a) Explanation Given data: The initial energy stored in the circuit is zero. Refer to figure given in the respective question. Calculation: Apply Kirchhoff’s current law for i 1 loop and write the differential equation. 150 i 1 ( t ) + 62.5 d i 1 d t + 25 d d t ( i 2 − i 1 ) + 12.5 d d t ( i 1 − i 2 ) − 25 d i 1 d t = 625 150 i 1 ( t ) + 25 d i 1 d t + 12.5 d i 2 d t = 0 (1) Apply Kirchhoff’s current law for i 2 loop and write the differential equation. 12.5 d d t ( i 2 − i 1 ) + 25 d i 1 d t + 100 i 2 = 0 100 i 2 + 12.5 d i 1 d t + 12.5 d i 2 d t = 0 (2) Apply Laplace transform for equation (1). 150 I 1 ( s ) + 25 s I 1 ( s ) + 12.5 s I 2 ( s ) = 0 ( 25 s + 150 ) I 1 ( s ) + 12.5 s I 2 ( s ) = 0 (3) Apply Laplace transform for equation (2). 100 I 2 ( s ) + 12.5 s I 1 ( s ) + 12.5 s I 2 ( s ) = 0 12.5 s I 1 ( s ) + ( 12.5 s + 100 ) I 2 ( s ) = 0 (4) Solve equation (3) and (4) to obtain the expression for I 1 ( s ) and I 2 ( s ) . I 1 ( s ) = 50 ( s + 8 ) s ( s + 4 ) ( s + 24 ) I 2 ( s ) = − 50 ( s + 4 ) ( s + 24 ) Write the partial fraction expansion of I 1 ( s ) as follows: I 1 ( s ) = K 1 s + K 2 ( s + 4 ) + K 3 ( s + 24 ) (5) Substitute 50 ( s + 8 ) s ( s + 4 ) ( s + 24 ) for I 1 ( s ) in equation (5). 50 ( s + 8 ) s ( s + 4 ) ( s + 24 ) = K 1 s + K 2 ( s + 4 ) + K 3 ( s + 24 ) Multiply both sides by ( s ) and evaluate both sides at s = 0 to find the value of K 1 . 50 ( s + 8 ) s s ( s + 4 ) ( s + 24 ) | s = 0 = K 1 s s | s = 0 + K 2 s ( s + 4 ) | s = 0 + K 3 s ( s + 24 ) | s = 0 50 ( s + 8 ) ( s + 4 ) ( s + 24 ) | s = 0 = K 1 + 0 + 0 K 1 = 50 ( 0 + 8 ) ( 0 + 4 ) ( 0 + 24 ) K 1 = 4.167 Multiply both sides by ( s + 4 ) and evaluate both sides at s = − 4 to find the value of K 2 . 50 ( s + 8 ) ( s + 4 ) s ( s + 4 ) ( s + 24 ) | s = − 4 = K 1 ( s + 4 ) s | s = − 4 + K 2 ( s + 4 ) ( s + 4 ) | s = − 4 + K 3 ( s + 4 ) ( s + 24 ) | s = − 4 50 ( s + 8 ) s ( s + 24 ) | s = − 4 = 0 + K 2 + 0 K 2 = 50 ( − 4 + 8 ) ( − 4 ) ( − 4 + 24 ) K 2 = − 2.5 Multiply both sides by ( s + 24 ) and evaluate both sides at s = − 24 to find the value of K 3 . 50 ( s + 8 ) ( s + 24 ) s ( s + 4 ) ( s + 24 ) | s = − 24 = K 1 ( s + 24 ) s | s = − 24 + K 27 ( s + 24 ) ( s + 3 ) | s = − 24 + K 3 ( s + 24 ) ( s + 7 ) | s = − 24 50 ( s + 8 ) s ( s + 4 ) | s = − 24 = 0 + 0 + K 3 K 3 = 50 ( − 24 + 8 ) ( − 24 ) ( − 24 + 4 ) K 3 = − 1 b) To determine Find the value of i 1 ( ∞ ) and i 2 ( ∞ ) . c) To determine Check whether the computed answers make sense in terms of circuit behavior or not.

10th Edition

ISBN: 9781292060545

Author: James W. Nilsson, Susan Riedel

Publisher: Pearson Education Limited

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Question

Chapter 12, Problem 39P

To determine

Find the expression for i1(t) and i2(t).

To determine

Find the value of i1(∞) and i2(∞).

To determine

Check whether the computed answers make sense in terms of circuit behavior or not.

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Chapter 12, Problem 33P

Chapter 12, Problem 40P

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Reversing 1⏀ Motors-all the wires are not used. Use the data sheet b on page 383 to draw the wiring diagram. Note: interchange the red and black leads to reverse the motor rotation. Use only the number of contacts required. Insulate any motor wire not used with a wire nut. Wire the motor to operate in forward and reverse at 115 VAC

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Chapter 12 Solutions

Electric Circuits, Global Edition

Ch. 12.4 - Prob. 1AP Ch. 12.5 - Prob. 2AP Ch. 12.7 - Prob. 3AP Ch. 12.7 - Prob. 4AP Ch. 12.7 - Prob. 5AP Ch. 12.7 - Prob. 6AP Ch. 12.7 - Prob. 7AP Ch. 12.7 - Prob. 8AP Ch. 12.7 - Prob. 9AP Ch. 12.8 - Use the initial- and final-value theorems to find...

Ch. 12 - Prob. 1P Ch. 12 - Prob. 2P Ch. 12 - Use step functions to write the expression for...Ch. 12 - Prob. 4P Ch. 12 - Explain why the following function generates an...Ch. 12 - Find the area under the function shown in Fig....Ch. 12 - Prob. 7P Ch. 12 - Prob. 8P Ch. 12 - Prob. 9P Ch. 12 - Prob. 10P Ch. 12 - Prob. 11P Ch. 12 - Prob. 12P Ch. 12 - Prob. 13P Ch. 12 - Prob. 14P Ch. 12 - Prob. 15P Ch. 12 - Prob. 16P Ch. 12 - Prob. 17P Ch. 12 - Prob. 18P Ch. 12 - Prob. 19P Ch. 12 - Prob. 20P Ch. 12 - Prob. 21P Ch. 12 - Prob. 22P Ch. 12 - Prob. 23P Ch. 12 - Prob. 24P Ch. 12 - Prob. 25P Ch. 12 - Prob. 26P Ch. 12 - Prob. 27P Ch. 12 - The switch in the circuit in Fig. P12.28LO has...Ch. 12 - Prob. 29P Ch. 12 - Prob. 30P Ch. 12 - Prob. 31P Ch. 12 - Prob. 33P Ch. 12 - Prob. 39P Ch. 12 - Prob. 40P Ch. 12 - Prob. 41P Ch. 12 - Prob. 42P Ch. 12 - Prob. 43P Ch. 12 - Prob. 44P Ch. 12 - Prob. 45P Ch. 12 - Use the initial-value theorem to find the initial...Ch. 12 - Prob. 47P Ch. 12 - Prob. 48P Ch. 12 - Prob. 49P Ch. 12 - Prob. 50P Ch. 12 - Prob. 51P Ch. 12 - Prob. 52P Ch. 12 - Prob. 53P Ch. 12 - Prob. 54P Ch. 12 - Prob. 55P Ch. 12 - Prob. 56P

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