ch31-p027 - 27. Let t be a time at which the capacitor is...

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where qQ e Rt L max / 1 2 = (see the discussion of the exponentially decaying amplitude in §31-5). One period later the charge on the fully charged capacitor is () 2 / max 2 2 where = , ' Rt T L e T ω −+ π = and the energy is 22 / max 2 . Rt T L q Q Ut T e CC += = The fractional loss in energy is || ( ) ( ) . /( ) / / / U U Ut Ut T Ut ee e e Rt L R t T L Rt L RT L = = =− −− + 1 Assuming that RT / L is very small compared to 1 (which would be the case if the resistance is small), we expand the exponential (see Appendix E). The first few terms are: e RT L RT L RT L
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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