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Unformatted text preview: Chapter 18 Direct Current Circuits Dr. G. Antar 2 OUTLINE Electromotive Force and potential difference Resistors in series and in parallel Kirchhoffs rules RC circuit Application to neurons Dr. G. Antar 3 Electromotive force ( emf , E ) Electromotive force ( emf , E ) is a term used to characterize electrical devices, where for a given device, if a charge Q passes across that device, and gains an energy U, the net emf for that device is the energy gained per unit charge E =U/Q This has units of volts (V), or Newtonmeter/Coulomb (Nm/C). It can be thought of as a voltage induced by the device in question. Dr. G. Antar 4 Sources of electromotive force (emf) In a closed circuit , the source that maintains the current is called a source of emf Any devices that increase the potential energy of charges circulating in circuits are sources of emf Examples: batteries, power supplies, generators SI units are Volts The emf E is the work done per unit charge. Since force has the unit of newton (N), emf is a misnomer, but one that over time has resisted change. Dr. G. Antar 5 emf and Internal Resistance In a battery the work done per unit charge goes to: 1. Internal heating of the battery since it has an internal resistance. 2. Outside voltage of the battery that we saw was denoted by V or V . Therefore, the terminal voltage is not equal to the emf. Dr. G. Antar 6 V and emf The schematic shows the internal resistance, r , that is now included. The terminal voltage is V ab = V b V a V ab = E Ir V ab = IR For the entire circuit, E = IR + Ir or I = E /(R+r) Equivalent circuit Dr. G. Antar 7 Internal Resistance and emf E is equal to the terminal voltage when the current is zero E = V Also called the opencircuit voltage R is called the load resistance The current depends on both the resistance external to the battery and the internal resistance. The typical values of internal resistance in batteries vary between 0.10.5 Ohm. Dr. G. Antar 8 Output power with internal resistance When R >> r , r can be ignored Generally assumed in problems The total power output is (recall P = I V ): I E = I 2 R + I 2 r When R >> r , most of the power delivered by the battery is transferred to the load resistor Dr. G. Antar 9 Resistors in Series When two or more resistors are connected endtoend, they are said to be in series The current is the same in all resistors because any charge that flows through one resistor flows through the other. Analog to water flowing in pipe with two constrictions corresponding to R 1 and R 2 . Dr. G. Antar 10 Resistors in Series: The voltages The sum of the potential differences across the resistors is equal to the total potential difference across the combination Potentials add Consequence of Conservation of Energy V ac = V ab + V bc I = I ab = I bc Dr. G. AntarDr....
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 Spring '09
 ANTAR
 Physics, Current, Force

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