quiz9fa00_sols

# quiz9fa00_sols - v S = 12 V,i S = 8 mA,R = 6 k ,L = 10 mH,C...

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1 EE2120 QUIZ No. 9 SOLUTION 1. (15pts)For the circuit in the f gure, use node analysis to determine the di f erential equation for the voltage, v C , across the capacitor. Note that you can de f ne a supernode. Use the following steps + + S v C v L v S i X i α X i R C L (a) (2pts)write the equation for the controlling variable The controlling variable is the current through the capacitor i X = C dv C dt (b) (3pts)express v L as a function of the capacitor voltage (and its derivatives) Using KVL v L v C = α i X = v L = v C + α C dv C dt (c) (6pts)write the node equation for the supernode v C v S R + C dv C dt i S + 1 L Z t −∞ v L ( x ) dx =0 (d) (2pts)eliminate integrals 1 R μ dv C dt dv S dt + C d 2 v C dt di S dt + 1 L ( v C + α C dv C dt )=0 (e) (2pts)arrange the terms in the di f erential equation C d 2 v C dt +( 1 R + α C L ) dv C dt + 1 L v C = 1 R dv S dt + di S dt 2. (10pts) For the same circuit assume the following values

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Unformatted text preview: v S = 12 V,i S = 8 mA,R = 6 k ,L = 10 mH,C = 2 F (a) (5pts)Determine the steady state value of the capacitor voltage. The capacitor acts as an open circuit. The controlling variable, i X ( ) = 0 and the dependent voltage source is zero (short circuit). In steady state the inductor acts as a short circuit. Hence the capacitor terminals are short circuited. v C ( ) = 0 Prepared by Dr. Jorge L. Aravena. Last revised on December 8, 2000 2 (b) (5pts)Determine the steady state value of the inductor current. All the currents f ow through the inductor. Use source superposition, for example. i L ( ) = i S + v S R = 8 mA + 2 mA...
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## This note was uploaded on 12/01/2011 for the course EE 2120 taught by Professor Aravena during the Fall '08 term at LSU.

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quiz9fa00_sols - v S = 12 V,i S = 8 mA,R = 6 k ,L = 10 mH,C...

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