Explanation Given data: Refer to Figure 16.37 in the textbook. The value of current source is, i s ( t ) = [ 6 u ( t ) + 3 δ ( t ) ] mA (1) Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (2) 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 (3) Here, L is the value of inductance. Calculation: The given circuit is redrawn as shown in Figure 1. Apply Laplace transform for equation (1) to find I s ( s ) . I s ( s ) = [ 6 s + 3 ( 1 ) ] m { ∵ L ( u ( t ) ) = 1 s L ( δ ( t ) ) = 1 } = [ 6 s + 3 ] 10 − 3 { ∵ 1 m = 10 − 3 } Substitute 2 Ω for R 1 in equation (1) to find Z R 1 . Z R 1 = 2 Substitute 1 Ω for R 2 in equation (1) to find Z R 2 . Z R 2 = 1 Substitute 0.2 H for L in equation (2) to find Z L . Z L = s ( 0.2 H ) = 0.2 s Convert the Figure 1 into s -domain as shown in Figure 2. Use source transformation method to convert the current source into voltage source. V s ( s ) = ( 2 ) [ 6 s + 3 ] 10 − 3 = [ 12 s + 6 ] 10 − 3 Now, the Figure 2 is reduced as shown in Figure 3. Refer to Figure 3, the resistors and inductor is connected in series. The equivalent impedance is calculated as follows: Z eq = 2 + 1 + 0.2 s = 3 + 0.2 s Now, the Figure 3 is reduced as shown in Figure 4. The current I ( s ) is calculated as follows: I ( s ) = ( 12 s + 6 ) 10 − 3 Z eq Substitute 3 + 0.2 s for Z eq in above equation to find I ( s ) . I ( s ) = ( 12 s + 6 ) 10 − 3 3 + 0.2 s = ( 12 + 6 s s ) 10 − 3 3 + 0.2 s = ( 6 s + 12 ) 10 − 3 0.2 s ( s + 15 ) = 5 ( 6 s + 12 ) 10 − 3 s ( s + 15 ) Simplify the above equation to find I ( s ) . I ( s ) = ( 30 s + 60 ) 10 − 3 s ( s + 15 ) (4) Take partial fraction for above equation

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 14P

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Find the expression of current i(t) for the circuit shown in Figure 16.37.

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Find the expression of current i ( t ) for the circuit shown in Figure 16.37.

Solution Summary: The author explains how to find the expression of current i(t) for the circuit shown in Figure 16.37.

Find the expression of current i(t) for the circuit shown in Figure 16.37.

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Chapter 16 Solutions