Explanation Given data: Refer to Figure P13.9 in the textbook. The initial energy is zero and switch is closed at time t = 0 . Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (1) Here, R is the value of resistance. Write a general expression to calculate the impedance of an inductor in s -domain. Z L = s L (2) Here, L is the value of inductance. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (3) Here, C is the value of capacitance. Calculation: The given circuit is redrawn as shown in Figure 1. Since the initial energy is zero, the initial current through inductor and voltage across the capacitor is equal to zero. v ( 0 ) = 0 V i ( 0 ) = 0 A For time t > 0 , the switch is closed and the circuit in Figure 1 is redrawn as shown in Figure 2. Substitute 140 for R in equation (1) to find Z R . Z R = 140 Substitute 5 m for L in equation (2) to find Z L . Z L = s ( 5 × 10 − 3 ) = 0.005 s Substitute 1.25 μ for C in equation (3) to find Z C . Z C = 1 s ( 1.25 × 10 − 6 ) = 8 × 10 5 s Convert the Figure 2 into s -domain as shown in Figure 3. Apply voltage division rule in Figure 3 to find V o . V o = ( ( 8 × 10 5 s ) 140 + 0.005 s + 8 × 10 5 s ) ( 90 s ) = ( ( 8 × 10 5 s ) 140 s + 0.005 s 2 + 8 × 10 5 s ) ( 90 s ) = ( 8 × 10 5 0.005 s 2 + 140 s + 8 × 10 5 ) ( 90 s ) V o = 144 × 10 8 s ( s 2 + 28000 s + 16 × 10 7 ) (4) From equation (4), the characteristic equation of denominator is written as follows: s 2 + 28000 s + 16 × 10 7 On solving the characteristic equation, s 2 + 28000 s + 16 × 10 7 = ( s + 8000 ) ( s + 20000 ) (5) Substitute equation (5) in equation (4) as follows, V o = 144 × 10 8 s ( s + 8000 ) ( s + 20000 ) (6) Take partial fraction for above equation. V o = 144 × 10 8 s ( s + 8000 ) ( s + 20000 ) = A s + B s + 8000 + C s + 20000 (7) Find the constant A . A = s ( 144 × 10 8 s ( s + 8000 ) ( s + 20000 ) ) | s = 0 = 144 × 10 8 ( 0 + 8000 ) ( 0 + 20000 ) = 144 × 10 8 16 × 10 7 = 90 Finding the constant B

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Chapter 13, Problem 9P

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Find the s-domain expression of Vo and time domain expression of vo.

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Ch. 13.2 - Prob. 1AP Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 3AP Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.3 - The dc current and dc voltage sources are applied...Ch. 13.3 - Prob. 6AP Ch. 13.3 - Using the results from Example 13.7 for the...Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.4 - Derive the numerical expression for the transfer...Ch. 13.5 - Find (a) the unit step and (b) the unit impulse...

Ch. 13.5 - The unit impulse response of a circuit is υo(t) =...Ch. 13.7 - The current source in the circuit shown is...Ch. 13.7 - For the circuit shown, find the steady-state...Ch. 13 - Prob. 1P Ch. 13 - Prob. 2P Ch. 13 - Prob. 3P Ch. 13 - Prob. 4P Ch. 13 - An 8 kΩ resistor, a 25 mH inductor, and a 62.5 pF...Ch. 13 - Prob. 6P Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Find the poles and zeros of the impedance seen...Ch. 13 - Prob. 9P Ch. 13 - Prob. 10P Ch. 13 - Prob. 13P Ch. 13 - Prob. 15P Ch. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - There is no energy stored in the circuit in Fig....Ch. 13 - Prob. 25P Ch. 13 - Prob. 28P Ch. 13 - The switch in the circuit seen in Fig. P13.32 has...Ch. 13 - Prob. 31P Ch. 13 - Prob. 33P Ch. 13 - Prob. 35P Ch. 13 - Prob. 46P Ch. 13 - Prob. 47P Ch. 13 - Find the transfer function H(s) − Vo/Vi for the...Ch. 13 - Prob. 49P Ch. 13 - Prob. 50P Ch. 13 - Prob. 51P Ch. 13 - Prob. 53P Ch. 13 - Prob. 54P Ch. 13 - The operational amplifier in the circuit in Fig....Ch. 13 - Find the transfer function Io/Ig as a function of...Ch. 13 - Prob. 58P Ch. 13 - Prob. 59P Ch. 13 - Prob. 60P Ch. 13 - Prob. 61P Ch. 13 - Assume the voltage impulse response of a circuit...Ch. 13 - Prob. 68P Ch. 13 - The input voltage in the circuit seen in Fig....Ch. 13 - Find the impulse response of the circuit shown in...Ch. 13 - Prob. 73P Ch. 13 - Prob. 74P Ch. 13 - Prob. 75P Ch. 13 - The op amp in the circuit seen in Fig. P13.81 is...Ch. 13 - Prob. 78P Ch. 13 - The transfer function for a linear time-invariant...Ch. 13 - Prob. 80P Ch. 13 - Prob. 81P Ch. 13 - Prob. 82P Ch. 13 - Prob. 84P Ch. 13 - Prob. 85P Ch. 13 - The parallel combination of R2 and C2 in the...Ch. 13 - Show that if R1C1 = R2C2 in the circuit shown in...Ch. 13 - The switch in the circuit in Fig P13.91 has been...Ch. 13 - Prob. 90P Ch. 13 - Prob. 91P

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