Explanation Given data: The characteristic equation is, s 2 + 100 s + 10 6 = 0 (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 of the resistor. 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 of the inductor. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (4) Here, C is the value of capacitance of the capacitor. Calculation: Using the equation (1), (2), and (3), consider the parallel RLC circuit with current source is drawn in s -domain as shown in Figure 1. Apply Kirchhoff’s current law at node V ( s ) in Figure 1. I ( s ) = V ( s ) R + V ( s ) s L + V ( s ) ( 1 s C ) = ( 1 R + 1 s L + s C ) V ( s ) = ( s L + R + s 2 R L C s R L ) V ( s ) = R L C ( s 2 + ( 1 R C ) s + 1 L C s R L ) V ( s ) Reduce the equation as follows, I ( s ) = C s ( s 2 + ( 1 R C ) s + 1 L C ) V ( s ) s I ( s ) C = ( s 2 + ( 1 R C ) s + 1 L C ) V ( s ) V ( s ) I ( s ) = s C s 2 + ( 1 R C ) s + 1 L C (5) The characteristic equation from the above equation (5) is, s 2 + ( 1 R C ) s + 1 L C = 0 (6) On comparing the equation (1) and (6)

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Author: Charles K Alexander, Matthew Sadiku

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Series and Parallel Circuit

Circuits can be classified as parallel and series depending on the manner in which components are connected to one another and the electrical source. The resultant output of the circuit depends on the electrical component.

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Chapter 16, Problem 6P

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Examine the design for a parallel RLC circuit which has the characteristic equation s2+100s+106=0.

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Chapter 16, Problem 5P

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Examine the design for a parallel RLC circuit which has the characteristic equation s 2 + 100 s + 10 6 = 0 .

Solution Summary: The author analyzes the design of a parallel RLC circuit with the characteristic equation s2+100s+106=0.

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Examine the design for a parallel RLC circuit which has the characteristic equation s2+100s+106=0.

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Chapter 16 Solutions