06 Ohm�s law - Ganago/OhmsLaw ,...

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Ganago / Ohm’s Law © 2010 Alexander Ganago Page 1 of 29 File: 2010‐01‐11 Ohm’s law In the beginning of the course, we discussed the current I through a circuit element and the voltage V across this element as two variables that hardly related to each other. Their magnitudes seemed totally independent; moreover, in some circuit elements, the current entered the more positive terminal, while in other elements the direction of current was opposite. (Recall that this distinction in current directions related to whether the elements absorbed or supplied electric power.) Such lack of clarity was typical of the state of knowledge in the early 1800s, when Georg Simon Ohm started his experiments on electric circuits. Through careful measurements and mathematical analysis of data, Georg Ohm found that the voltage V across a circuit element was directly proportional to the current I through this element. His finding, which we call Ohm’s law, served as breakthrough for electric circuit analysis. Figure 2‐5. German physicist Georg Simon Ohm (16 March 1789 – 6 July 1854) formulated the relationship between electric voltage and current based on his experiments with circuits done when he taught physics at a prestigious high school in 1820s. The mathematical expression of Ohm’s law is: V = I R [equation 2‐1] Here the coefficient R between the voltage V across the circuit element and the current I through this element is called electric resistance .
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Ganago / Ohm’s Law © 2010 Alexander Ganago Page 2 of 29 File: 2010‐01‐11 Ohm’s law The SI unit of resistance is named ohm after its discoverer; the symbol is capital Greek letter Ω ( omega ), chosen because of its consonance with the scientist’s name. The units of measure are: 1 volt = (1 ohm) (1 amp), or 1 V = (1 Ω ) (1 A) [equation 2‐2] An alternative formulation of Ohm’s law uses conductance G, which is reciprocal of resistance R: I = G V, where G = 1/R [equation 2‐3] The unit of conductance used to be called mho , that is ohm spelled backwards; then its symbol was the capital omega flipped over (put on its head). The contemporary SI unit of conductance is siemens, abbreviated S, called after German inventor and industrialist Ernst Werner von Siemens (see Figure 2‐6). Figure 2‐6. Ernst Werner von Siemens (13 December 1816 – 6 December 1892) was a German inventor and industrialist, founder of one of the largest electro‐technological companies in the world, which is known today as Siemens AG. The fourth (out of fourteen) son of a tenant farmer, he left school without finishing education to become a soldier. When he become inventor and founded his own company, his
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Ganago / Ohm’s Law © 2010 Alexander Ganago Page 3 of 29 File: 2010‐01‐11 Ohm’s law younger brothers became its representatives in England (Carl Wilhelm Siemens was knighted and became Sir William) and in Russia (Carl Heinrich was ennobled by Tsar Nicholas II). The SI unit of conductance was named in his honor.
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