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where
qQ
e
Rt
L
max
/
1
2
=
−
(see the discussion of the
exponentially decaying amplitude
in §315). 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.
 Spring '08
 Any
 Physics, Charge, Energy

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