00 KCL rev F09 - EECS 314 / Kirchhoff's Current Law 9/1/10...

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EECS 314 // Kirchhoff's Current Law 9/1/10 © 2010 A. Ganago 1 We begin with basic laws applicable to all circuits In today’s discussion, it does not matter what exactly the circuit elements are; but pay attention to their connections © 2009 A. Ganago 1 KCL © 2009 A. Ganago 2 Gustav Kirchhoff (1824-1887) formulated Basic Circuit Laws in 1847: Kirchhoff’s Current Law (KCL) Kirchhoff’s Voltage Law (KVL) These general laws apply to circuits regardless of the types of charge carriers (electrons, holes, ions) KCL Note his age… Gustav Kirchhoff (1824-1887) formulated Basic Circuit Laws when he was 23 years old… • Like a Master’s grad student of today… • Then he went on to more glory © 2009 A. Ganago KCL 3 © 2009 A. Ganago 4 Basic facts about charges (1) • Electric charges are of two types •Denoted positive and negative • Elementary positive charge (such as of a proton) equals 1.602 · 10 -19 C •The unit of an electric charge is coulomb • Elementary negative charge (of an electron) has the same magnitude KCL © 2009 A. Ganago 5 • The size of an elementary charge is so small that charges seem continuous – Old terms and formulas (still in use) describe the charges and currents as fluids and their flow Basic facts about charges (2) KCL © 2009 A. Ganago 6 • Modern applications such as nanotechnology have to treat charges as discrete, but in this course we use the traditional formulas Basic facts about charges (3) KCL
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EECS 314 // Kirchhoff's Current Law 9/1/10 © 2010 A. Ganago 2 © 2009 A. Ganago 7 I = dQ dt Definition of electric current dQ is the electric charge that crosses a surface, such as the cross-section of a wire, during the time interval dt I is the electric current Unit: 1 ampere = 1 A = 1 C / 1 sec KCL Similarities (1) • The definition of electric charge is similar to that of mass flow, for example, of incompressible liquid (water, etc.) © 2009 A. Ganago KCL 8 © 2009 A. Ganago 9 Flow = dm dt Definition of mass flow Of course, mass m is not continuous but we use this formula for simplicity, assuming that the change of mass dm is much larger than the mass of a molecule or atom KCL © 2009 A. Ganago 10 Conventions used in circuits (1) Direction of electric current is the chosen as the direction of motion of positive charges – Thanks, Ben Franklin … – Don’t worry about electrons and positive ions – just be consistent in bookkeeping! KCL © 2009 A. Ganago 11 Conventions used in circuits (2) The conventional direction of electric current is opposite to the direction, in which electrons move Electric current flow through a wire Electrons flow through the wire KCL © 2009 A. Ganago 12 Conventions used in circuits (3) Both the magnitude and the direction of the electric current determine the amount of charges moving in the circuit + 5 A - 5 A The same current can be shown in two ways… KCL
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EECS 314 // Kirchhoff's Current Law 9/1/10 © 2010 A. Ganago 3 © 2009 A. Ganago 13 Practical Application (1)
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This note was uploaded on 12/06/2010 for the course EECS 314 taught by Professor Ganago during the Spring '07 term at University of Michigan.

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00 KCL rev F09 - EECS 314 / Kirchhoff's Current Law 9/1/10...

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