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19. (a) The charge (as a function of time) is given by
q
=
Q
sin
ωt
,where
Q
is the maximum charge on the
capacitor and
ω
is the angular frequency of oscillation. A sine function was chosen so that
q
=0
at time
t
= 0. The current (as a function of time) is
i
=
dq
dt
=
ωQ
cos
ωt ,
and at
t
=0,itis
I
=
ωQ
.S
ince
ω
=1
/
√
LC
,
Q
=
I
√
LC
=(2
.
00 A)
p
(3
.
00
×
10
−
3
H)(2
.
70
×
10
−
6
F) = 1
.
80
×
10
−
4
C
.
(b) The energy stored in the capacitor is given by
U
E
=
q
2
2
C
=
Q
2
sin
2
ωt
2
C
and its rate of change is
dU
E
dt
=
Q
2
ω
sin
ωt
cos
ωt
C
.
We use the trigonometric identity cos
ωt
sin
ωt
=
1
2
sin(2
ωt
) to write this as
dU
E
dt
=
ωQ
2
2
C
sin(2
ωt
)
.
The greatest rate of change occurs when sin(2
ωt
)=1or2
ωt
=
π/
2 rad. This means
t
=
π
4
ω
=
πT
4(2
π
)
=
T
8
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Charge, Current

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