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(b) The voltage v(t) = 2t (v) for t>0 v(t) (+ 8Ω 2F (b) Circuit B i(t) (4) What is the current of the capacitor for t>0 for i(t = 0) = 0 (5) How much power is in the capacitor for t>0 (Draw the curve) (6) How much is the energy stored in the induct for Energy(t = 0) = 0 J

(b) The voltage v(t) = 2t (v) for t>0 v(t) (+ 8Ω 2F (b) Circuit B i(t) (4) What is the current of the capacitor for t>0 for i(t = 0) = 0 (5) How much power is in the capacitor for t>0 (Draw the curve) (6) How much is the energy stored in the induct for Energy(t = 0) = 0 J

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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The complete response is the sum of the natural response and the forced response X = Xn+Xf Natural response of a first-order circuit Natural response of a second-order circuit CASE Overdamped Critically damped Underdamped az S1 = FORCING FUNCTION K Kt K₁² K sin cot Ke at Forced response of a first-order, or a second-order circuit + A₁ NATURAL FREQUENCIES $1,52 = -α± √√² - 0² $1,$₂=-α S1, S2 = -x±j√√/0²-a² -α±jood dx dt d²x dt² Solution of the Second-Order Differential Equation d²x x(t) = xn(t) + xf (t) a2 dt² + a。x = f(t) + A1 dx dt "xn(t)" = Aest Xn(t) = Ke-t/t + a。x = 0 -a₁ + √²-4a₂a0 242 - Xn(t) = A₁e³₁ª + A₂e³₂t ASSUMED RESPONSE A At + B At² +Bt+C A sin cot + B cos cot Ae-at NATURAL RESPONSE, Xn Ale+Azer (A₁+A₂t)e-at (A, cos coat+A₂ sin coat)e xn(t) = ? (a₂s² + a₁s+ao) = 0 -α₁ - √²-4a₂a0 242 NATURAL RESPONSE, Xn A₁ est + A₂e21 -α1 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)ext
Transcribed Image Text:The complete response is the sum of the natural response and the forced response X = Xn+Xf Natural response of a first-order circuit Natural response of a second-order circuit CASE Overdamped Critically damped Underdamped az S1 = FORCING FUNCTION K Kt K₁² K sin cot Ke at Forced response of a first-order, or a second-order circuit + A₁ NATURAL FREQUENCIES $1,52 = -α± √√² - 0² $1,$₂=-α S1, S2 = -x±j√√/0²-a² -α±jood dx dt d²x dt² Solution of the Second-Order Differential Equation d²x x(t) = xn(t) + xf (t) a2 dt² + a。x = f(t) + A1 dx dt "xn(t)" = Aest Xn(t) = Ke-t/t + a。x = 0 -a₁ + √²-4a₂a0 242 - Xn(t) = A₁e³₁ª + A₂e³₂t ASSUMED RESPONSE A At + B At² +Bt+C A sin cot + B cos cot Ae-at NATURAL RESPONSE, Xn Ale+Azer (A₁+A₂t)e-at (A, cos coat+A₂ sin coat)e xn(t) = ? (a₂s² + a₁s+ao) = 0 -α₁ - √²-4a₂a0 242 NATURAL RESPONSE, Xn A₁ est + A₂e21 -α1 (A₁+A₂t)e (A₁ cos wat+A₂ sin wat)ext
(b) The voltage v(t) = 2t (v) for t>0 v(t) Vin M R₁ U₂0 (b) Circuit B U10-W R₁ ww 8Ω Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) www R₁ 그 Vout= (a) Inverting amplifier R₂ : Rn 2F -Ovout= R₁ R₁ R₁ - Vout - | i(t) Vin R₁ R₁ R₁ U1+R₂ U₂+...+ (un) R₁ R₁ (d) Summing amplifier (4) What is the current of the capacitor for t>0 ? for i(t = 0) = 0 (5) How much power is in the capacitor for t>0? (Draw the curve) (6) How much is the energy stored in the inductor for t>0? for Energy(t = 0) = 0 J Vin O- R₁. im R₁ ovout = (1 + R ₁) Vin (b) Noninverting amplifier R₂K₁ U10-W R₂JK2 U20-W R/K3 V30-W R₂/(1-(K₁ + K₂ + K3)) R(K4-1) Vin (c) Voltage follower (buffer amplifier) Rp Ovout Vin Ovout K4(K1v1 + K₂v2 + K303) (e) Noninverting summing amplifier
Transcribed Image Text:(b) The voltage v(t) = 2t (v) for t>0 v(t) Vin M R₁ U₂0 (b) Circuit B U10-W R₁ ww 8Ω Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) www R₁ 그 Vout= (a) Inverting amplifier R₂ : Rn 2F -Ovout= R₁ R₁ R₁ - Vout - | i(t) Vin R₁ R₁ R₁ U1+R₂ U₂+...+ (un) R₁ R₁ (d) Summing amplifier (4) What is the current of the capacitor for t>0 ? for i(t = 0) = 0 (5) How much power is in the capacitor for t>0? (Draw the curve) (6) How much is the energy stored in the inductor for t>0? for Energy(t = 0) = 0 J Vin O- R₁. im R₁ ovout = (1 + R ₁) Vin (b) Noninverting amplifier R₂K₁ U10-W R₂JK2 U20-W R/K3 V30-W R₂/(1-(K₁ + K₂ + K3)) R(K4-1) Vin (c) Voltage follower (buffer amplifier) Rp Ovout Vin Ovout K4(K1v1 + K₂v2 + K303) (e) Noninverting summing amplifier
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