Explanation Given data: Refer to given circuit in the textbook. At time t = 0 the switch moves to position ‘b’. 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 Z M = s M (2) Here, L is the value of inductance, and M is the value of mutual inductance. Calculation: The given circuit is redrawn as shown in Figure 1. The T-equivalent circuit of the mutually connected series aiding inductors is shown in Figure 2. Implement the Figure 2 in Figure 1 as shown in Figure 3. Consider, L eq1 = L 1 + M L eq2 = L 2 + M M eq = − M Now, the Figure 3 is drawn as shown in Figure 4. For a DC circuit at steady state condition the switch is in positon ‘a’ for time t < 0 and the inductor acts like a short circuit. Now, the Figure 4 is reduced as shown in Figure 5. Refer to Figure 5, the short circuited inductor ( L eq2 ) is connected in parallel with the resistor R 3 . Since, the inductor is short circuited the entire current flows through it. Now, the Figure 5 is reduced as shown in Figure 6. Refer to Figure 6, the inductor L eq1 and L eq2 are connected in series. For a series connection, the current is same. i L 1 ( 0 − ) = i L 2 ( 0 − ) The current through inductors is calculated as follows: i L 1 ( 0 − ) = i L 2 ( 0 − ) = 90 V 5 Ω = 18 A The current through inductor is always continuous so that, i L 1 ( 0 ) = i L 1 ( 0 − ) = i L 1 ( 0 + ) = 18 A i L 2 ( 0 ) = i L 2 ( 0 − ) = i L 12 ( 0 + ) = 18 A For time t > 0 , the switch moves to position ‘b’ and the circuit in Figure 4 is reduced as shown in Figure 7. The Figure 7 can also be redrawn as shown in Figure 8. Use equation (1) to find Z R 2 . Z R 2 = 20 Ω Use equation (1) to find Z R 3 . Z R 3 = 10 Ω Use equation (2) to find Z L eq1 . Z L eq1 = s ( 4 H ) = 4 s Ω Use equation (2) to find Z L eq2 . Z L eq2 = s ( 3 H ) = 3 s Ω Use equation (2) to find Z M eq Z M eq = s ( − 1 H ) = − s Ω Convert the Figure 8 into s -domain as shown in Figure 9. The value of L eq1 i L 1 ( 0 ) is calculated as follows: L eq1 i L 1 ( 0 ) = ( 4 H ) ( 18 A ) = 72 V The value of L eq2 i L 2 ( 0 ) is calculated as follows: L eq2 i L 2 ( 0 ) = ( 3 H ) ( 18 A ) = 54 V Now, the Figure 9 is redrawn as shown in Figure 10 with the calculated values. Apply Kirchhoff’s current law at node V in Figure 10. V − 72 4 s + 20 + V − s + 10 + V + 54 3 s = 0 V 4 s + 20 − 72 4 s + 20 + V − s + 10 + V 3 s + 54 3 s = 0 V 4 s + 20 + V − s + 10 + V 3 s = 72 4 s + 20 − 54 3 s V ( 1 4 s + 20 + 1 − s + 10 + 1 3 s ) = 72 4 s + 20 − 54 3 s Simplify the above equation as follows: V ( 3 s ( − s + 10 ) + 3 s ( 4 s + 20 ) + ( 4 s + 20 ) ( − s + 10 ) 3 s ( 4 s + 20 ) ( − s + 10 ) ) = 72 ( 3 s ) − 54 ( 4 s + 20 ) 3 s ( 4 s + 20 ) V ( − 3 s 2 + 30 s + 12 s 2 + 60 s − 4 s 2 + 40 s − 20 s + 200 3 s ( 4 s + 20 ) ( − s + 10 ) ) = 216 s − 216 s − 1080 3 s ( 4 s + 20 ) V ( 5 s 2 + 110 s + 200 3 s ( 4 s + 20 ) ( − s + 10 ) ) = − 1080 3 s ( 4 s + 20 ) Simplify the above equation to find V

11th Edition

ISBN: 9780134747224

Author: Riedel

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Videos

Question

Chapter 13, Problem 42P

To determine

Find the current io for time t>0.

Expert Solution & Answer

Chapter 13 Solutions

EBK ELECTRIC CIRCUITS

Ch. 13.2 - The parallel circuit in Example 13.1 is placed in...Ch. 13.3 - Prob. 2AP Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.3 - The dc current and dc voltage sources are applied...Ch. 13.3 - Prob. 6AP Ch. 13.3 - Using the results from Example 13.7 for the...Ch. 13.3 - The energy stored in the circuit shown is zero at...Ch. 13.4 - Derive the numerical expression for the transfer...Ch. 13.5 - Find (a) the unit step and (b) the unit impulse...Ch. 13.5 - The unit impulse response of a circuit is υo(t) =...

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.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,