Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Textbook Question
Chapter 9, Problem 19E
Design a complete source-free parallel RLC circuit which exhibits an over-damped response, has a settling time of 1 s, and has a damping ratio of 15.
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The RLC network below:a) Provide the second order differential equation describing this circuit b) Compute the undamped natural frequency of the circuit and the damping ratio.c) What type of response does i(t) exhibit for t > 0 ? Explain why.
*The resistance, inductance, and capacitance in a parallel RLC circuit are 1900 Ω , 250 mH , and 9 nF , respectively. *
Pt A. Calculate the minimum root of the characteristic equation that describes the voltage response of the circuit.
Pt B. Calculate the maximum root of the characteristic equation that describes the voltage response of the circuit.
Pt C.Will the response be over-, under-, or critically damped?
Pt D. What value of R will yield a damped frequency of 12 krad/s?
Pt E. What are the roots of the characteristic equation for the value of R found in Part D?
Pt F. What value of R will result in a critically damped response?
A RL circuit has an emf of 5 volts, a resistance of 50 ohms, an inductance of 1 henry, and no initial current. Find (a) the current in the circuit at any time t and (b) its steady-state component.
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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- Make the equation s(s+1)(s+2)+K=0 in the form of 1+KF(s) and explain the drawing of root-locus curves. (Note: Indicate the splitting points, centers and angles of the asymptotes)arrow_forwardConsider the RLC circuit shown where the initial current flowing through the circuit at time t = 0 is I_0 = 5 and the initial charge on the capacitor at time t = 0 is Q_0 = 2. The components have values of R = 100 ohms, L = 5 H, and C = 1/450,500 F. Write the differential equation for Q(t), the charge across the capacitor, assuming the voltage source V(t) = 0arrow_forwardDesign an RLC circuit with 6 uH inductance and 1 uF capacitance. Calculate the minimum value of resistance (R) for the circuit to be damped? What is the oscillation frequency of the circuit if R=1 ohms?arrow_forward
- Consider the natural behavior of a critically damped series RLC circuit in which the initial current is zero. Determine the time at which the current reaches the maximum value in R=5W and L=10 mH.arrow_forwardShow the comparison between the 2nd order damped spring model and the 2nd RLC circuit system.arrow_forwardDetermine the natural response of the given parallel RLC circuit below that is Vc(t) at t ≥ 0 seconds. Specifically, solve for Vc(1)arrow_forward
- For a certain source-free parallel RLC circuit, R = 1 k , C = 3 μF, and L is such that the circuit response is overdamped. (a) Determine the value of L. (b) Write the equation for the voltage v across the resistor if it is known that v(0−) = 9 V and dv/dt|t=0+ = 2 V/s.arrow_forwardIn the circuit given below, R1 = 60 Ω. Calculate the value of R needed to have a critically damped response. The value of R is ______ ohms.arrow_forwardCompare the performances of the first order system, the overdamped, underdamped and critically damped second order system.arrow_forward
- If ? = 50Ω, L = 1.5H, what value of C will cause a sourceless series RLC circuit to be a) overdamped ?, b) critically damped ?, c) underdamped?arrow_forwardAn RL circuit has an emf given (in volts) by 4 cos t, a resistance of 100 ohms, an inductance of 4 henries, and no initial current. Find the time when the current is 2 A for the first timarrow_forwardIn the circuit , the resistor isadjusted for critical damping. The initial capacitor voltage is 20 V, andthe initial inductor current is 30 mA.1. Find the numerical value of R.2. Find the numerical values of i and di/dt immediately after theswitch is closed.3. Find vC(t) for t≥0.arrow_forward
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