HW17%20solution

# HW17%20solution - ECE 201 Spring 2010 Homework 17 Solutions...

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ECE 201 Spring 2010 Homework 17 Solutions Problem 27 (a) Let V be the common voltage across C 1 and C 2 . Thus ( C 1 + C 2 ) dV dt = i s ( t ) C 2 dV dt = i C 2 ( t ) i C 2 ( t ) = C 2 C 1 + C 2 i s ( t ) (b) Using KVL across the second loop and relation from part (a), we get r m i C 2 ( t ) - ( L 1 + L 2 ) di dt = 0 v out ( t ) = L 2 di dt = r m L 2 C 2 ( L 1 + L 2 )( C 1 + C 2 ) i s ( t ) Problem 38 (a) Starting from the right end and combining the inductors in series and parallel consecutively, we get L eq as L eq = 4 + ((36) || (10 + ((1 + 5) || (3)))) = 4 + ((36) || (10 + ((6) || (3)))) 1

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= 4 + ((36) || (10 + (2))) = 4 + ((36) || (12)) = 4 + 9 = 13 mH (b) Clearly, the given circuit has 1.2 mH and 0.6 mH in parallel, and this com- bination is in series with 2.4 mH, the equivalent of which is in parallel with 7 mH. Thus L eq = 7 || (2 . 4 + (1 . 2 || 0 . 6)) = 7 || (2 . 4 + 0 . 4)
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