Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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1. An RLC circuit consists of a resistor, inductor, and a capacitor in series along
with a battery as their components. Expressed from total energy, we see the
total charge as determined by the differential equation
dd²q
L
+ R
dt2
%3D
dt
C
Show that from the general solution for a harmonic oscillator under a damped
oscillation with the expression that is analogous,
d²x
dx
+b-
0,
m-
+ kx
dt2
dt
gives us the solution of charge as
q(t) = Qmaxe"
R/2L
cos wat,
where the angular frequency of the circuit is
271/2
1
Wa =
LC
2L
Hint: Start with working through finding a general solution for the harmonic
ocillator for mechanical energy. Apply it to Electromagnetic energy to find the
solution above. We can find that this type of solution is similar.
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Transcribed Image Text:1. An RLC circuit consists of a resistor, inductor, and a capacitor in series along with a battery as their components. Expressed from total energy, we see the total charge as determined by the differential equation dd²q L + R dt2 %3D dt C Show that from the general solution for a harmonic oscillator under a damped oscillation with the expression that is analogous, d²x dx +b- 0, m- + kx dt2 dt gives us the solution of charge as q(t) = Qmaxe" R/2L cos wat, where the angular frequency of the circuit is 271/2 1 Wa = LC 2L Hint: Start with working through finding a general solution for the harmonic ocillator for mechanical energy. Apply it to Electromagnetic energy to find the solution above. We can find that this type of solution is similar.
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