Transcript AC Circuits

Inductance Ch. 30
Self-inductance and inductors
Magnetic field energy
RL circuit
LC circuit
RLC series circuit
C 2012 J. F. Becker
(sec. 30.2)
(sec. 30.3)
(sec. 30.4)
(sec. 30.5)
(sec. 30.6)
PREPARATION FOR FINAL EXAM
At a minimum the following should be reviewed:
Gauss's Law - calculation of the magnitude of the electric field caused by
continuous distributions of charge starting with Gauss's Law and completing all the
steps including evaluation of the integrals.
Ampere's Law - calculation of the magnitude of the magnetic field caused by
electric currents using Ampere's Law (all steps including evaluation of the integrals).
Faraday's Law and Lenz's Law - calculation of induced voltage and current,
including the direction of the induced current.
Calculation of integrals to obtain values of electric field, electric potential, and
magnetic field caused by continuous distributions of electric charge and current
configurations (includes the Law of Biot and Savart for magnetic fields).
Maxwell's equations - Maxwell's contribution and significance.
DC circuits - Ohm's Law, Kirchhoff's Rules, power, series-parallel combinations.
Series RLC circuits - phasor diagrams, phase angle, current, power factor
Vectors - as used throughout the entire course.
Learning Goals - we will learn: ch 30
• How to relate the induced emf in a circuit
to the rate of change of current in the
same circuit.
• How to calculate the energy stored in a
magnetic field.
• Why electrical oscillations occur in circuits
that include both an inductor (L) and a
capacitor (C).
RL
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 inductor 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
2
U=Pt =i Rt
2
P = i DVab
P = i L di/dt
dU = L i di
Energy density of
B field is
RL circuit
(similar to an RC 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)
Q30.7
An inductor (inductance L) and
a capacitor (capacitance C) are
connected as shown.
If the values of both L and C
are doubled, what happens to
the time required for the
capacitor charge to oscillate
through a complete cycle?
A. It becomes 4 times longer.
B. It becomes twice as long.
C. It is unchanged.
D. It becomes 1/2 as long.
E. It becomes 1/4 as long.
q(t) vs time for damped oscillations in a series RLC
circuit with initial charge Q.
Series RLC circuit
(switch d-a)
Inductor for Exercise 30.9
Review
See
www.physics.sjsu.edu/becker/physics51
C 2012 J. F. Becker