Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter 9, Problem 29E
(a)
To determine
Derive an expression for
(b)
To determine
Derive an expression for
(c)
To determine
If the damping ratio is increased, does the circuit become more or less under-damped? Explain.
(d)
To determine
Compute
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Q: For the following system
Ris)
Cis)
K
s (s+4) (s+6)
1- Draw the Root Locus.
2- Find the values of dominant roots at damping ratio (C = 0.5).
3- Find the value of K at damping ratio (C = 0.5).
4- Find the value of the third root at damping ratio (C = 0.5).
If 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 corrent
Consider the following circuit. In the circuit, A=3, R1= 4N, R2= 4N,and a
=5
R2
2F
R1
aic(t)
A - Au(t) (1
velt)
-tic(t)
a) Determine the capacitor voltage at t=0
K
and
b) The expression for V(s) is-
s+p
Determine K
c) Determine the value of v.(t) at t=2 s
d) What is the value of the time constant of the circuit for t>0?
+
Chapter 9 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 9.1 - A parallel RLC circuit contains a 100 2 resistor...Ch. 9.2 - After being open for a long time, the switch in...Ch. 9.2 - Prob. 3PCh. 9.2 - Prob. 4PCh. 9.3 - (a) Choose R1 in the circuit of Fig. 9.14 so that...Ch. 9.4 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.6 - Let is = 10u(t) 20u(t) A in Fig. 9.31. Find (a)...Ch. 9.6 - Let vs = 10 + 20u(t) V in the circuit of Fig....
Ch. 9.7 - Alter the capacitor value and voltage source in...Ch. 9 - For a certain source-free parallel RLC circuit, R...Ch. 9 - Element values of 10 mF and 2 nH are employed in...Ch. 9 - If a parallel RLC circuit is constructed from...Ch. 9 - Prob. 4ECh. 9 - You go to construct the circuit in Exercise 1,...Ch. 9 - A parallel RLC circuit has inductance 2 mH and...Ch. 9 - Prob. 7ECh. 9 - A parallel RLC circuit has R = 1 k, L = 50 mH. and...Ch. 9 - Prob. 9ECh. 9 - Prob. 10ECh. 9 - The current flowing through a 5 resistor in a...Ch. 9 - For the circuit of Fig.9.40, obtain an expression...Ch. 9 - Consider the circuit depicted in Fig. 9.40. (a)...Ch. 9 - With regard to the circuit represented in Fig....Ch. 9 - (a) Assuming the passive sign convention, obtain...Ch. 9 - With regard to the circuit presented in Fig. 9.42,...Ch. 9 - Obtain expressions for the current i(t) and...Ch. 9 - FIGURE 9.43 Replace the 14 resistor in the...Ch. 9 - Design a complete source-free parallel RLC circuit...Ch. 9 - For the circuit represented by Fig. 9.44, the two...Ch. 9 - Prob. 21ECh. 9 - Prob. 22ECh. 9 - A critically damped parallel RLC circuit is...Ch. 9 - A source-free parallel RLC circuit has an initial...Ch. 9 - A critically damped parallel RLC circuit is...Ch. 9 - For the circuit of Fig. 9.45, is(t) = 30u(t) mA....Ch. 9 - Prob. 27ECh. 9 - The circuit of Fig. 9.44 is rebuilt such that the...Ch. 9 - Prob. 29ECh. 9 - Prob. 30ECh. 9 - The source-free circuit depicted in Fig. 9.1 is...Ch. 9 - (a) Graph the current i for the circuit described...Ch. 9 - Analyze the circuit described in Exercise 31 to...Ch. 9 - A source-free parallel RLC circuit has capacitance...Ch. 9 - Prob. 35ECh. 9 - Obtain an expression for vL(t), t 0, for the...Ch. 9 - For the circuit of Fig. 9.47, determine (a) the...Ch. 9 - (a) Design a parallel RLC circuit that provides a...Ch. 9 - The circuit depicted in Fig. 9.48 is just barely...Ch. 9 - When constructing the circuit of Fig. 9.48, you...Ch. 9 - The circuit of Fig. 9.22a is constructed with a...Ch. 9 - Prob. 42ECh. 9 - Prob. 43ECh. 9 - The simple three-element series RLC circuit of...Ch. 9 - Prob. 45ECh. 9 - Prob. 46ECh. 9 - Prob. 47ECh. 9 - With reference to the series RLC circuit of Fig....Ch. 9 - Obtain an expression for i1 as labeled in Fig....Ch. 9 - The circuit in Fig. 9.52 has the switch in...Ch. 9 - For the circuit in Fig. 9.52, determine the value...Ch. 9 - In the series circuit of Fig. 9.53, set R = 1 ....Ch. 9 - Evaluate the derivative of each current and...Ch. 9 - Consider the circuit depicted in Fig. 9.55. If...Ch. 9 - Prob. 55ECh. 9 - In the circuit shown in Fig. 9.56, (a) obtain an...Ch. 9 - Prob. 57ECh. 9 - For the circuit represented in Fig. 9.57, (a)...Ch. 9 - FIGURE 9.57 Replace the 1 resistor in Fig. 9.57...Ch. 9 - A circuit has an inductive load of 2 H, a...Ch. 9 - (a) Adjust the value of the 3 resistor in the...Ch. 9 - Determine expressions for vC(t) and iL(t) in Fig....Ch. 9 - The capacitor in the LC circuit in Fig. 9.60 has...Ch. 9 - Suppose that the switch in the circuit in Fig....Ch. 9 - The capacitor in the circuit of Fig. 9.63 is set...Ch. 9 - The physical behavior of automotive suspension...Ch. 9 - A lossless LC circuit can be used to provide...
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- For the RLC circuit shown below, we wish to find v(t) for t>0. a. Derive the governing equation for the voltage v using KCL at the top node using the following definitions: a w3 = You should obtain 2RC LC a?v + dt2 1 dv +v = 0 d?v + 2a + wzv = 0 or RC dt LC dt2 dt c. If R=50 2, is the system underdamped, critically damped, or overdamped? What is the equation that describes v(t)? 1H 1 mF + AIarrow_forward4. In the circuit below, find the nonnegative value of R for critical damping. R vs(t) L=12 H C = 3 F +21arrow_forwardIf 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_forward
- 4. For the system in figure (a) as shown R(s) + K (s + 1)(s + 2)(s + 3)(s + 4) (a) R(s) + K(s + a) Cls) (s + 1)(s + 2)(s + 3)(x + 4) (b) sketch the root locus and do the following. a. Find the asymptotes. b. Find the breakaway points. c. Find the range of K for stability. d. Find the value of K to yield a 0.7 damping ratio for the dominant second-order pair. e. To improve stability, we desire the root locus to cross the jw-axis at j5.5. To accomplish this, the open-loop transfer funcion is cascaded with a zero, as shown in figure (b). Find the value of a and sketch the new root locus. f. Repeat part (c) for the new root locus. g. Compare the results of part (c) and part (f). What improvement in transient response do you notice?arrow_forwardQ. A closed loop system is shown in following figure! K s(s + 6) -C(s) R(s)- 0.2 The system is to have a damping ratio of 0.7. Determine the value of Kto satisfy this condition.arrow_forward• Determine the un-damped natural frequency and damping ratio of the following second order system. C(s) 4. R(s) 5 + 2s + 4arrow_forward
- 7) What is the damping ratio of the closed loop system shown in the figure? a) 0 R(s) b) 1 5 (s+1)(s+3) C(s)arrow_forwardExample: Find v(t) and iL(t) in the parallel RLC circuit shown in Figure below if the circuit parameters are R = 2 N, C = 1/5 F, and L = 5 H. Let us assume that the initial conditions on the storage elements are iz(0) = -1 A and vɖ0) = 4 V. v(1)arrow_forward6- The series RLC circuit in figure Q1 is underdamped if: R 1 a) = a b) > c) ?< y(t) CL u(t)arrow_forward
- 4. A series RLC circuit has the following component values: R = 20 N, L = 4 H, C = 8 mF, E(t) = 1157 sin t V a. Determine the type of damping b. Determine the steady-state current in the circuitarrow_forwardHomeworkl: A second-order series RLC circuit, shown in Figure below, has some damping due to the resistor. Determine: 1. The key parameters for this circuit in terms of R, L, and C. 2. The time response and the error signal for this system if it is called undamped system. i R Vi Vo 7 Scanned with CamScanner Computer Technology Eng. Dept. Control Enginecering Fundamentals Third Class Answer: c(t) = (1- coswnt) u(t) e(t): = coswnt u(t) Homework?arrow_forwardIf R = 50 N, L = 1.5 H, what value of C will make an RLC series circuit: (a) overdamped, (b) critically damped, (c) underdamped?arrow_forward
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