Explanation Given data: Refer to Figure 16.77 in the textbook. The switch is in position 1 for t < 0 . The switch is at the top of the capacitor at time t = 0 . 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. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (3) Here, C is the value of capacitance. Calculation: The given circuit is redrawn as shown in Figure 1. For a DC circuit, at steady state condition when the switch is in position ‘1’ at time t = 0 − the capacitor acts like open circuit and the inductor acts like short circuit. Now, the Figure 1 is reduced as shown in Figure 2. Refer to Figure 2, the resistors R 1 and R 2 are connected in series. The current through the inductor is calculated as follows: i L ( 0 − ) = 120 V 4 Ω + 16 Ω = 120 V 20 Ω = 6 A Refer to Figure 2, there is no capacitor placed in the circuit. Therefore, the voltage across the capacitor is zero. v C ( 0 − ) = 0 V The current through inductor and voltage across capacitor is always continuous so that, i ( 0 ) = i L ( 0 − ) = i L ( 0 + ) = 6 A v ( 0 ) = v C ( 0 − ) = v C ( 0 + ) = 0 V For time t > 0 , the switch is moved from position ‘1’ to the top of the capacitor. Now the Figure 1 is reduced as shown in Figure 3. Substitute 16 Ω for R 2 in equation (1) to find Z R 2 . Z R 2 = 16 Substitute 4 H for L in equation (2) to find Z L . Z L = s ( 4 H ) = 4 s Substitute 1 16 F for C in equation (3) to find Z C . Z C = 1 s ( 1 16 F ) = 16 s Using element transformation methods with initial conditions convert the Figure 3 into s -domain. Apply Kirchhoff’s voltage law for the circuit shown in Figure 4. 16 s I ( s ) + 4 s I ( s ) − ( 4 s ) i ( 0 ) s + 16 I ( s ) = 0 16 s I ( s ) + 4 s I ( s ) − 4 i ( 0 ) + 16 I ( s ) = 0 I ( s ) [ 16 s + 4 s + 16 ] = 4 i ( 0 ) I ( s ) [ 16 + 4 s 2 + 16 s s ] = 4 i ( 0 ) Substitute 6 for i ( 0 ) in above equation

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ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 54P

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Find the expression of voltage v(t) for t>0 in the circuit of Figure 16.77.

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Chapter 16, Problem 53P

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Find the expression of voltage v ( t ) for t > 0 in the circuit of Figure 16.77.

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

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Find the expression of voltage v(t) for t>0 in the circuit of Figure 16.77.

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Chapter 16 Solutions

Find the expression of voltage v ( t ) for t &gt; 0 in the circuit of Figure 16.77.

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

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Find the expression of voltage v(t) for t>0 in the circuit of Figure 16.77.

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Chapter 16 Solutions

Find the expression of voltage v ( t ) for t > 0 in the circuit of Figure 16.77.