Explanation Given data: Refer to Figure 8.3 in the textbook for the given circuit. The current response for the given circuit is given as follows: i ( t ) = B 1 e − 2000 t cos ( 1500 t ) + B 2 e − 2000 t sin ( 1500 t ) , t ≥ 0 The initial current through the inductor ( I 0 ) is 7.5 mA . The initial voltage across the capacitor ( V 0 ) is − 30 V . The capacitance of the capacitor is given as follows: C = 80 nF Formula used: Write the condition for underdamped response of the given circuit as follows: α 2 < ω 0 2 (1) Here, α is the neper frequency and ω 0 is the resonant radian frequency. Write the expression for resonant radian frequency for the given circuit as follows: ω 0 = 1 L C (2) Here, L is the inductance of the inductor, and C is the capacitance of the capacitor. Write the expression for neper frequency for the given circuit as follows: α = R 2 L (3) Here, R is the resistance of the resistor. Refer to Equation (8.32) in the textbook and write the expression of current response i ( t ) for underdamped response of a series RLC circuit as follows: i ( t ) = B 1 e − α t cos ( ω d t ) + B 2 e − α t sin ( ω d t ) , t ≥ 0 (4) Here, B 1 , B 2 are arbitrary constants and ω d is the damped frequency. Write the expression to obtain the value of B 1 . B 1 = I 0 (5) Write the expression to obtain the value of B 2 . − α B 1 + ω d B 2 = 1 L ( − R I 0 − V 0 ) (6) Write the expression for damped frequency in the circuit as follows: ω d = ( ω 0 ) 2 − α 2 (7) Calculation: As the given current response is same as the expression in Equation (4), the given response is a underdamped response. Compare given current response with the expression in Equation (4) and writ the value of α and ω d as follows: α = 2000 rad / s ω d = 1500 rad / s Rearrange the expression in Equation (7) for the resonant radian frequency as follows: ω 0 = ( ω d ) 2 + α 2 Substitute 2000 rad / s for α and 1500 rad / s for ω d as follows: ω 0 = ( 1500 rad / s ) 2 + ( 2000 rad / s ) 2 = 2500 rad / s Rearrange the expression in Equation (1) for the inductance of the inductor as follows; L = 1 C ( ω 0 ) 2 Substitute 80 nF for C and 2500 rad / s for ω 0 to obtain the value of inductance of the inductor

10th Edition

ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

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Chapter 8, Problem 39P

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Find the values of R, L, B1 and B2 for the given expression of i(t).

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Chapter 8, Problem 38P

Chapter 8, Problem 40P

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Chapter 8 Solutions

Electric Circuits, Global Edition

Ch. 8.1 - The resistance and inductance of the circuit in...Ch. 8.2 - Use the integral relationship between iL and v to...Ch. 8.2 - Prob. 3AP Ch. 8.2 - Prob. 4AP Ch. 8.2 - Prob. 5AP Ch. 8.3 - Prob. 6AP Ch. 8.4 - The switch in the circuit shown has been in...Ch. 8.4 - Prob. 8AP Ch. 8 - Prob. 1P Ch. 8 - Prob. 2P

Ch. 8 - The resistance in Problem 8.1 is decreased to80 Ω...Ch. 8 - Prob. 4P Ch. 8 - Prob. 5P Ch. 8 - The natural voltage response of the circuit in...Ch. 8 - Prob. 7P Ch. 8 - Prob. 8P Ch. 8 - The natural response for the circuit shown in Fig....Ch. 8 - Prob. 10P Ch. 8 - The two switches in the circuit seen in Fig.P8.11...Ch. 8 - The resistor in the circuit of Fig. P8.11 is...Ch. 8 - The resistor in the circuit of Fig.P8.11 is...Ch. 8 - The switch in the circuit of Fig. P8.17 has been...Ch. 8 - The inductor in the circuit of Fig. P8.17 is...Ch. 8 - The inductor in the circuit of Fig. P8.17 is...Ch. 8 - Design a parallel RLC circuit (see Fig. 8.1) using...Ch. 8 - Prob. 18P Ch. 8 - Prob. 19P Ch. 8 - Find υ(t) for t ≥ 0 in the circuit in Problem 8.19...Ch. 8 - Prob. 21P Ch. 8 - Prob. 22P Ch. 8 - The initial value of the voltage υ in the circuit...Ch. 8 - Prob. 24P Ch. 8 - Prob. 25P Ch. 8 - Prob. 26P Ch. 8 - Prob. 27P Ch. 8 - Prob. 28P Ch. 8 - Prob. 29P Ch. 8 - Prob. 30P Ch. 8 - The switch in the circuit in Fig. P8.31 has been...Ch. 8 - Prob. 32P Ch. 8 - There is no energy stored in the circuit in Fig....Ch. 8 - For the circuit in Fig. P8.30, find υo for t ≥...Ch. 8 - The switch in the circuit in Fig. P8.36 has been...Ch. 8 - Prob. 36P Ch. 8 - Prob. 37P Ch. 8 - Prob. 38P Ch. 8 - Prob. 39P Ch. 8 - Find the voltage across the 80 nF capacitor for...Ch. 8 - The initial energy stored in the 31.25 nF...Ch. 8 - In the circuit in Fig. P8.42, the resistor is...Ch. 8 - Design a series RLC circuit (see Fig. 8.3) using...Ch. 8 - Change the resistance for the circuit you designed...Ch. 8 - Prob. 45P Ch. 8 - Prob. 46P Ch. 8 - The switch in the circuit shown in Fig. P8.48 has...Ch. 8 - The switch in the circuit in Fig. P8.48 has been...Ch. 8 - The initial energy stored in the circuit in Fig....Ch. 8 - The resistor in the circuit shown in Fig. P8.50 is...Ch. 8 - The resistor in the circuit shown in Fig. P8.50 is...Ch. 8 - Prob. 52P Ch. 8 - The two switches in the circuit seen in Fig. P8.53...Ch. 8 - Prob. 55P Ch. 8 - Prob. 57P Ch. 8 - Prob. 58P Ch. 8 - Prob. 59P Ch. 8 - Prob. 60P Ch. 8 - Prob. 61P Ch. 8 - Derive the differential equation that relates the...Ch. 8 - The voltage signal of Fig. P8.63(a) is applied to...Ch. 8 - The circuit in Fig. P8.63 (b) is modified by...Ch. 8 - Prob. 65P Ch. 8 - Prob. 66P Ch. 8 - Prob. 67P Ch. 8 - Prob. 68P

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