lec08.pdf - Scott Hughes 3 March 2005 Massachusetts...

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Scott Hughes 3 March 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 8: EMF, Circuits, Kirchhoff’s rules 8.1 EMF: Electromotive force The workings of our technological civilization are largely based on the idea that we use electric currents as a means to get devices to do work for us. In this lecture, we will begin to understand at a fundamental level how this works. In order for a current to flow, we must create a potential difference over some conductive material; and, we must have continuous source of charges that can flow through our conduc- tor. Such a source, with a “built-in” potential difference is called a source of “electromotive force” (a rather misleading name, since it isn’t a force). This is usually abbreviated EMF, and is often denoted E . The simplest example of an EMF source is a battery. A battery is a device that maintains a separation of charges between two terminals. Current can flow inside the battery from one terminal to another via an electrochemical reaction. One example, used in many car batteries, is based on the electrochemistry of lead. Two terminals, one of lead oxide, another of porous lead, are immersed in sulphuric acid. E - + H + PbO 2 Pb When immersed in the acid, it is energetically favorable for the porous lead terminal to provide free electrons, producing lead sulfate and free hydrogen ions in the solution: Pb + HSO - 4 PbSO 4 + H + + 2e - At the lead oxide electrode, a reaction which absorbs free electrons and free hydrogen ions is energetically favorable: PbO 2 + 3H + + HSO - 4 + 2e - PbSO 4 + 2H 2 O If it is possible for both electrons and H + ions to travel from one terminal to the other, then the net chemical reaction Pb + PbO 2 + 2H 2 SO 4 2PbSO 4 + 2H 2 O 72
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can proceed. When the terminals of the battery shown above are not connected, there is no way for electrons to get from one terminal to another. An electric field inside the battery builds up, pointing from the + terminal to the - terminal. This field opposes the motion of H + ions — they cannot cross to the + terminal, and the reaction stops. When the terminals are connected by a conductor, on the other hand, electrons freely flow to the + terminal. The electric field is reduced, the H + ions can now easily move across, and the reaction runs happily. The EMF of the battery is just the potential of the + terminal with respect to the - terminal: E = - Z + term - term ~ E · d~s . This EMF is then the potential difference that is available to drive currents in an electrical circuit. 8.2 Circuits and Kirchhoff’s second rule Suppose we take a battery that provides EMF V and connect its terminals with conducting material of resistance R : V R (The symbol on the left is used for a battery in a circuit; the long bar denotes the + terminal, the short bar denotes - . The symbol on the right describes a “resistor”, some conducting material with known resistance R .) How much current flows in this circuit? From Ohm’s law, we must have V = IR I = V/R .
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