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We wish to find v(1) for 1>0 in the RLC circuit shown below where the elements are in series. a. Derive the governing equation for the voltage v using KCL at the top node using the following definitions: a = w: = . You should obtain (see attached for a similar 9 2RC derivation from the book) 1/² v = 0 This will get you a governing equation in the same form as that derived for the case we did in class where the R, L, and C were in series. d²v 1 dv dt² RC dt or b. What is the particular solution in this case, i.e., what is the value of v after a very long time after the voltage and current have reached steady state? dv +2a+wv=0 c. If R=15.82, is the system underdamped, critically damped, or overdamped? What is the equation that describes v(t)? dt d. Determine the final equation for v using the initial conditions v(0)=5V and i(0)=0. (Hint: use KCL and i(0)=0 to find at t=0). e. Plot v(1) until the transient dies out.

We wish to find v(1) for 1>0 in the RLC circuit shown below where the elements are in series. a. Derive the governing equation for the voltage v using KCL at the top node using the following definitions: a = w: = . You should obtain (see attached for a similar 9 2RC derivation from the book) 1/² v = 0 This will get you a governing equation in the same form as that derived for the case we did in class where the R, L, and C were in series. d²v 1 dv dt² RC dt or b. What is the particular solution in this case, i.e., what is the value of v after a very long time after the voltage and current have reached steady state? dv +2a+wv=0 c. If R=15.82, is the system underdamped, critically damped, or overdamped? What is the equation that describes v(t)? dt d. Determine the final equation for v using the initial conditions v(0)=5V and i(0)=0. (Hint: use KCL and i(0)=0 to find at t=0). e. Plot v(1) until the transient dies out.

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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We wish to find v(1) for 1>0 in the RLC circuit shown below where the elements are in series. a. Derive the governing equation for the voltage v using KCL at the top node using the following definitions: a = w = == You should obtain (see attached for a similar 2RC derivation from the book) d²v 1 dv + dt2 RC dt LC This will get you a governing equation in the same form as that derived for the case we did in class where the R, L, and C were in series. e. Plot v(t) until the transient dies out. Circuit v = 0 b. What is the particular solution in this case, i.e., what is the value of v after a very long time after the voltage and current have reached steady state? of c. If R=15.8 Q2, is the system underdamped, critically damped, or overdamped? What is the equation that describes v(t)? resistances or d. Determine the final equation for v using the initial conditions v(0)=5V and i(0)=0. (Hint: use KCL and i(0)=0 to find at t=0). dt and 1H sources LC (a) d²v dt2 1 mF dv + 2α t dt V ELE +w/v = 0 RM 2(1) (b) Section 4.5 Second-Order Circuits i(1) FC 193
Transcribed Image Text:We wish to find v(1) for 1>0 in the RLC circuit shown below where the elements are in series. a. Derive the governing equation for the voltage v using KCL at the top node using the following definitions: a = w = == You should obtain (see attached for a similar 2RC derivation from the book) d²v 1 dv + dt2 RC dt LC This will get you a governing equation in the same form as that derived for the case we did in class where the R, L, and C were in series. e. Plot v(t) until the transient dies out. Circuit v = 0 b. What is the particular solution in this case, i.e., what is the value of v after a very long time after the voltage and current have reached steady state? of c. If R=15.8 Q2, is the system underdamped, critically damped, or overdamped? What is the equation that describes v(t)? resistances or d. Determine the final equation for v using the initial conditions v(0)=5V and i(0)=0. (Hint: use KCL and i(0)=0 to find at t=0). dt and 1H sources LC (a) d²v dt2 1 mF dv + 2α t dt V ELE +w/v = 0 RM 2(1) (b) Section 4.5 Second-Order Circuits i(1) FC 193
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