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 .