Explanation Given Data: Refer to Figure 18.45 in the textbook for the given circuit. The value of input current is given as follows: i s = 5 e − t u ( t ) A (1) Formula used: Consider the expression for Impedance of capacitor in Fourier transform. Z ( ω ) = 1 j ω C (2) Here, ω is angular frequency in rad/sec and C is capacitance in Farad (F). Calculation: Write the Fourier transform of input current as follows: I S ( ω ) = 5 1 + j ω { ∵ F [ e − a t u ( t ) ] = 1 a + j ω } Redraw Figure 18.45 as shown in Figure 1. Substitute 20 × 10 − 3 F for C from Figure 1 in Equation (2) as follows: Z ( ω ) = 1 j ω ( 20 × 10 − 3 ) = 10 3 j 20 ω = 50 j ω By current division rule, write the expression for I 0 ( ω ) in Figure 1 as follows: I o ( ω ) = [ 40 40 + Z ( ω ) ] I s ( ω ) = [ 40 ( 40 + 50 j ω ) ] I s ( ω ) = [ j 40 ω 40 ( j ω + 50 40 ) ] I s ( ω ) I o ( ω ) = [ j ω ( 1.25 + j ω ) ] I s ( ω ) (3) Substitute 5 1 + j ω for I S ( ω ) in Equation (3) as follows: I o ( ω ) = ( j ω 1.25 + j ω ) ( 5 1 + j ω ) = 5 j ω ( 1 + j ω ) ( 1.25 + j ω ) Write the expression for output voltage using Ohm’s law as follows: V o ( ω ) = I o ( ω ) Z ( ω ) (4) Substitute the value of I o ( ω ) and Z ( ω ) in Equation (4) as follows: V o ( ω ) = [ 5 j ω ( 1 + j ω ) ( 1.25 + j ω ) ] ( 50 j ω ) = 250 ( j ω + 1 ) ( j ω + 1.25 ) Replace ( j ω ) with ( s ) to avoid complex algebra as follows: V o ( s ) = 250 ( s + 1 ) ( s + 1.25 ) Write the partial fraction expansion of V o ( s ) as follows: V o ( s ) = A ( s + 1 ) + B ( s + 1

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Chapter 18, Problem 43P

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Find the value of vo(t) for the circuit in Figure 18.45.

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Chapter 18, Problem 42P

Chapter 18, Problem 44P

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Ch. 18.8 - Prob. 12PP Ch. 18 - Prob. 1RQ Ch. 18 - Prob. 2RQ Ch. 18 - The inverse Fourier transform of ej2+j is (a) e2t...Ch. 18 - Prob. 4RQ Ch. 18 - Prob. 5RQ Ch. 18 - Prob. 6RQ Ch. 18 - Prob. 7RQ Ch. 18 - Prob. 8RQ Ch. 18 - A unit step current is applied through a 1-H...Ch. 18 - Prob. 10RQ Ch. 18 - Prob. 1P Ch. 18 - Prob. 2P Ch. 18 - Prob. 3P Ch. 18 - Prob. 4P Ch. 18 - Prob. 5P Ch. 18 - Prob. 6P Ch. 18 - Prob. 7P Ch. 18 - Prob. 8P Ch. 18 - Prob. 9P Ch. 18 - Prob. 10P Ch. 18 - Prob. 11P Ch. 18 - Prob. 12P Ch. 18 - Prob. 14P Ch. 18 - Prob. 15P Ch. 18 - Prob. 16P Ch. 18 - Prob. 17P Ch. 18 - Given that F=Fft, prove the following results,...Ch. 18 - Prob. 19P Ch. 18 - Prob. 21P Ch. 18 - Prob. 22P Ch. 18 - Prob. 23P Ch. 18 - Prob. 24P Ch. 18 - Prob. 25P Ch. 18 - Prob. 26P Ch. 18 - Prob. 27P Ch. 18 - Prob. 28P Ch. 18 - Prob. 29P Ch. 18 - For a linear system with input x(t) and output...Ch. 18 - Prob. 31P Ch. 18 - Prob. 32P Ch. 18 - Prob. 33P Ch. 18 - Prob. 34P Ch. 18 - Prob. 35P Ch. 18 - Prob. 36P Ch. 18 - Prob. 37P Ch. 18 - Prob. 38P Ch. 18 - Prob. 39P Ch. 18 - Prob. 40P Ch. 18 - Prob. 41P Ch. 18 - Prob. 42P Ch. 18 - Prob. 43P Ch. 18 - Prob. 44P Ch. 18 - Prob. 45P Ch. 18 - Prob. 46P Ch. 18 - Prob. 47P Ch. 18 - Prob. 49P Ch. 18 - Prob. 51P Ch. 18 - Prob. 52P Ch. 18 - Prob. 53P Ch. 18 - Prob. 54P Ch. 18 - Prob. 55P Ch. 18 - Prob. 56P Ch. 18 - Prob. 57P Ch. 18 - Prob. 58P Ch. 18 - Prob. 59P Ch. 18 - Prob. 60P Ch. 18 - Prob. 61P Ch. 18 - Prob. 62P Ch. 18 - Prob. 63P Ch. 18 - Prob. 64P Ch. 18 - Prob. 65P Ch. 18 - Prob. 66P Ch. 18 - Given a signal g(t) = sinc(200 t), find the...Ch. 18 - Prob. 68CP Ch. 18 - Prob. 69CP

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