Explanation Given data: Refer to Figure 16.94 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 a capacitor in s -domain. Z C = 1 s C (2) Here, C is the value of capacitance. Write a general expression to calculate the reflected impedance of an ideal transformer. Z in = Z L n 2 (3) Here, Z L is the impedance of secondary side, and n is the turns ratio of a transformer. Write an expression to calculate the turns ratio of a transformer. n = N secondary N primary . (4) Here, N primary is the number of turns in the primary winding, and N secondary is the number of turns in the secondary winding. Calculation: The given circuit is redrawn as shown in Figure 1. Refer to Figure 1, the value of N primary is 1 , and N secondary is 2 . Substitute 1 for N primary , and 2 for N secondary in equation (4) to find n . n = 2 1 = 2 Substitute 1 Ω for R 1 in equation (1) to find Z R 1 . Z R 1 = 1 Ω Substitute 8 Ω for R 2 in equation (1) to find Z R 2 . Z R 2 = 8 Ω Substitute 0.25 F for C in equation (2) to find Z C . Z C = 1 s ( 0.25 F ) = 4 s Apply Laplace transform for v s ( t ) to find V s ( s ) . V s ( s ) = 160 ( 1 s + 1 ) { ∵ L ( e − a t u ( t ) ) = 1 s + a } = 160 s + 1 Convert the Figure 1 into s -domain. Refer to Figure 2, the secondary side of transformer consists of capacitor and resistor which are connected in parallel. Therefore, the load impedance is calculated as follows: Z L = 4 s ∥ 8 = ( 4 s ) ( 8 ) 4 s + 8 = ( 4 ( 8 ) s ) ( 4 + 8 s s ) = ( 4 ) ( 8 ) 4 ( 2 s + 1 ) Z L = 8 2 s + 1 Refer to Figure 2, the primary side has impedance of a resistance. Therefore, the reflected impedance of a primary side mentioned in equation (1) is written as follows: Z in = 1 + Z L n 2 Substitute 8 2 s + 1 for Z L , and 2 for n in above equation to find Z in . Z in = 1 + ( 8 2 s + 1 ) 2 2 = 1 + 8 4 ( 2 s + 1 ) = 1 + 2 ( 2 s + 1 ) = 2 s + 1 + 2 2 s + 1 = 2 s + 3 2 s + 1 Now, the Figure 2 is reduced as shown in Figure 3. Apply current division rule for Figure 3 to find I o ( s )

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 71P

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Find the expression of current io(t) for the circuit given in Figure 16.94.

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Find the expression of current i o ( t ) for the circuit given in Figure 16.94.

Solution Summary: The author explains how to calculate the expression of current i_o(t) for the circuit given in Figure 16.94.

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Find the expression of current io(t) for the circuit given in Figure 16.94.

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