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Extra problem 1: For the RC circuit shown in Figure 8.15 of Bolton's textbook (page 197), write the first- order differential equation with a numerical value for the time-constant t = RC for the parameter values F = 22 k2 and C= 4.7 uF. main

Extra problem 1: For the RC circuit shown in Figure 8.15 of Bolton's textbook (page 197), write the first- order differential equation with a numerical value for the time-constant t = RC for the parameter values F = 22 k2 and C= 4.7 uF. main

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 T from Bateso Chapter 8, Problems: 4, 6 (page 207) Chapter 10, Problems: 11, 13 (page 254) Extra problem 1: For the RC circuit shown in Figure 8.15 of Bolton's textbook (page 197), write the first- order differential equation with a numerical value for the time-constant T = RC for the parameter values R = 22 k2 and C= 4.7 µF. 5 Extra problem 2: Determine the frequency-domain function F(s) for each of the following time-domain functions f(t) using Laplace Transforms. a. f(t)=7.8 b. f(t)=3.2 cos 1000t c. f(t)= 120 sin 25t d. f(t)= 18t e. f(t)=16e& 1. O Search T f(t)=85 A d²x +5= 6 di² dt dx(0) Y dx & 4- 7 * 8 U T ( O f10 O 2 O P A S prt so
Transcribed Image Text:1 T from Bateso Chapter 8, Problems: 4, 6 (page 207) Chapter 10, Problems: 11, 13 (page 254) Extra problem 1: For the RC circuit shown in Figure 8.15 of Bolton's textbook (page 197), write the first- order differential equation with a numerical value for the time-constant T = RC for the parameter values R = 22 k2 and C= 4.7 µF. 5 Extra problem 2: Determine the frequency-domain function F(s) for each of the following time-domain functions f(t) using Laplace Transforms. a. f(t)=7.8 b. f(t)=3.2 cos 1000t c. f(t)= 120 sin 25t d. f(t)= 18t e. f(t)=16e& 1. O Search T f(t)=85 A d²x +5= 6 di² dt dx(0) Y dx & 4- 7 * 8 U T ( O f10 O 2 O P A S prt so
▬▬ 8.3 DYNAMIC SYSTEMS EXAMPLE Develop a model for the electrical system described by the circuit shown in Figure 8.15. The input is the voltage v when the switch is closed and the output is the voltage vc across the capacitor. Using Kirchhoff's voltage law gives and, since VR = Ri and i=C(dvc/dt) we obtain the equation: V=UR + VC and so v=RC FIGURE 8.15 Electrical system with resistance and capacitance. The relationship between an input v and the output vc is a first-order differential equation. The term first order is used because it includes as its highest derivative dv/dt. O Search duc dt VR + oc R EXAMPLE Develop a model for the circuit shown in Figure 8.16 when we have an input voltage v when the switch is closed and take an output as the voltage vc across the capacitor. Applying Kirchhoff's voltage law gives TVC V = VR + V₁ + VC di v-Ri+Ldt Since i = C(dvc/dt), then di/dt = C(d²vc/df) and thus we can write ducd²uc + UC 197 D 1668
Transcribed Image Text:▬▬ 8.3 DYNAMIC SYSTEMS EXAMPLE Develop a model for the electrical system described by the circuit shown in Figure 8.15. The input is the voltage v when the switch is closed and the output is the voltage vc across the capacitor. Using Kirchhoff's voltage law gives and, since VR = Ri and i=C(dvc/dt) we obtain the equation: V=UR + VC and so v=RC FIGURE 8.15 Electrical system with resistance and capacitance. The relationship between an input v and the output vc is a first-order differential equation. The term first order is used because it includes as its highest derivative dv/dt. O Search duc dt VR + oc R EXAMPLE Develop a model for the circuit shown in Figure 8.16 when we have an input voltage v when the switch is closed and take an output as the voltage vc across the capacitor. Applying Kirchhoff's voltage law gives TVC V = VR + V₁ + VC di v-Ri+Ldt Since i = C(dvc/dt), then di/dt = C(d²vc/df) and thus we can write ducd²uc + UC 197 D 1668
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