Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Chapter 16, Problem 3P
To determine
Find the expression of voltage
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Given the following circuit below, at t=0 the switch closes:
+ Vs
R₁
m
Vs = 9V R₁
Ry = 10kΩ
Xt=0
R2
i(t)
R₂ = 5kN
C
C = 200μF
(a) Use the differential equation method to determine the output current
Q2:
Using any convolution method, find the equation for the convolution and sketch it over time. Make sure to
clearly label 5t if appropriate.
g(t) = u(t) = u(t − 1)
-
h(t) = 2 × (u(t) — u(t – 12)
-
Answer the given question with a proper explanation and step-by-step solution.
a)Determine and sketch the convolution of following two signalsx(t) = 1-t for -1 < t < 1elsewhere 0h(t) = dell(t+1) + 2 dell (t + 2)
Chapter 16 Solutions
Fundamentals of Electric Circuits
Ch. 16.2 - Determine vo(t) in the circuit of Fig. 16.6,...Ch. 16.2 - Prob. 2PPCh. 16.2 - Prob. 3PPCh. 16.3 - For the circuit shown in Fig. 16.12 with the same...Ch. 16.3 - Prob. 5PPCh. 16.3 - The initial energy in the circuit of Fig. 16.17 is...Ch. 16.4 - Prob. 7PPCh. 16.4 - Prob. 8PPCh. 16.4 - Prob. 9PPCh. 16.5 - Obtain the state variable model for the circuit...
Ch. 16.5 - Prob. 11PPCh. 16.5 - Prob. 12PPCh. 16.6 - For what value of is the circuit in Fig. 16.29...Ch. 16.6 - Prob. 14PPCh. 16.6 - Prob. 15PPCh. 16.6 - Synthesize the function Vo(s)Vin=2ss2+6s+10 using...Ch. 16 - Prob. 1RQCh. 16 - The current through an RL series circuit with...Ch. 16 - Prob. 3RQCh. 16 - Prob. 4RQCh. 16 - Prob. 5RQCh. 16 - Prob. 6RQCh. 16 - Prob. 7RQCh. 16 - Prob. 8RQCh. 16 - Prob. 9RQCh. 16 - Prob. 10RQCh. 16 - The current in an RLC circuit is described by...Ch. 16 - The differential equation that describes the...Ch. 16 - Prob. 3PCh. 16 - If R = 20 , L = 0.6 H, what value of C will make...Ch. 16 - The responses of a series RLC circuit are vc(t) =...Ch. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - The step responses of a series RLC circuit are Vc...Ch. 16 - The step response of a parallel RLC circuit is v =...Ch. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - For the circuit in Fig. 16.38. calculate the value...Ch. 16 - The capacitor in the circuit of Fig. 16.39 is...Ch. 16 - If is(t) = 7.5e2t u(t) A in the circuit shown in...Ch. 16 - Find v(t), t 0 in the circuit of Fig. 16.41. Let...Ch. 16 - The switch in Fig. 16.42 moves from position A to...Ch. 16 - Find i(t) for t 0 in the circuit of Fig. 16.43.Ch. 16 - In the circuit of Fig. 16.44, the switch moves...Ch. 16 - Find the voltage across the capacitor as a...Ch. 16 - Obtain v (t) for t 0 in the circuit of Fig....Ch. 16 - The switch in the circuit of Fig. 16.47 has been...Ch. 16 - Calculate v(t) for t 0 in the circuit of Fig....Ch. 16 - Prob. 26PCh. 16 - Find v (t) for t 0 in the circuit in Fig. 16.50.Ch. 16 - For the circuit in Fig. 16.51, find v(t) for t 0.Ch. 16 - Prob. 29PCh. 16 - Find vo(t), for all t 0, in the circuit of Fig....Ch. 16 - Prob. 31PCh. 16 - For the network in Fig. 16.55, solve for i(t) for...Ch. 16 - Using Fig. 16.56, design a problem to help other...Ch. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - The switch in the circuit of Fig. 16.61 is moved...Ch. 16 - Prob. 39PCh. 16 - Prob. 40PCh. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Prob. 43PCh. 16 - Prob. 44PCh. 16 - Find v(t) for t 0 in the circuit in Fig. 16.68.Ch. 16 - Prob. 46PCh. 16 - Determine io(t) in the network shown in Fig....Ch. 16 - Prob. 48PCh. 16 - Find i0(t) for t 0 in the circuit in Fig. 16.72....Ch. 16 - Prob. 50PCh. 16 - In the circuit of Fig. 16.74, find i(t) for t 0.Ch. 16 - Prob. 52PCh. 16 - In the circuit of Fig. 16.76, the switch has been...Ch. 16 - Prob. 54PCh. 16 - Prob. 55PCh. 16 - Calculate io(t) for t 0 in the network of Fig....Ch. 16 - Prob. 57PCh. 16 - Prob. 58PCh. 16 - Find vo(t) in the circuit of Fig. 16.82 if vx(0) =...Ch. 16 - Prob. 60PCh. 16 - Prob. 61PCh. 16 - Using Fig. 16.85, design a problem to help other...Ch. 16 - Consider the parallel RLC circuit of Fig. 16.86....Ch. 16 - The switch in Fig. 16.87 moves from position 1 to...Ch. 16 - For the RLC circuit shown in Fig. 16.88, find the...Ch. 16 - For the op amp circuit in Fig. 16.89, find v0(t)...Ch. 16 - Given the op amp circuit in Fig. 16.90, if v1(0+)...Ch. 16 - Prob. 68PCh. 16 - Prob. 69PCh. 16 - Using Fig. 16.93, design a problem to help other...Ch. 16 - Prob. 71PCh. 16 - The transfer function of a system is H(s)=s23s+1...Ch. 16 - Prob. 73PCh. 16 - Design a problem to help other students better...Ch. 16 - Prob. 75PCh. 16 - For the circuit in Fig. 16.95, find H(s) =...Ch. 16 - Obtain the transfer function H(s) = VoVs for the...Ch. 16 - Prob. 78PCh. 16 - For the circuit in Fig. 16.97, find: (a) I1/Vs (b)...Ch. 16 - Refer to the network in Fig. 16.98. Find the...Ch. 16 - Prob. 81PCh. 16 - Prob. 82PCh. 16 - Refer to the RL circuit in Fig. 16.101. Find: (a)...Ch. 16 - A parallel RL circuit has R = 4 and L = 1 H. The...Ch. 16 - Prob. 85PCh. 16 - Prob. 86PCh. 16 - Prob. 87PCh. 16 - Prob. 88PCh. 16 - Develop the state equations for the circuit shown...Ch. 16 - Prob. 90PCh. 16 - Prob. 91PCh. 16 - Prob. 92PCh. 16 - Prob. 93PCh. 16 - Prob. 94PCh. 16 - Prob. 95PCh. 16 - Prob. 96PCh. 16 - A system is formed by cascading two systems as...Ch. 16 - Determine whether the op amp circuit in Fig....Ch. 16 - It is desired realize the transfer function...Ch. 16 - Prob. 100PCh. 16 - Prob. 101PCh. 16 - Synthesize the transfer function...Ch. 16 - Prob. 103CPCh. 16 - Prob. 104CPCh. 16 - Prob. 105CP
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- The particular integral of the differential equation (D+7)(D – 7)y = sec²x – tan²x is. 1 7 -1 49 1 49 –1 14arrow_forwardThe circuit below is at steady state before the switch closes att = 0. Find the voltage across the capacitor v(t) at t > 0. 50 mF sw2arrow_forwardCompute the convolution between signal F(t) and G(t) by shifting F(t), i.e., use the following equation to compute your convolution F(t) * G(t) = | F(t – t)G(t) dr - 00 F(T) = U(T-155)-U(t+155) G() 100+ 50 -100 100 Recommended steps to follow while solving 1. Draw the signal F(t) by properly labelling the axis 2. Draw the signal G(t) by properly labelling the axis 3. Draw the signal F(t – t) by properly labelling the axis and mentioning the condition of t 4. Draw the signal G(t) by properly labelling the axis 5. Compute the convolution now by properly defining ranges of t for which two signals do not overlap, partially overlap or full overlap.arrow_forward
- If the input to the RLC circuit shown on the right is v₂ (t) = u(t). a. Find the output voltage transform across each element. b. Compare the three outputs with regard to Vs(s) their respective poles and zeros. c. Use the initial- and final-value theorems to determine the value of the voltage across each element at t = 0 and t = ∞. What conclusions can one draw regarding the results? RVR(S) + Ls VL(S) 1/Cs HH + Vc(s) VLC(S)arrow_forward1. For the series RLC circuit shown below, find the input/output differential + x(t) t=0 - i(t) R C ww the +VR(t)- +vc(t)- V₁.(t) L equation forarrow_forwardQ4 The response x(t) of a system to a forcing funetion u(t) is determined by the differential equation d'x + 2dx + 5x = 3 du 2u dr dr drarrow_forward
- Calculate the convolution for the continuous time signal h (t) shown in the figure below.and draw. (*:convolution) h(t) * h(t) * h(t)arrow_forwardQuestion regarding a signals and systems course, u(t) is the unit-step function, and r(t) is the ramp function. Imagine x(t)= r(t-1)-r(t-2)+u(t-3)-u(t-4)-r(t-5)+r(t-6): a) Draw x(t) b) Draw 2x(t+2) c) Draw x(t+2) + x(t+3)arrow_forward1) For the continuous-time signal x(t) indicated in Figure 1, sketch and label the following signals, also verify your results using MATLAB. (a) x(-t) (b) x(t + 2) (c) x(2t + 2) (d) x(1 – 3t) x(t) 1arrow_forward
- 4- The input to the circuit shown below is the voltage of the voltage source. The output is the inductor current. Represent the circuit by a second-order differential equation that shows how the output of this circuit is related to the input for t > 0. t = 0 Us R₁ www R2 ↓i(t) + v (t)arrow_forwardIf F(s) = (260/(S- + 60S+ 3604)) and it is known that inductor had no current at t = 0, which of the following most accurately describes F(s): O A. It could be the natural and step response of a series RLC circuit or the step response of a parallel RLC circuit O B. It could be the natural response of a parallel RLC circuit O C. It could be the natural or step response of both the parallel and series RLC circuits O D. It could be the natural response or the step response of a parallel RLC circuit O E. None of the choices are correntarrow_forwardR =73 Find the complete response v0(t) and i0(t) of the circuit shown below.arrow_forward
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