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Admin:
• Assignment 9 is posted
• 2 more AC analysis problems
• RC circuits
• Due Monday (May 4th)
•
•
•
•
Second mid-term date is Wednesday May 6th
The test will cover everything after Thevenin’s theorem
Review Lecture Monday (May 4th). Any requests?
Any students with accommodations can use the test
center – fill out the DSS form.
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• Thursday 2pm – 4pm
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• Tuesday 2pm – 4pm.
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AC circuit 1
Find the equivalent impedance
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AC circuit 2
Find the current through Z3
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30-5 LC Circuits and
Electromagnetic Oscillations
An LC circuit is a charged capacitor
shorted through an inductor.
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30-5 LC Circuits and
Electromagnetic Oscillations
The charge and current both oscillate,
but with different phases.
.
Copyright © 2009 Pearson Education, Inc.
30-5 LC Circuits and
Electromagnetic Oscillations
The total energy in the circuit is
constant; it oscillates between the
capacitor and the inductor:
http://en.wikipedia.org/wiki/LC_circuit#/med
a/File:Tuned_circuit_animation_3.gif
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30-5 LC Circuits and
Electromagnetic Oscillations
Many applications:
Oscillators
Crystal set
radio tuner
Tuners
Resonators
Filters
Mixers
https://www.youtube.com/wat
ch?v=qAvVjGZnBrw
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30-5 LC Circuits and
Electromagnetic Oscillations
Example 30-7: LC circuit.
A 1200-pF capacitor is fully charged by a 500-V
dc power supply. It is disconnected from the
power supply and is connected, at t = 0, to a 75mH inductor. Determine:
(a) the initial charge on the capacitor;
(b) the maximum current;
(c) the frequency f and period T of oscillation;
(d) the total energy oscillating in the system.
U
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30-6 LC Oscillations with Resistance
(LRC Circuit)
Any real (nonsuperconducting) circuit will
have resistance.
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30-6 LC Oscillations with Resistance
(LRC Circuit)
Now the voltage drops around the circuit give
The solutions to this equation are damped
harmonic oscillations. The system will be
underdamped for R2 < 4L/C, and overdamped
for R2 > 4L/C. Critical damping will occur
when R2 = 4L/C.
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30-6 LC Oscillations with Resistance
(LRC Circuit)
This figure shows the three cases of
underdamping, overdamping, and
critical damping.
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30-6 LC Oscillations with Resistance
(LRC Circuit)
The angular frequency for
underdamped oscillations is given by
.
The charge in the circuit as a
function of time is
.
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30-6 LC Oscillations with Resistance
(LRC Circuit)
Example 30-8: Damped oscillations.
At t = 0, a 40-mH inductor is placed in series with a
resistance R = 3.0 Ω and a charged capacitor C = 4.8 μF.
(a) Show that this circuit will oscillate.
(b) Determine the frequency.
(c) What is the time required for the charge amplitude to
drop to half its starting value?
(d) What value of R will make the circuit nonoscillating?
Underdamped R2 < 4L/C,
overdamped for R2 > 4L/C.
Critical damping will occur when R2 = 4L/C.
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