( a ) Explanation Given data: Value of resistor R is 4 Ω , Value of inductor L is 2.22 H and Value of capacitor C is 12.5 mF . Formula used: The expression for the exponential damping coefficient in parallel R L C circuit is as follows: α = 1 2 R C (1) Here, α is the exponential damping coefficient, R is the resistance of a parallel R L C circuit and C is the capacitance of a parallel R L C circuit. The expression for the resonating frequency in parallel R L C circuit is as follows: ω 0 = 1 L C (2) Here, ω 0 is the resonating frequency and L is the inductance of a parallel R L C circuit. The expression for the two solutions of the characteristic equation of a parallel R L C circuit is as follows: s 1 = − α + α 2 − ω 0 2 (3) s 2 = − α − α 2 − ω 0 2 (4) Here, s 1 and s 2 is the solutions of the characteristic equation of a parallel R L C circuit. Calculation: Substitute 4 Ω for R and 12.5 mF C in the equation (1): α = 1 2 × 4 Ω × 12.5 mF { ∵ 1 mF = 1 × 10 − 3 F } = 1 2 × 4 Ω × 12.5 × 10 − 3 F = 1 0.1 α = 10 s − 1 Substitute 12.5 mF for C and 2.22 H for L in equation (2): ω 0 = 1 2.22 × 12.5 mF { ∵ 1 mF = 1 × 10 − 3 F } = 1 27 ( b ) To determine Find the value of α , ω 0 , s 1 and s 2 . ( c ) To determine Find the value of damping ratio.

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

9th Edition

ISBN: 9781259989452

Author: Hayt

Publisher: Mcgraw Hill Publishers

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It is that part of network analysis where the configuration is called graph or structure of the network system when all of the elements (e.g., R, L, and C) in a network system are substituted with lines having circles/rings or dots across both endpoints.…

Question

Chapter 9, Problem 4E

(a)

To determine

Find the value of α, ω0, s1 and s2.

(b)

To determine

Find the value of α, ω0, s1 and s2.

(c)

To determine

Find the value of damping ratio.

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Chapter 9, Problem 3E

Chapter 9, Problem 5E

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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. 3P Ch. 9.2 - Prob. 4P Ch. 9.3 - (a) Choose R1 in the circuit of Fig. 9.14 so that...Ch. 9.4 - Prob. 6P Ch. 9.5 - Prob. 7P Ch. 9.5 - Prob. 8P Ch. 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. 4E Ch. 9 - You go to construct the circuit in Exercise 1,...Ch. 9 - A parallel RLC circuit has inductance 2 mH and...Ch. 9 - Prob. 7E Ch. 9 - A parallel RLC circuit has R = 1 k, L = 50 mH. and...Ch. 9 - Prob. 9E Ch. 9 - Prob. 10E Ch. 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. 21E Ch. 9 - Prob. 22E Ch. 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. 27E Ch. 9 - The circuit of Fig. 9.44 is rebuilt such that the...Ch. 9 - Prob. 29E Ch. 9 - Prob. 30E Ch. 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. 35E Ch. 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. 42E Ch. 9 - Prob. 43E Ch. 9 - The simple three-element series RLC circuit of...Ch. 9 - Prob. 45E Ch. 9 - Prob. 46E Ch. 9 - Prob. 47E Ch. 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. 55E Ch. 9 - In the circuit shown in Fig. 9.56, (a) obtain an...Ch. 9 - Prob. 57E Ch. 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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