Explanation Given data: Refer to Figure 16.71 in the textbook. 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. Apply Laplace transform for v s ( t ) to find V s ( s ) . V s ( s ) = 7.5 s + 2 { ∵ L ( e − a t u ( t ) ) = 1 s + a } Substitute 10 Ω for R in equation (1) to find Z R . Z R = 10 Substitute 0.25 H for L in equation (2) to find Z L . Z L = s ( 0.25 H ) = 0.25 s Substitute 0.2 F for C in equation (3) to find Z C . Z C = 1 s ( 0.2 F ) = 5 s Convert the Figure 1 into s -domain. Apply nodal analysis at node V o ( s ) for the circuit shown in Figure 2. V o ( s ) − 3 V x ( s ) 0.25 s + V o ( s ) ( 5 s ) + ( V o ( s ) − 7.5 s + 2 ) 10 = 0 V o ( s ) 0.25 s − 3 V x ( s ) 0.25 s + s V o ( s ) 5 + V o ( s ) 10 − 7.5 10 ( s + 2 ) = 0 V o ( s ) 0.25 s + s V o ( s ) 5 + V o ( s ) 10 − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 V o ( s ) [ 1 0.25 s + s 5 + 1 10 ] − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 Simplify the above equation as follows: V o ( s ) [ 1 0.25 s + s 5 + 1 10 ] − 7.5 10 ( s + 2 ) − 3 V x ( s ) 0.25 s = 0 V o ( s ) [ 40 + 2 s 2 + s ] − 7

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ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 48P

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Find the expression of voltage across the resistor Vx(s) in the circuit of Figure 16.71.

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Chapter 16, Problem 47P

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Find the expression of voltage across the resistor V x ( s ) in the circuit of Figure 16.71.

Solution Summary: The author explains how to find the expression of voltage across the resistor V_x(s).

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Find the expression of voltage across the resistor Vx(s) in the circuit of Figure 16.71.

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