22.
(a) The figure implies that the the instantaneous current through the leftmost inductor is the same
as that through the rightmost one, which means there is no current through the middle inductor
(at any instant). Applying the loop rule to the outer loop (including the rightmost and leftmost
inductors), with the current suitably related to the rate of change of charge, we find
2L
d
2
q
dt
2
+
2
C
q = 0
=
⇒ ω =
1
(2L)(C/2)
=
1
√
LC
.
(b) In this case, we see that the middle inductor must have current 2i(t) flowing downward, and
application of the loop rule to, say, the left loop leads to
L
d
2
q
dt
2
+ L
2
d
2
q
dt
2
+
1
C
q = 0
=
⇒ ω =
1
(3L)(C)
=
1
√
3LC
.
Document Outline
- Main Menu
- Chapter 1 Measurement
- Chapter 2 Motion Along a Straight Line
- Chapter 3 Vectors
- Chapter 4 Motion in Two and Three Dimensions
- Chapter 5 Force and Motion I
- Chapter 6 Force and Motion II
- Chapter 7 Kinetic Energy and Work
- Chapter 8 Potential Energy and Conservation of Energy
- Chapter 9 Systems of Particles
- Chapter 10 Collisions
- Chapter 11 Rotation
- Chapter 12 Rolling, Torque, and Angular Momentum
- Chapter 13 Equilibrium and Elasticity
- Chapter 14 Gravitation
- Chapter 15 Fluids
- Chapter 16 Oscillations
- Chapter 17 Waves—I
- Chapter 18 Waves—II
- Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
- Chapter 20 The Kinetic Theory of Gases
- Chapter 21 Entropy and the Second Law of Thermodynamics
- Chapter 22 Electric Charge
- Chapter 23 Electric Fields
- Chapter 24 Gauss’ Law
- Chapter 25 Electric Potential
- Chapter 26 Capacitance
- Chapter 27 Current and Resistance
- Chapter 28 Circuits
- Chapter 29 Magnetic Fields
- Chapter 30 Magnetic Fields Due to Currents
- Chapter 31 Induction and Inductance
- Chapter 32 Magnetism of Matter: Maxwell’s Equation
- Chapter 33 Electromagnetic Oscillations and Alternating Current
- 33.1 - 33.10
- 33.1
- 33.2
- 33.3
- 33.4
- 33.5
- 33.6
- 33.7
- 33.8
- 33.9
- 33.10
- 33.11 - 33.20
- 33.11
- 33.12
- 33.13
- 33.14
- 33.15
- 33.16
- 33.17
- 33.18
- 33.19
- 33.20
- 33.21 - 33.30
- 33.21
- 33.22
- 33.23
- 33.24
- 33.25
- 33.26
- 33.27
- 33.28
- 33.29
- 33.30
- 33.31 - 33.41
- 33.31
- 33.32
- 33.33
- 33.34
- 33.35
- 33.36
- 33.37
- 33.38
- 33.39
- 33.40
- 33.41 - 33.50
- 33.41
- 33.42
- 33.43
- 33.44
- 33.45
- 33.46
- 33.47
- 33.48
- 33.49
- 33.50
- 33.51 - 33.60
- 33.51
- 33.52
- 33.53
- 33.54
- 33.55
- 33.56
- 33.57
- 33.58
- 33.59
- 33.60
- 33.61 - 33.70
- 33.61
- 33.62
- 33.63
- 33.64
- 33.65
- 33.66
- 33.67
- 33.68
- 33.69
- 33.70
- 33.71 - 33.80
- 33.71
- 33.72
- 33.73
- 33.74
- 33.75
- 33.76
- 33.77
- 33.78
- 33.79
- 33.80
- 33.81 - 33.90
- 33.81
- 33.82
- 33.83
- 33.84
- 33.85
- 33.86
- 33.87
- 33.88
- 33.89
- 33.90
- 33.91 - 33.92
- 33.91
- 33.92
- 33.1 - 33.10
- Chapter 34 Electromagnetic Waves
- Chapter 35 Images
- Chapter 36 Interference
- Chapter 37 Diffraction
- Chapter 38 Special Theory of Relativity
- Chapter 39 Photons and Matter Waves
- Chapter 40 More About Matter Waves
- Chapter 41 All About Atoms
- Chapter 42 Conduction of Electricity in Solids
- Chapter 43 Nuclear Physics
- Chapter 44 Energy from the Nucleus
- Chapter 45 Quarks, Leptons, and the Big Bang
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