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• Problem 3. (a) The Circuit A shown is at the steady state, before the switch opens at time t = 0. 8Ω ww vs (t) + t = 0 692 (a) Circuit A 4H 1292 Ji(t) (1) Derive the first order differential equation of i(t) over t for t≥ 0. (2) Determine i(t) for t≥ 0. vs (t) = vs(t) = 8 (v) vs(t = 0) = 8 Vs(t) = 8e-2t for t < 0. (v) at t = 0. +8 (v) for t≥ 0.

• Problem 3. (a) The Circuit A shown is at the steady state, before the switch opens at time t = 0. 8Ω ww vs (t) + t = 0 692 (a) Circuit A 4H 1292 Ji(t) (1) Derive the first order differential equation of i(t) over t for t≥ 0. (2) Determine i(t) for t≥ 0. vs (t) = vs(t) = 8 (v) vs(t = 0) = 8 Vs(t) = 8e-2t for t < 0. (v) at t = 0. +8 (v) for t≥ 0.

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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• Problem 3. (a) The Circuit A shown is at the steady state, before the switch opens at time t = 0. vs(t) t = 0 ■ Vin 8Ω m www R₁ (a) Circuit A ww R₁ 51 692 U10-M R₁ (a) Inverting amplifier U₂0-M Un m R₁ Vout= Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) ww R₁ R₁ R₁ 4H 1 { ↓i(t) Ovout=1 120 R₁ R₁ - Vout R₁ Vin (d) Summing amplifier (1) Derive the first order differential equation of i(t) over t for t≥ 0. Vin O (2) Determine vs(t) = R₁. R₁ ww vs(t) = 8 (v) vs(t = 0) = 8 · vs(t) = 8e-²t + 8 (v) U20 Vout vin = (1 + R ₁) ³₁ (b) Noninverting amplifier 010-M R₂K1 i(t) for t≥ 0. R₂K₂ R/K3 U30M R₂/(1-(K₁ + K₂ + K3)) fort < 0. (v) at t = 0. R(K-1) Rp2 Vin 올 (c) Voltage follower (buffer amplifier) for t≥ 0. -Ovout Vin (e) Noninverting summing amplifier Ovout K4(K₁v1 + K₂v2 + K303)
Transcribed Image Text:• Problem 3. (a) The Circuit A shown is at the steady state, before the switch opens at time t = 0. vs(t) t = 0 ■ Vin 8Ω m www R₁ (a) Circuit A ww R₁ 51 692 U10-M R₁ (a) Inverting amplifier U₂0-M Un m R₁ Vout= Brief catalog of the Operational Amplifier circuits (Based on the ideal operational amplifier) ww R₁ R₁ R₁ 4H 1 { ↓i(t) Ovout=1 120 R₁ R₁ - Vout R₁ Vin (d) Summing amplifier (1) Derive the first order differential equation of i(t) over t for t≥ 0. Vin O (2) Determine vs(t) = R₁. R₁ ww vs(t) = 8 (v) vs(t = 0) = 8 · vs(t) = 8e-²t + 8 (v) U20 Vout vin = (1 + R ₁) ³₁ (b) Noninverting amplifier 010-M R₂K1 i(t) for t≥ 0. R₂K₂ R/K3 U30M R₂/(1-(K₁ + K₂ + K3)) fort < 0. (v) at t = 0. R(K-1) Rp2 Vin 올 (c) Voltage follower (buffer amplifier) for t≥ 0. -Ovout Vin (e) Noninverting summing amplifier Ovout K4(K₁v1 + K₂v2 + K303)
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
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