A source free RLC circuit is shown in the Figure 4:+V (t);3mH1.801.333 mFFigure 4(a) Determine the damping condition of this circuit.(b) Derive the expression of the current i(t) equation for t> 0 s. The initial condition,i(0) = 0.5 A and v(0) = 10 VHint: i(t) = e-at(A cos wat + B sin wat) and v(t) = Ldidt

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Answered: A source free RLC circuit is 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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In the circuit below, find the nonnegative value of R for critical damping. R + + v,(t)t L = 12 H C = 3 F
The capacitor in the circuit below is initially uncharged and the switch SW is closed at time dv(t) t=0. We derived the governing equation in class using KCL (iR-ic) to be Vç − v(t) = RC Derive the same equation using KVL. dt v(t) Vs SW ww R C
1. The initial voltage across the capacitor (t = 0 ^ +). 2. An expression that determines the voltage V_c as a function of time. 3. An expression that determines the voltage V_R as a function of time. 4. An expression for the current flowing through the 7 Ω resistor as a function of time. 5. The current flowing through the 7Ω resistor immediately after the switch changes position and at steady state.
Exercise 3) In the LRC circuit below, at time t = 0 the current in the inductor is io = 0.354 A. A voltage is applied to the circuit at time t = ti sec and held constant until t = t2 sec before it is turned off, as shown on the right. Consider R = 1 N, L = 2 H and C = 0.5 F. R L v(t)A 1 v(t) C ti t2 t We wish to determine the current through the circuit i(t) considering the applied voltage v(t) and the initial current in the inductor io using the Laplace transform. Follow the steps below. (a) Write the differential equation relating i(t) and v(t). At this time the values of t1 and t2 do not need to be specified. (b) Take the Laplace transform of (a) considering the initial current in the inductor. (c) Solve for the current using the inverse Laplace transform.
The circuit below is the problem we did in class for R=300 Q (overdamped) and 200 2 (critically damped). Compute a, @, and for R=100 2 (the underdamped case) and determine v.(t). You should obtain v.(t) = 10 – 10e-at cos(@nt) – 5.77e-at sin(@nt) ell SW1 L1 10 mH R + 10V C1 1 µF
In the figure below, the switch in the circuit has been closed for a long time. At t= 0, it opens. iL 2H t = 0 160 60 – Va + 20mF Ve 5V a) Redraw the circuit where Va is 15 V b) Find the following values: vc(0+ ), ic(0+ ), iL(0+ ), vL(0+ ), v.(∞), iL(∞) c) Indicate whether this circuit is overdamped or underdamped. Explain how you determined that. d) Find a new value for the capacitor that will make the system critically damped.
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Q6) a)Match the signals below with the candidate sketches below (i.e., you are supposed to choose which graph below corresponds to the signal below). Note: u(t) is the unit step function; i.e., u(t) = 1 for t>=0s and u(t) = 0 for t<0s. X₁(t) = u(t+1)-u(t-3) X₂(t) = u(t-3)-u(t-4) X3(t) = u(t+1)-u(t-1) d(t) = x₁(-t) e(t) = 2 x₁(t-1.5) f(t) = x₁(2t + 1.5) g(t) = x4(2t) h(t) = x3(t/2) i(t) = 2 x3(t) j(t) = -0.5 x₂(t) k(t) = x₁(1.5 t + 2.5) y(t) = 2 x₁(-t/2+1.5) 432 1 0 -1 4321OT 0 -1 -6-4-20 2 4 6 (1) 4321OT 0 -1 -6-4-20 246 (5) n -6-4-20 2 4 6 (9) 43210 3 -1 4321OT -1 43210 -6-4-20246 (2) -1 -6-4-20246 (6) 2 -6-4-20246 (10) 4321OT 0 4321OT -6-4-2 0 2 4 6 (3) -6-4-2 0 2 4 6 (7) 4321O -6-4-20246 (11) 4321OT 0 -1 -6-4-20 2 4 6 (4) 4321OT -6-4-20 2 4 6 (8) 43210 3 2 0 -6-4-20 246 (12)
NOTE: Solve this as soon as possible, I need this urgently. For the circuit given below, L=5 H, C=20 mF, and R=5 Ohms, show that it is underdamped , overdamped or critially damped circuit t=0 R L3 C=
4. Consider the following RLC circuit, where L = 1H, R = 50, C = 250mF. Vgen = 10t-10. There is initial charge on the capacitor as q(0) = 2.5 Coulumb. The switch has been open for a long time and closes at t = 0. a) Write the differential equation describing the current in the circuit for t> 0. b) What are the initial values for current, i.e., [(0) and i'(0)? c) Write the characteristic equation and identify the type of the circuit (overdamped. underdamped, or critically damped). O
For the circuit shown, V1 is a 5 Volt step function at t=0. Find the voltage across the capacitor, Vc(t) and the current in the circuit, i(t), for t>0 a) If R1 = 400 0. b) If R1 = 200 Q. c) If R1 = 100 0. R1 L1 V1 C1 10 mH Os 1 pF
In the circuit, the resistor is adjusted for critical damping. The initial capacitorvoltage is 15V , and the initial inductor current is 6 mAa) Find the numerical value for Rb) Find the numerical values of i and di ⁄ dt immediately after the switch is closedc) Find vc(t) for t bigger than or equal to 0

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