Explanation Given data: Refer to Figure 13.18 in the textbook for the circuit with coupled coils. From Figure 13.18, the value of ω is 2 rad/s . Calculation: Consider the expression for the coupling coefficient. k = M L 1 L 2 Substitute 1 H for M , 2 H for L 1 , and 1 H for L 2 . k = 1 H ( 2 H ) ( 1 H ) = 1 2 = 0.7071 Consider the expression for the inductive reactance. X L = j ω L (1) Consider the expression for the capacitive reactance. X C = 1 j ω C (2) Substitute 1 H for L and 2 for ω in equation (1). X L = j ( 2 ) ( 1 H ) = j 2 Substitute 2 H for L and 2 for ω in equation (1). X L = j ( 2 ) ( 2 H ) = j 4 Substitute 1 8 F for C and 2 for ω in equation (2). X C = 1 j ( 2 ) ( 1 8 F ) = − j 4 Ω Modify the Figure 13.18 by transforming the time-domain circuit with coupled-coils to frequency domain of the circuit with coupled-coils. The frequency domain equivalent circuit is shown in Figure 1. From Figure 1, consider that the loops 1 and 2 contain the currents I 1 and I 2 respectively. Apply Kirchhoff's voltage law to the loop 1 in Figure 1. ( 4 − j 4 + j 4 ) I 1 − j 2 I 2 = 100 2 I 1 − j I 2 = 50 (3) Apply Kirchhoff's voltage law to the loop 2 in Figure 1. − j 2 I 1 + ( 2 + j 2 ) I 2 = 0 (4) Write equations (3) and (4) in matrix form as follows. [ 2 − j − j 2 ( 2 + j 2 ) ] [ I 1 I 2 ] = [ 50 0 ] (5) Write the MATLAB code to solve the equation (5). A = [2 -1*j;-j*2 (2+j*2)]; B = [50; 0]; C = inv(A)*B The output in command window: C = 19.2308 + 3.8462i 7.6923 + 11.5385i From the MATLAB output, the currents I 1 and I 2 are, I 1 = ( 19.2308 + j 3.8462 ) A = 19.658 ∠ 11.31 ° A And I 2 = ( 7.6923 + j 11.5385 ) A = 13.87 ∠ 56.31 ° A Write the current I 1 and I 2 in time-domain. i 1 = 19.658 cos ( 2 t + 11.31 ° ) A (6) i 2 = 13.87 cos ( 2 t + 56

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 13.3, Problem 3PP

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Calculate the coupling coefficient and the stored energy in the coupled coils at t=1.5 ms.

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Chapter 13.2, Problem 2PP

Chapter 13.4, Problem 4PP

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Chapter 13 Solutions

Fundamentals of Electric Circuits

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Calculate the coupling coefficient and the stored energy in the coupled coils at t = 1.5 ms .

Calculate the coupling coefficient and the stored energy in the coupled coils at t=1.5 ms.

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Chapter 13 Solutions