To determine Find v o ( t ) when t ≥ 0 for the given circuit using PSPICE. Explanation Formula used: Write the condition for under-damped response for a parallel RLC circuit as follows: ω 0 2 > α 2 (1) Here, α is the neper frequency and ω 0 is the resonant radian frequency. Write the condition for critically damped response for a parallel RLC circuit as follows: α 2 = ω 0 2 (2) Write the condition for over-damped response for a parallel RLC circuit as follows: ω 0 2 < α 2 (3) Write the expression for resonant radian frequency for the given circuit as follows: ω 0 = 1 L C (4) 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 = 1 2 R C (5) Here, R is the resistance of the resistor. Write the expression of required voltage response v ( t ) in the given circuit for underdamped response as follows: v o ( t ) = B 1 e − α t cos ω d t + B 2 e − α t sin ω d t , t ≥ 0 (6) Here, B 1 , B 2 are arbitrary constants and ω d is the damped frequency. Write the expression for damped frequency in the circuit as follows: ω d = ( ω 0 ) 2 − α 2 (7) Write the expression to obtain the value of B 1 . B 1 = V 0 (8) Write the expression to obtain the value of B 2 . − α B 1 + ω d B 2 = 1 C ( − V 0 R − I 0 ) (9) Calculation: From the given data, the voltage response is required to be determined across the inductor in the circuit. As the source is not connected to the inductor for t < 0 , the initial value of the current through the inductor is 0 A. I 0 = 0 A From the given circuit, the 50 V source is connected to the capacitor for t < 0 . As the capacitor gets open circuit at steady state, the initial value of voltage across capacitor is equal to the voltage across the 4 k Ω resistor. Therefore, write the expression for initial value of voltage across the capacitor as follows: V 0 = v C ( 0 − ) = v C ( 0 + ) = v 4 k Ω Use voltage division rule and find the initial value of voltage across the capacitor as follows: V 0 = ( 50 V ) ( 4 k Ω 6 k Ω + 4 k Ω ) = ( 50 V ) ( 4 10 ) = 20 V Find the equivalent resistance (Thevenin’s resistance) of the circuit for t ≥ 0 by redrawing the given circuit as shown in Figure 1. From the circuit in Figure 1, write the expression for equivalent resistance (Thevenin’s resistance) as follows: R Th = v Th i T (10) From the circuit in Figure 1, write the expression for v Th as follows: v Th = − 10 i ϕ + i T ( 150 Ω ‖ 60 Ω ) (11) Use current division rule and write the expression for i ϕ in the circuit as follows: i ϕ = − i T ( 150 Ω 150 Ω + 60 Ω ) = ( − 150 210 ) i T Substitute ( − 150 210 ) i T for i ϕ in Equation (11) as follows: v Th = − 10 ( − 150 210 ) i T + i T ( 150 Ω ‖ 60 Ω ) = ( 1500 210 ) i T + i T [ ( 150 Ω ) ( 60 Ω ) 150 Ω + 60 Ω ] = ( 1500 210 ) i T + ( 9000 210 ) i T = ( 10 , 500 210 ) i T Substitute ( 10 , 500 210 ) i T for v Th in Equation (10) to obtain the Thevenin’s resistance in the circuit for t ≥ 0 . R Th = ( 10 , 500 210 ) i T i T = 50 Ω Modify the expression in Equation (5) for t ≥ 0 as follows: α = 1 2 R Th C Substitute 50 Ω for R Th and 8 μ F for C to obtain the value of α

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Chapter 8, Problem 14P

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Chapter 8 Solutions

EBK ELECTRIC CIRCUITS

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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