Table 1: Laplace Transform PropertiesLinearity L {af(t)} = aF(s)SuperpositionModulation L {e-at f(t)} = F(s + a)Time-Shifting L{f(t-7)u(t-7)} = e-TF(s)Scaling L{f(at)} = F(2)| L { $(10)} = 8= 8F(s)-f(0)L{f(t)} = F(s)L {fi(t) + f₂(t)} = F₁(s) + F₂(s)Real Differentiation LReal IntegrationComplex DifferentiationL {tf(t)}-F(s)dsComplex Integration {f} = f* F(®)LConvolution L {f(t) *g(t)} = F(s). G(s)Table 2: Common Laplace Transform Pairsf(t)F(s)8(t)u(t)tu(t)e-atu(t)te-atu(t)cos(wt)u(t)sin(wt)u(t)11s+a1(s + a)²88² +w²8² +w² (c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function,i. Calculate the time constant T.ii.111.Calculate vc (t) at t = ∞.Obtain an expression for vc (t) valid for all values of t.4u(t) V+3 ΚΩMwww1 ΚΩ .Figure Q2-24 μF+VC

We need to find out the voltage across capacitor for given circuit.

Answered: (c) Consider the circuit shown in…

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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Ri 20HF R2 Vc 0.5mH R3 12V 30.4mH 10µF 25V Assume the above circuit has been in this state for a very long time. Determine the current through the 0.4mH inductor i, given R1 =70 R2=72 R3=52 Note: Round your answer to the nearest single digit decimal place. Your answer should be in Amps. For example, if you compute 15.43 Amps then enter 15. Find i a Type here to search Cbp
For the circuit in Figure 3 the switch is in the left position for several minutes: (a) Find the Initlal voltage, o on the capacitor just before the switch is flipped (b) Find an expression v(t) that describes the voltage across the 20 N resistor after the switch has been Figure 3 1Ω 60 N flipped to the right NOTE: Remember what we said in class: use a Circuit-Specific Equation to get a value you know. Then solve for whatever else the problem asks for O 12 V 5 2 -50 μF 80 Ω 20Ω
Plot i(t) and v(t) versus t.
Given the following values V1 = 12V , V2 = 5V , R1 = 10Ω, R2 = 5Ω, R3 = 10Ω, C1 = 2C2 = 4µF and C3 = 6µF. 1. Calculate the equivalent capacitor Ca in (a). 2. What is the value of the voltage va before the switch is closed? 3. Find an expression of the current iC3(t) for all t. Draw your simplified circuits whenever it is necessary to explain your working steps
E R₁ t = 0 + VI R₂ Figure 1: An RC circuit. C HH Consider the circuit shown in Figure 1, where E = 3V R₁ = 20 R₂ R3 R4 = = R3 ww 6Ω 8Ω 40 fl 4A/V = = u Vi + R4 The circuit has been in steady-state before the switch has been switched at t = 0. Determine the current i4(t) for t > 0+. Show how you can validate your results. Hint. Determine first the voltage accross the capacitor for t> 0+ and use it to derive the current for i4(t) for t > 0+.
Q.2 (a) A system as presented in Figure Q2(a) has four input signals, which are m(t), n(t),p(t) and q(t). The inputs are m(t) = 2 sin(2t), n(t) = 3-4 sin(5t - π), p(t) = 6 cos (7t + r) and q (t) = 4 cos(7t + π). n(t) m(t)+ p(t)+ + q(t) Figure Q2(a) r(t) (i) Represent r(t) using Fourier series in the combined Trigonometric form. (ii) Illustrate the single-sided frequency spectrum (magnitude and phase) of r(t).
Below is a circuit diagram. Each of the L; are different inductors(each having and induction of 1 henry), while the R1 is a resistor( with a resistance of 4 ohms). We will make the following assumption: the input voltage V(t) = 0 when t > 0. Below is the circuit diagram: ell L2 1H Loop 2 R1 Loop 1 L2 1H ell L3 1H 2 Calculations For the circuit above, find the following: Set up the system of differential equations. • Find the general solution for a given time t. • Find the exact solution if you are given that Io = L ell
In the circuit below, given R1 = R2 = 18 ohms, R3 = 10 ohms, and L = 1.7 H. Determine the current at i(0.05) given that us(t) is the step function described in diagram below. You will first need to determine i(t) and then determine the current at the specific point in time given to you. Enter your answer to 2 decimal places in Amps. R₁ D (1) Vg(1) 0 R₂ R3 ele
The circuit contains two capacitors in series and two resistors in parallel with each other connected to an ideal source with e = 50V. Initially, the capacitors are empty, then at t = 0 the switch is closed. Given R1 = 7.02, R2 = 82, C = 6.0F, and C2 = 8F а. what is the voltage, as a function of time, across C1 and C2? b. What is the current, as a function of time, through R1 and R2? Ce R2
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V1 + I S1 M R1 C1 S2 Figure 4: A circuit with multiple switches L1 R2 Given the circuit in figure 4 with component values R₁ = 10 k2, R₂ = 20 k2, C₁ = 1µF, L₁ = 2 mH, and V₁ = 5 V. All switches are closed, and the circuit has reached steady state (t <0 seconds). At time t = 0 seconds switch S₂ is opened and at time t = 5 seconds switch S₁ is opened. Hint: Take your time to consider carefully what the state is of the circuit for each switch. a) Calculate the voltage over the capacitor for all time b) Calculate the current over the inductor for all time.

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(c) Consider the circuit shown in Figure Q2-2, where u(t) is the unit-step function, i. Calculate the time constant T. ii. 111. Calculate vc (t) at t = ∞. Obtain an expression for vc (t) valid for all values of t. 4u(t) V + 3 ΚΩ M www 1 ΚΩ . Figure Q2-2 4 μF + VC