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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 dq L dt2 dt

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 dq L dt2 dt

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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.
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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