Explanation Given data: Refer to Figure 16.35 in the textbook. Formula used: Write a general expression to calculate the impedance of a resistor in s- domain. Z R ( s ) = R (1) Here, R is the value of resistance. Write a general expression to calculate the impedance of a inductor in s- domain. Z L ( s ) = 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 ( s ) = 1 s C (3) Here, C is the value of capacitance. Write a general expression to calculate the Laplace transform of the step input. ℒ ( u ( t ) ) = 1 s Given data: The given circuit is redrawn as shown in Figure 1. Apply Laplace transform to the voltage source v . V ( s ) = 8 ( 1 s ) { ∵ ℒ ( u ( t ) ) = 1 s } = 8 s Substitute 1 for R in equation (1) to find Z R . Z R ( s ) = 1 Substitute 1 for L in equation (2) to find Z L . Z L ( s ) = s ( 1 ) = s Substitute 1 for C in equation (3) to find Z C . Z C ( s ) = 1 s ( 1 ) = 1 s Convert the Figure 1 into s- domain. Refer to Figure 2, the impedance of resistor; inductor and capacitor are connected in series. Write an expression to calculate the equivalent impedance of series connected resistor, inductor and capacitor. Z ( s ) = Z R ( s ) + Z L ( s ) + Z C ( s ) (4) Substitute 1 for Z R ( s ) , s for Z L ( s ) , and 1 s for Z C ( s ) in equation (4) to find Z ( s ) . Z ( s ) = 1 + s + 1 s = s 2 + s + 1 s The reduced diagram Figure 2 is shown in Figure 3. Write an expression to calculate the current in s- domain. I ( s ) = V ( s ) Z ( s ) (5) Substitute 8 s for V ( s ) , and s 2 + s + 1 s for Z ( s ) in equation (5) to find I ( s ) . I ( s ) = ( 8 s ) ( s 2 + s + 1 s ) I ( s ) = 8 s 2 + s + 1 (6) From equation (6), the characteristic equation is written as follows, s 2 + s + 1 = 0 (7) Write a general expression to calculate the roots of characteristic equation in the form of a s 2 + b s + c = 0 . s 1 , 2 = − b ± b 2 − 4 a c 2 a (8) Here, a is the coefficient of second order term, b is the coefficient of first order term, and c is the coefficient of constant term. Comparing the equation (7) with quadratic equation a s 2 + b s + c = 0 , a = 1 b = 1 c = 1 Substitute 1 for a , 1 for b , and 1 for c in equation (8) to find s 1 , 2

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Transfer function

A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.

Convolution Integral

Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is …

Question

Chapter 16, Problem 12P

To determine

Find the expression of current i(t) in the circuit of Figure 16.35.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 11P

Chapter 16, Problem 13P

Students have asked these similar questions

box fill calculations

Two trade size 3 raceways enter a pull box directly across from each other. No other raceways enter the box. What are the minimum dimensions of the box?11. Length ______________________12. Width ______________________13. Depth ______________________Two trade size 3 raceways enter a pull box at right angles to each other. No other racewaysenter the box. What are the minimum dimensions of the box?14. Length ______________________15. Width ______________________16. Depth ______________________

not use ai please

Chapter 16 Solutions

Fundamentals of Electric Circuits

Ch. 16.2 - Determine vo(t) in the circuit of Fig. 16.6,...Ch. 16.2 - Prob. 2PP Ch. 16.2 - Prob. 3PP Ch. 16.3 - For the circuit shown in Fig. 16.12 with the same...Ch. 16.3 - Prob. 5PP Ch. 16.3 - The initial energy in the circuit of Fig. 16.17 is...Ch. 16.4 - Prob. 7PP Ch. 16.4 - Prob. 8PP Ch. 16.4 - Prob. 9PP Ch. 16.5 - Obtain the state variable model for the circuit...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Find the expression of current i ( t ) in the circuit of Figure 16.35.

Solution Summary: The author explains how to find the expression of current i(t) in the circuit of Figure 16.35.

Concept explainers

Find the expression of current i(t) in the circuit of Figure 16.35.

Want to see the full answer?

Chapter 16 Solutions