Explanation Given data: Refer to Figure 16.73 in the textbook. The initial current through inductor i ( 0 ) is 2 A . 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. Calculation: The given circuit is redrawn as shown in Figure 1. Refer to Figure 2, the voltage v ( t ) is the voltage across the inductor L 1 . The dependent source and the inductor ( L 1 ) is connected in parallel. For the parallel connection, the voltage is same. Therefore, v ( t ) = 2 i ( t ) (3) Apply Laplace transform for above equation to find V ( s ) . V ( s ) = 2 I ( s ) (4) Substitute 2 Ω for R in equation (1) to find Z R . Z R = 2 Ω Substitute 10 H for L 1 in equation (2) to find Z L 1 . Z L 1 = s ( 10 H ) = 10 s Substitute 2 H for L 2 in equation (2) to find Z L 2 . Z L 2 = s ( 2 H ) = 2 s Using element transformation methods with initial condition convert the Figure 1 into s -domain. Apply Kirchhoff’s voltage for Loop 2 in Figure 2

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 50P

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Find the expression of voltage v(t) for t>0 shown in Figure 16.73.

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Chapter 16, Problem 49P

Chapter 16, Problem 51P

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Chapter 16 Solutions

Fundamentals of Electric Circuits

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