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Inductance Ch. 30
Mutual Inductance
Self-inductance and inductors
Magnetic field energy
RL circuit
LC circuit
RLC series circuit
C 2009 J. Becker
(sec. 30.1)
(sec. 30.2)
(sec. 30.3)
(sec. 30.4)
(sec. 30.5)
(sec. 30.6)
MUTUAL INDUCTANCE
The current i1 in coil #1
gives rise to a flux
through coil #2. If i1
changes, an emf is
induced in coil #2 (and
vice versa) according to
Faraday’s Law:
where MUTUAL INDUCTANCE is
C 2004 Pearson Educational / Addison Wesley
SELF-INDUCTANCE (L)
An inductor (L) – When the current in the circuit
changes the flux changes, and a self-induced emf
appears in the circuit. A self-induced emf always
opposes the change in the current that produced the
emf (Lenz’s law).
Across a resistor the potential drop is always from a to
b. BUT across an inductor an increasing current causes
a potential drop from a to b; a decreasing current
causes a potential rise from a to b.
(a) A decreasing current induces in the conductor an
emf that opposes the decrease in current.
(b) An increasing current induces in the inductor an emf
that opposes the increase. (Lenz’s law)
c. Physics, Halliday, Resnick, and Krane, 4th edition, John Wiley & Sons, Inc. 1992.
A resistor is a
device in which
energy is
irrecoverably
dissipated.
Energy stored in a
current-carrying
inductor can be
recovered when
the current
decreases to zero
and the B field
collapses.
Power = energy /
time
P = DVab i = (i R) i =
2
2
i R U = i R (time)
P = DVab i = i L
di/dt
dU = L i di
Energy density of
B field is
RL circuit
Increasing current vs time
for RL circuit.
Decreasing current vs time
for RL circuit.
Oscillation in an
LC circuit.
Energy is
transferred
between the E
field of the
capacitor and the
B field of the
inductor.
Oscillation in an LC circuit.
Energy is transferred between the E field
and the B field.
c. Physics, Halliday, Resnick, and Krane, 4th edition, John Wiley & Sons, Inc. 1992.
Oscillating LC circuit
oscillating at a
frequency
w (radians / second)
q(t) vs time for damped oscillations in a series RLC
circuit with initial charge Q.
Series RLC circuit
Inductor for Exercise 30.7
Series RL circuit
for Exercises 30.69, 30.70, 30.75
RL circuit for Exercises 30.71 and 30.72
Circuit for Challenge Problem 30.78
Review
See www.physics.edu/becker/physics51
C 2009 J. Becker