69.
(a) The energy stored in the capacitor is given by U
E
= q
2
/2C. Since q is a periodic function of t with
period T , so must be U
E
. Consequently, U
E
will not be changed over one complete cycle. Actually,
U
E
has period T /2, which does not alter our conclusion.
(b) Similarly, the energy stored in the inductor is U
B
=
1
2
i
2
L. Since i is a periodic function of t with
period T , so must be U
B
.
(c) The energy supplied by the generator is
P
avg
T = (I
rms
E
rms
cos φ)T =
1
2
T
E
m
I cos φ
where we substitute I
rms
= I/
√
2 and
E
rms
=
E
m
/
√
2.
(d) The energy dissipated by the resistor is
P
avg,resistor
T = (I
rms
V
R
)T = I
rms
(I
rms
R)T =
1
2
T
I
2
R .
(e) Since
E
m
I cos φ =
E
m
I(V
R
/
E
m
) =
E
m
I(IR/
E
m
) = I
2
R, the two quantities are indeed the same.