Explanation Given data: Refer to Figure 16.9 in the textbook. The value of initial current i L ( 0 ) = 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 resistor. Write a general expression to calculate the impedance of a inductor in s -domain. Z L = s L (2) Here, L is the value of inductor. Calculation: The given circuit is redrawn as shown in Figure 1. Substitute 1 Ω for R in equation (1) to find Z R 1 . Z R 1 = 1 Ω Substitute 2 Ω for R in equation (1) to find Z R 2 . Z R 2 = 2 Ω Substitute 2 H for L in equation (2) to find Z L . Z L = s ( 2 H ) = 2 s Apply Laplace transform for v s ( t ) to find V s ( s ) . V s ( s ) = 15 s + 2 { ∵ L ( e − a t u ( t ) ) = 1 s + a } Using element transformation methods with initial conditions convert the Figure 1 into s -domain. Apply nodal analysis at node V o ( s ) for Figure 2. V o ( s ) − 15 s + 2 1 + V o ( s ) 2 s + i L ( 0 ) s + V o ( s ) 2 = 0 V o ( s ) − 15 s + 2 + V o ( s ) 2 s + 0 s + V o ( s ) 2 = 0 { ∵ i L ( 0 ) = 0 } V o ( s ) − 15 s + 2 + V o ( s ) 2 s + 0 + V o ( s ) 2 = 0 V o ( s ) [ 1 + 1 2 s + 1 2 ] = 15 s + 2 Simplify the above equation to find V o ( s ) . V o ( s ) = ( 15 s + 2 ) [ 1 + 1 2 s + 1 2 ] = ( 15 s + 2 ) [ 2 s + 1 + s 2 s ] = 15 ( 2 s ) ( s + 2 ) ( 3 s + 1 ) = 30 s ( s + 2 ) ( 3 s + 1 ) Simplify the above equation to find V o ( s ) . V o ( s ) = 30 s 3 ( s + 2 ) ( s + 1 3 ) = 10 s ( s + 2 ) ( s + 1 3 ) Take partial fraction for above equation

6th Edition

ISBN: 8220102801448

Author: Alexander

Publisher: YUZU

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Chapter 16.2, Problem 2PP

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Find the expression of output voltage $vo(t)$ for the circuit shown in Figure 16.9.

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Find the expression of output voltage v o ( t ) for the circuit shown in Figure 16.9.

Solution Summary: The author explains how to find the expression of output voltage v_o(t) for the circuit shown in Figure 16.9.

Find the expression of output voltage $vo(t)$ for the circuit shown in Figure 16.9.

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Chapter 16 Solutions

Find the expression of output voltage v o ( t ) for the circuit shown in Figure 16.9.

Solution Summary: The author explains how to find the expression of output voltage v_o(t) for the circuit shown in Figure 16.9.

Find the expression of output voltage vo(t)<m:math><m:mrow><m:msub><m:mi>v</m:mi><m:mi>o</m:mi></m:msub><m:mrow><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> for the circuit shown in Figure 16.9.

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Chapter 16 Solutions

Find the expression of output voltage $vo(t)$ for the circuit shown in Figure 16.9.