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Unformatted text preview: 1 February 18, 2008 Physics 132Winter 2008 Prof. Jim BeattyOhio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 18 February 18, 2008 Physics 132Winter 2008 Prof. Jim BeattyOhio State 2 Writing Circuit Equations At an EMF device: Add + E going from  to + Add  E going from + to  At a Resistor: Add IR going in direction of I Add +IR going opposite from I At a capacitor: Define the positive plate. Going from + to : Q/C Going from  to +: +Q/C Start at junctions. (Single loop circuits have no junctions.) Label each branch with an I. (Directions are arbitrary, but you need to put them on the diagram!) At each junction, Σ I = 0 (Kirchhoff’s Current Law) For each closed loop, Σ V = 0 (Kirchhoff’s Voltage Law) You get one equation for each junction and for each closed loop. You will get more than enough equations to solve for all the unknowns. Loop Rules 2 February 18, 2008 Physics 132Winter 2008 Prof. Jim BeattyOhio State 3 Charging a Capacitor through a Resistor With switch open, Q=0 and V c =0. Close the switch. V c is still zero until current has time to charge C. Loop equation: E C R i Loop rule for a capacitor: Define the positive plate. Going from + to : Q/C Going from  to +: +Q/C E − iR − Q / C = Initially Q=0 so i= E /R. Current flows until E =Q/C. Then i=0 February 18, 2008 Physics 132Winter 2008 Prof. Jim BeattyOhio State 4 Kirchhoff Analysis of an RC Circuit E − iR − Q / C = E C R i i = dQ dt for positive plate on ‘upstream’ side of C E − dQ dt R − Q / C = A differential equation Uniqueness theorems give us a ‘license to guess’. 3 February 18, 2008 Physics 132Winter 2008 Prof. Jim BeattyOhio State 5 The Solution E − dQ dt R − Q / C = C E − dQ dt RC − Q = Guess: Q ( t ) = ae bt + d dQ dt = abe bt C E − abe bt ( ) RC − ae bt − d = CE − d ( ) − bRC + 1 ( ) ae bt = Zero if both terms in parentheses are zero. d = C E b = − 1 RC Q ( t ) = C E − ae − t RC Choose a so Q(t=0) is zero....
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This note was uploaded on 04/18/2008 for the course PHYS 132 taught by Professor Beatty during the Winter '08 term at Ohio State.
 Winter '08
 Beatty
 Magnetism

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