Explanation Given data: Refer to Figure 11.30 in the textbook for the given circuit. The source voltage is given as follows: v s ( t ) = 10 u ( t ) V Formula used: Write the expression for power absorbed by the inductor in the given circuit as follows: p L ( t ) = v L ( t ) i L ( t ) (1) Here, v L ( t ) is the voltage across the inductor and i L ( t ) is the current through the inductor. Write the expression for voltage across the inductor as follows: v L ( t ) = L d [ i L ( t ) ] d t (2) Write the expression for Neper frequency as follows: α = 1 2 R C (3) Here, R is the value of resistance and C is the value of capacitance. Write the expression for resonant radian frequency as follows: ω 0 = 1 L C (4) Here, L is the value of inductance. Write the expression for under-damped response for a parallel RLC circuit as follows: ω 0 2 > α 2 (5) Write the expression for over-damped response for a parallel RLC circuit as follows: ω 0 2 < α 2 (6) Write the expression for critically damped response for a parallel RLC circuit as follows: α 2 = ω 0 2 (7) Writ the expression for damped frequency as follows: ω d = ( ω 0 ) 2 − α 2 (8) Calculation: From the given circuit, short the voltage source and draw the circuit as shown in Figure 1 to obtain the parallel RLC circuit. Find the equivalent resistance in the circuit as follows: R = 1 Ω ‖ 10 Ω = ( 1 Ω ) ( 10 Ω ) 1 Ω + 10 Ω = 10 11 Ω Redraw the circuit in Figure 1 as shown in Figure 2. From the circuit in Figure 2, write the values of resistance, inductance, and capacitance of the parallel RLC circuit as follows: R = 10 11 Ω L = 0.5 H C = 2 F Substitute 10 11 Ω for R and 2 F for C in Equation (3) to obtain the neper frequency. α = 1 ( 2 ) ( 10 11 Ω ) ( 2 F ) = 11 40 rad / s = 0.275 rad / s Substitute 0.5 H for L and 2 F for C in Equation (4) to obtain the resonant radian frequency. ω 0 = 1 ( 0.5 H ) ( 2 F ) = 1 1 rad / s = 1 rad / s Substitute 0.275 rad / s for α and 1 rad / s for ω 0 in Equation (5) as follows: ( 1 rad / s ) 2 > ( 0.275 rad / s ) 2 1 ( rad / s ) 2 > 0.075625 ( rad / s ) 2 The expression is satisfied. Therefore, the response is the under-damped response. As the Equation (5) is satisfied, it is not required to check the Equations (6) and (7). From the given circuit, find the required parameters as follows: v s ( t ) = 10 u ( t ) V V 0 = 10 V I 0 = 10 V 1 Ω = 10 A From the given circuit, write the required initial values as follows: i L ( 0 ) = 0 A v L ( 0 − ) = 0 V v L ( 0 + ) = 0 V v C ( 0 + ) = 0 V d d t i L ( 0 + ) = d d t ( 0 ) = 0 As the response for the given circuit is under-damped, write the expression for current i L ( t ) as follows: i L ( t ) = I 0 + e − α t [ B 1 cos ( ω d t ) + B 2 sin ( ω d t ) ] (9) Here, B 1 , B 2 are constants. Find B 1 as follows: B 1 = − I 0 = − 10 A Write the expression to find B 2 as follows: d d t i L ( 0 + ) = − α B 1 + ω d B 2 From Equation (8), substitute ( ω 0 ) 2 − α 2 for ω d as follows: d d t i L ( 0 + ) = − α B 1 + B 2 ( ω 0 ) 2 − α 2 Substitute 0 for d d t i L ( 0 + ) , − 10 A for B 1 , 0.275 rad / s for α , and 1 rad / s for ω 0 as follows: 0 = − ( 0.275 rad / s ) ( − 10 A ) + B 2 ( 1 rad / s ) 2 − ( 0.275 rad / s ) 2 Simplify the expression as follows: B 2 = − 2.75 1 2 − 0

9th Edition

ISBN: 9780073545516

Author: Hayt, William H. (william Hart), Jr, Kemmerly, Jack E. (jack Ellsworth), Durbin, Steven M.

Publisher: Mcgraw-hill Education,

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Chapter 11, Problem 8E

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Find the power absorbed by the inductor at t=0 and t=1 s in the given circuit in Figure 11.30 in the textbook.

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Chapter 11, Problem 7E

Chapter 11, Problem 9E

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Chapter 11 Solutions

Engineering Circuit Analysis

Ch. 11.1 - A current source of 12 cos 2000t A, a 200 ....Ch. 11.2 - Given the phasor voltage across an impedance ,...Ch. 11.2 - Prob. 3P Ch. 11.2 - Prob. 4P Ch. 11.2 - A voltage source vs is connected across a 4...Ch. 11.3 - If the 30 mH inductor of Example 11.7 is replaced...Ch. 11.4 - Calculate the effective value of each of the...Ch. 11.5 - For the circuit of Fig. 11.16, determine the power...Ch. 11.6 - Prob. 10P Ch. 11 - Prob. 1E

Ch. 11 - Determine the power absorbed at t = 1.5 ms by each...Ch. 11 - Calculate the power absorbed at t = 0, t = 0+, and...Ch. 11 - Three elements are connected in parallel: a 1 k...Ch. 11 - Let is = 4u(t) A in the circuit of Fig. 11.28. (a)...Ch. 11 - Prob. 6E Ch. 11 - Assuming no transients are present, calculate the...Ch. 11 - Prob. 8E Ch. 11 - Prob. 9E Ch. 11 - Prob. 10E Ch. 11 - The phasor current I=915mA (corresponding to a...Ch. 11 - A phasor voltage V=10045V (the sinusoid operates...Ch. 11 - Prob. 13E Ch. 11 - Prob. 14E Ch. 11 - Find the average power for each element in the...Ch. 11 - (a) Calculate the average power absorbed by each...Ch. 11 - Prob. 17E Ch. 11 - Prob. 18E Ch. 11 - Prob. 19E Ch. 11 - The circuit in Fig. 11.36 has a series resistance...Ch. 11 - Prob. 21E Ch. 11 - Prob. 22E Ch. 11 - Prob. 23E Ch. 11 - Prob. 24E Ch. 11 - Prob. 25E Ch. 11 - Prob. 26E Ch. 11 - Prob. 27E Ch. 11 - Prob. 28E Ch. 11 - Prob. 29E Ch. 11 - Prob. 30E Ch. 11 - Prob. 31E Ch. 11 - Prob. 32E Ch. 11 - Prob. 33E Ch. 11 - (a) Calculate both the average and rms values of...Ch. 11 - Prob. 35E Ch. 11 - FIGURE 11.43 Calculate the power factor of the...Ch. 11 - Prob. 37E Ch. 11 - Prob. 38E Ch. 11 - Prob. 40E Ch. 11 - Prob. 41E Ch. 11 - Prob. 42E Ch. 11 - Prob. 43E Ch. 11 - Compute the complex power S (in polar form) drawn...Ch. 11 - Calculate the apparent power, power factor, and...Ch. 11 - Prob. 46E Ch. 11 - Prob. 48E Ch. 11 - Prob. 49E Ch. 11 - Prob. 50E Ch. 11 - Prob. 51E Ch. 11 - Prob. 52E Ch. 11 - FIGURE 11.49 Instead of including a capacitor as...Ch. 11 - Prob. 54E Ch. 11 - A load is drawing 10 A rms when connected to a...Ch. 11 - For the circuit of Fig. 11.50, assume the source...Ch. 11 - Prob. 57E Ch. 11 - A source 45 sin 32t V is connected in series with...Ch. 11 - Prob. 60E Ch. 11 - FIGURE 11.51 The circuit in Fig. 11.51 uses a Pi...Ch. 11 - Prob. 62E Ch. 11 - Prob. 63E Ch. 11 - You would like to maximize power transfer to a 50 ...

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Find the power absorbed by the inductor at t = 0 and t = 1 s in the given circuit in Figure 11.30 in the textbook.

Solution Summary: The author analyzes the power absorbed by the inductor in Figure 11.30 in the book.

Find the power absorbed by the inductor at t=0 and t=1 s in the given circuit in Figure 11.30 in the textbook.

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Chapter 11 Solutions