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.