measurements of Electrical Current (Silver, 1998).

The paper was ignored by most of Ohm’s German colleagues. One critic who did not ignore it said, “A physicist who professed such heresies was unworthy to teach science.” Ohm, unfortunately, had presented his work at a time and place where experiment was disdained as a means of acquiring knowledge. He did not receive a university position and even had to resign from the Jesuit College. After six dismal years, King Ludwig I of Bavaria helped Ohm obtain a professorship at the Polytechnic School of Nuremberg. Ohm eventually received recognition for his work. In 1841, he was awarded the Copley Medal by the Royal Society of London, and in 1842 he was honoured as the Society’s most distinguished foreign member.

Furthermore, Ohm’s law provides a nice working definition for measuring the resistance of an ohmic device. The definition does not, however, give us a good sense of what causes some objects to have higher resistances than others. An object’s resistance depends on properties of the object including among other things its dimensions and the type of material of which it is made (Everdell, 1998). For example, scientists have determined that the electrical resistance of cylindrical objects is directly proportional to their length L and inversely proportional to their cross-sectional area A:

R = pL

A

The proportionally constant p (rho) is called the object’s resistively; it depends on the type of material of which it is made and on its temperature. The equation above seems reasonable. The longer an object is, the more difficult it is for charge to cross it (like water that must travel a long distance along a slope that has very small inclination). Also, resistance increases as an object’s cross-sectional area decreases because few electric charges are available to pass the small cross section.

The resistivity p of a material depends in intrinsic properties of that type of material, such as the number of electrons per unit volume that are able to move and the hindrance these electrons experience as they travel through the material. Copper has low resistivity because of its large concentration of free electrons and the relative lack of hindrance experienced by the electrons while moving through the copper. On the other hand, the resistivity of glass is about 1020 times greater than that of copper because it contains so few free electrons (Hook, 2002). Copper is an example of a material called an electrical conductor (low resistivity) whereas glass is an example of an electrical insulator (high resistivity that prohibits the flow of electricity). The conductivity o of a substance is the inverse of its resistivity (o = 1/p). Thus, a material with low resistivity has high conductivity and is a good conductor of electricity, and vice versa.

Reference:

1. Crandall, Christian S. (2004). The Psychological Foundations of Culture. Lawrence Erlbaum Associates. Mahwah, NJ.
2. Everdell, William R. (1998). The First Moderns: Profiles in the Origins of Twentieth-Century Thought. University of Chicago Press. Chicago.
3. Hook, Ernest B. (2002). Prematurity in Scientific Discovery: On Resistance and Neglect. University of California Press. Berkeley, CA.
4. Leroy, Francis (2003). A Century of Nobel Prizes Recipients: Chemistry, Physics, and Medicine, p.3. New York.
5. Silver, Brian L. (1998). The Ascent of Science. Oxford University Press. Place of New York.

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