Transcript PowerPoint Ch 32

Lecture PowerPoint
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 32
Inductance and Circuit
Oscillations
Main Points of Chapter 32
• Inductance and Inductors
• Energy in Inductors and in the Magnetic Field
• RL Circuits
• LC Circuits
• RLC Circuits, Damped Oscillations, and Energy
32-1 Inductance and Inductors
• Faraday’s Law: Changing current in a
circuit will induce emf in that circuit as
well as others nearby
• Self-Inductance: Circuit induces emf in
itself
• Mutual Inductance: Circuit induces emf
in second circuit
32-1 Inductance and Inductors
emf induced through self-inductance:
(32-2)
The inductance L is a proportionality
constant that depends on the geometry
of the circuit
32-1 Inductance and Inductors
emf induced in circuit 2 by changing
currents in circuit 1, through mutual
inductance:
(32-5)
32-1 Inductance and Inductors
(32-5)
• The mutual inductance M depends
only on the geometry of the two-circuit
system
• subscripts are omitted, as M21 = M12
32-1 Inductance and Inductors
Units of inductance: Henry
(32-6)
Modification of Kirchhoff’s loop rule:
In moving across an inductor of inductance L
along (or against) the presumed direction of
the current I, the potential change is ΔV = –L
dI/dt (or +L dI/dt, respectively).
Magnetic materials will change selfinductance by changing magnetic flux
32-2 Energy in Inductors
• Work must be done to create
current through inductor
• This changes the energy stored in
the inductor
• Starting from zero current:
(32-13)
32-3 Energy in Magnetic Fields
The energy in a solenoid depends on the
current, and therefore on the magnetic field
created by the current:
(32-15)
giving the energy density of the magnetic field:
(32-16)
32-4 Time Dependence in RL Circuits
When the switch closes, the inductor keeps
the current from attaining its maximum value
immediately. That is when the current is
changing most rapidly, and when the potential
drop across the conductor is at a maximum.
32-4 Time Dependence in RL Circuits
Current as a function of time:
(32-19)
32-5 Oscillations in LC Circuits
• Start with charged
capacitor
• It will discharge through
inductor, and then recharge
in opposite sense
• If no resistance, will
continue indefinitely
32-5 Oscillations in LC Circuits
Charge on capacitor oscillates with frequency ω:
(32-23)
Charge as a function of time:
(32-25)
Here, Q0 is the original charge and φ sets the
phase at t = 0.
32-6 Damped Oscillations in RLC Circuits
Charge equation:
(32-28)
Solution:
(32-30)
where
(32-31)
and
(32-32)
32-6 Damped Oscillations in RLC Circuits
32-6 Damped Oscillations in RLC Circuits
For a certain value of R, ω′ = 0. This
is called critical damping.
(32-33)
32-7 Energy in LC and RLC Circuits
• In a pure LC circuit, energy is transferred back
and forth between the capacitor’s electric field
and the inductor’s magnetic field.
• Including a resistor causes I2R losses, which
show up as heat.
Summary of Chapter 32
• Definition of inductance:
(32-1)
• Induced emf:
(32-2)
• emf induced in a
second loop:
(32-5)
• Energy in an
inductor:
(32-13)
• Energy density of a
magnetic field:
(32-16)
Summary of Chapter 32, cont.
• LC circuit oscillations:
(32-23)
• RLC circuit oscillations:
(32-30)