where qQeRtLmax/12=−(see the discussion of the exponentially decaying amplitudein §31-5). One period later the charge on the fully charged capacitor is ()2/max 22where=,'Rt TLeTω−+π=and the energy is 22/max 2.Rt T LqQUt TeCC+==The fractional loss in energy is ||()()./()///∆UUUt Ut TUteeeeRt LR t TLRt LRT L==−=−−−+−−1Assuming that RT/Lis 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: eRTLRTLRT 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.