Explanation Given data: Refer to Figure 16.57 in the textbook. Formula used: Write a general expression to calculate the impedance of resistor in s -domain. Z R ( s ) = R (1) Here, R is the value of resistance. Write a general expression to calculate the impedance of a inductor in s -domain. Z L ( s ) = s L (2) Here, L is the value of inductance. Calculation: The given circuit is redrawn as shown in Figure 1. Substitute 1 Ω for R 1 in equation (1) to find Z R 1 ( s ) . Z R 1 ( s ) = 1 Ω Substitute 4 Ω for R 2 in equation (1) to find Z R 2 ( s ) . Z R 2 ( s ) = 4 Ω Substitute 1 4 H for L 1 in equation (2) to find Z L 1 ( s ) . Z L 1 ( s ) = s ( 1 4 H ) = 0.25 s Substitute 1 H for L 2 in equation (2) to find Z L 2 ( s ) . Z L 2 ( s ) = s ( 1 H ) = s Apply Laplace transform for v i ( t ) to find V i ( s ) . V i ( s ) = 20 s { ∵ L ( u ( t ) ) = 1 s } Convert the Figure 1 into s -domain as shown in Figure 2. Apply Kirchhoff’s voltage law for Loop 1 in Figure 2. 20 s − ( 1 ) I 1 ( s ) − ( 0.25 s ) I 1 ( s ) + ( 0.25 s ) I 2 ( s ) = 0 20 s = ( 1 ) I 1 ( s ) + ( 0.25 s ) I 1 ( s ) − ( 0.25 s ) I 2 ( s ) I 1 ( s ) ( 1 + 0.25 s ) − I 2 ( s ) ( 0.25 s ) = 20 s (3) Apply Kirchhoff’s voltage law for Loop 2 in Figure 2. 4 I 2 ( s ) + s I 2 ( s ) + ( 0.25 s ) I 2 ( s ) − ( 0.25 s ) I 1 ( s ) = 0 − ( 0.25 s ) I 1 ( s ) + ( 1.25 s + 4 ) I 2 ( s ) = 0 ( 1.25 s + 4 ) I 2 ( s ) = ( 0.25 s ) I 1 ( s ) Simplify the above equation to find I 2 ( s )

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 34P

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Chapter 16, Problem 33P

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Find the value of mesh currents I 1 ( s ) and I 2 ( s ) .

Solution Summary: The author explains the formula used to calculate the impedance of a resistor in s -domain.

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