61.

(a) The rms current is

I

rms

=

E

rms

Z

=

E

rms

R

2

+ (2πf L

− 1/2πfC)

2

=

75.0 V

(15.0 Ω)

2

+

{2π(550 Hz)(25.0 mH) − 1/[2π(550 Hz)(4.70µF)]}

2

=

2.59A .

(b) The various rms voltages are:

V

ab

=

I

rms

R = (2.59A)(15.0 Ω) = 38.8 V

V

bc

=

I

rms

X

C

=

I

rms

2πf C

=

2.59A

2π(550 Hz)(4.70 µF)

= 159V

V

cd

=

I

rms

X

L

= 2πI

rms

f L = 2π(2.59A)(550 Hz)(25.0 mH) = 224 V

V

bd

=

|V

bc

− V

cd

| = |159.5 V − 223.7 V| = 64.2 V

V

ad

=

V

2

ab

+ V

2

bd

=

(38.8 V)

2

+ (64.2 V)

2

= 75.0 V

(c) For L and C, the rate is zero since they do not dissipate energy. For R,

P

R

=

V

2

ab

R

=

(38.8 V)

2

15.0 Ω

= 100 W .