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Ohm and Ohm's Law

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During the last few decades, there were energetic collapses when entire cities or even countries all over the world were out of electric power for a quiet long period of time. I got curious about the physics of this phenomenon. In the Internet I found that black outs can be explained by the overuse of electric energy in countries that decided either not to build energy plants anymore due to ecological issues or to disconnect their energetic systems from joint ones due to political considerations. To diminish the likelihood of such events folks in these countries should be agitated not to use electricity for cooking and heating. It was fifteen years ago when the last big power station was built in Europe. The German government launched several programs to encourage the use of alternative sources of energy, but estimated indicate that they can satisfy less than 10 % of nation's demand for electricity. Europe can experience black outs due to a significant frost. Therefore, it should consider cooperation with Baltic countries, Ukraine, and Belarus in relation of creation a joint energetic system (Europe Faces, 2008). Thus, I know the answer: energetic collapses are caused by overuse of electricity. The probability of their appearance can be diminished by creation of joint energetic systems, by building new big power plants, and to some extent by using alternative sources of energy. But to satisfy my curiosity I would like to arrive to this answer using laws of Physics. A global black out is happening on the planetary scale, and it resembles the consequence of a short circuit in an ordinary house. The latter can be explained by Ohm’s Law. Indeed, s/c assumes low impedance. Due to Ohm’s Law, the value of the current is so huge that Joule’s heat generated by itself can cause flaming of electric wiring in the house. Therefore, safety fuses are installed in this wiring. They burn before wiring gets significantly heated. It is fuse burning that causes ordinary house black out. Nevertheless, electric lines of an energetic system are far from being flamed due to overload. Therefore, research is needed to be done to find out what physics lies behind energetic collapses of the planetary scale. Before doing the research, it is a good idea to get inspired by stunning examples from the life of such a great scientist as Georg Simon Ohm.

So, Ohm is a great scientist. Since Ohm’s Law explains the nature of ordinary house black out, it is likely that this law explains also the nature of the energetic collapse on the planetary scale.

In what follows from Ohm’s biography, I am going to find out the answers to the following questions:

1. Why is he considered to be a great scientist?

2. Are there inspiring facts in his life?

The mechanism of global black out creation is likely to be much more complicated than the fuse burning in the ordinary house example. Therefore, I am not planning to describe this mechanism in this work. On the other hand, the danger of energetic system line overload should significantly overweight the negative consequences of a global black out. Hence, the identification of this danger is a feasible task for this research. In doing this, I am going to address the following questions:

3. What is the mechanism of transformation of different types of energy to the electric energy on the power plant?

4. What consequences does overload impose on this mechanism?

5. How do these consequences influence customers?

To answer them, I am going to analyze the knowledge that I obtained in this class.

Why is Georg Simon Ohm considered to be a great scientist?

In 1827, he developed his theory of electricity in which he was opposing the notion “of action at a distance” (Georg Simon, n. d.). It is this opposition that inspired “significant developments in physics, from the concept of a field, to description of quantum entanglement and the mediator particles of the standard model” (Action at a distance (physics), 2012). Another thing that makes him a great scientist is that his famous law led to creation of the circuit theory at the end of the 19th century (Georg Ohm, 2012). Only in 1970, an alternative scattering approach to conductivity was offered. There is experimental evidence that is contrary to this approach, Ohm’s one fails to describe properly the electric current propagation in a “coherent diffusive classical conductor” (Nazarov, 1994).

Are there inspiring facts in his life?

The Ohm’s father did not have an opportunity to study in school, but he acquired excellent knowledge in the fields of Mathematics, Physics, Chemistry, and Philosophy studying on his own. Moreover, he was able to communicate it to his sons Georg and Martin, who later became famous scientists (Georg Simon, n. d.).

What is the mechanism of transformation of different types of energy to the electric energy on the power plant?

On each big power plant there is an electric generator. Depending on the type of a power plant the respective type of energy transform to kinetic energy of the generator turbine. The turbine is placed in the external magnetic field. The value of magnetic flux that flows through the turbine circuit depends on angle between the turbine circuit plane and the direction of the magnetic field  as shown on Figure 1 and equals , where

is the inductance of the magnetic field,  is the area of the turbine circuit. If the frequency of the turbine rotation is, then. According to Faraday’s law of induction "theinducedemfin a circuitisdirectlyproportionaltothetimerateofchangeofthemagneticfluxthroughthecircuit" (Murrieta, n. d.). Therefore, the frequency of the electromotive force generated in the turbine circuit is equal to the frequency of the turbine rotation.

What consequences does overload impose on this mechanism?

According to Lentz’s Law the current in this circuit flows "in the direction that creates a magnetic field that opposes the change in magnetic flux through the loop". This direction is shown on Figure 2 (Murrieta, n. d.). The external magnetic field creates a force acting on the current. The magnitude of this force is proportional to the value of the current. Its direction

is determined by Fleming's left hand rule. To apply this rule I need to stretch my fingers on a left hand as it is shown on Figure 3. If the first finger and the second one point in directions of the magnetic field and the current respectively, then the thumb points in the direction of the force acting on the current (Fleming’s left hand rule for motors, 2012). Applying this rule to the set up depicted on Figure 2 (Murrieta, n. d.), I can conclude that it creates a torque that opposes the turbine rotation and is proportional to the value of the current.

The increased consumers’ use of electric power assumes increased value of an electric current in the turbine circuit. The last increase entails the increase of the value of the above mentioned torque that opposes the turbine rotation. At some moment, the plant will reach its capacity and will not be able to maintain the standard value of the line frequency.

How do these consequences influence customers?

At home, I have the fixed voltage in a power socket. Impedances of device circuit components depend upon the utility frequency. These components are balanced with respect to phase shifts and amplitude changes assuming the standard utility frequency. However, when this frequency significantly differs from the standard one, some resonant effects could happen (Bendat & Piersol, 1971). These effects can be explained by Ohm’s Law. According to this law, the amplitude of the alternating current that flows through a circuit component is equals the amplitude of the voltage across this component divided by the impendence of this component. If the power line frequency changes to that, at which this impendence is significantly smaller than its value at the standard utility frequency, then I will have a drastic increase in the amplitude of the current. Since Joule’s heat is a quadratic function of the value of a current, the deviation of this frequency value from its standard one that lasts for a long period of time will result in huge counts of burnt devices all over the country. At first glance, it seems that the global black out imposes also the global dangers on the devices. Indeed, this event is characterized by an abrupt change in the dependence of voltage in a power socket on time. Such a change, in any signal results in significant large frequency components of the signal (Lehar, n. d.). It entails more significant changes in the circuit component impendence and more drastic changes in current than in the case of small deviation of the utility frequency value from the standard one. But it lasts for a very short period of time. Besides, surge protectors are specifically designed to alleviate consequences of ordinary house black outs (Christie, 2011). Therefore, a small deviation of the line frequency from its standard value, that lasts for a long period of time, is more harmful to devices than a global energetic collapse.

Thus, to my mind, Georg Simon Ohm’s greatness stems from the following. Firstly, he was one of those scientists who were opposing the notion “of action at a distance” (Georg Simon, n. d.). It is this opposition, which inspired “significant developments in physics, from the concept of a field, to description of quantum entanglement and the mediator particles of the standard model” (Action at a distance (physics), 2012). Secondly, the circuit theory, developed at the end of the 19th century, is based on his theory of electricity (Georg Ohm, 2012). I was surprised to find out that the experimental evidence has been observed recently that the circuit theory does not describe the conductivity of some classical conductors properly (Nazarov, 1994). The fact that the Ohm’s father got educated by himself and was able to communicate his knowledge to his sons Georg and Martin who later became great scientists inspired me to do research (Georg Simon, n. d.). I got interested in physics of global energetic collapses that were happening all over the world during the last few decades. In the Internet, I found that black outs can be explained by the overuse of electricity (Europe Faces, 2008). They resemble the ordinary house black outs that are happening to prevent flaming of the house wiring. But energetic system lines are far from being flamed due to the overload. This research has identified that energetic system line overload can entail the following danger.

Each big power plant has an electric generator. It generates alternating electromotive force, which frequency is determined by the frequency of the turbine rotation and is equal to the power line frequency. The turbine is placed in the external magnetic field. This field produces the torque that opposes the turbine rotation. The value of this torque is proportional to the value of the current in the turbine circuit. Overuse of electricity results in an increase of the value of this current to such extent that power plant capacity is not enough to maintain the constant frequency of the turbine rotation. A small deviation of the utility frequency value from the standard one that lasts for a long period of time can result in increased rates of burnt devices all over the country.

The energetic collapse also imposes global danger to devices. Since its duration is very short and surge protectors are designed specifically to alleviate its consequences (Christie, 2011). A small deviation of the line frequency from its standard value that lasts for a long period of time is more harmful to the devices than a global energetic collapse.

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