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14 Electromagnetism II
The rms current, I e =
V e
Z
=
50
500
= 0.1 A
PD across the capacitor, V c = I e X c = 0.1 × 400 = 40 V
(b) Power, P = V e I e cos α = V e I e
R
Z
= 50 × 0.1 ×
300
500
= 3.0 W
14.2 (a) X L = 2π fL = 2π ×
200
π
× 10 × 10
−3
= 4
Z =
R 2 + X 2 =
3 2 + 4 2 = 5
I e = V e /Z = 5/5 = 1.0 A
V R = I e R = 1.0 × 3 = 3.0 V
V L = I e X L = 1.0 × 4 = 4.0 V
(b) Phase angle between V e and I e is given by
tan α =
X L
R
=
4
3
⇒ α = 53
◦
V e leads I e by 53
◦
14.3 U =
1
2
L I
2
L =
2U
I 2 =
2 × 10
5 2 = 0.8 H
14.4 (a) f =
1
2π
√
LC
=
1
2π
√
4 × 10 −6 × 5 × 10 −11
= 1.125 × 10 −7 Hz
(b) λ =
c
f
=
3 × 10 8
1.125 × 10 7 = 26.67 m
14.5 (a) Z =
(X L − X C ) 2 + R 2 =
(12 − 20) 2 + 6 2 = 10
(b) P = I e V e
R
Z
=
V 2
e R
Z 2 =
(250) 2 × 6
10 2
= 3750 W
14.6 At ω 0 = 600 rad/s, X L = X C
∴ ω 0 L =
1
ω 0 C
⇒
1
LC
= ω
2
0
At ω = 60 rad/s,
X C
X L
=
1/ωc
ωL
=
1
ω 2 LC
=
ω 2
0
ω 2 =
(600) 2
60 2 = 100