ExampleProb1

# ExampleProb1 - Example S-Domain Problem(A2.1 1H t=0 For t <...

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©B obY o rk Back to TOC Example S-Domain Problem (A2.1) t = 0 1 F 2 2 10 V 1H 10V (0 ) 5A 2 L i  Step 1: Find initial conditions for t < 0 For t < 0 the switch is open and the circuit is in the steady state. The switch is thrown at t = 0. Find V out ( t ) 1 In the steady-state the inductor is a short-circuit and the capacitor is an open-circuit, so the equivalent circuit is as shown at right, giving: 2 10 V 1 (0 ) L i (0 ) c v (0 ) 0 C v Step 2: For t > 0, transform circuit to s -domain and solve for V out ( s ) 2 s 2 s 1 5 10 s   (2 / 3) 2 / 2 () (2 / 3) (2 / ) 3 s Zs ss V out ( s ) 2 s s 10 5 s    Continued next page… V out ( s ) V out ( t ) 2 3 Combine voltage sources in series Combine resistors in parallel (1)(2) 2 12 3 R Parallel RC impedance

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©B obY o rk Back to TOC Example (A2.1) continued Step 3: Partial Fraction Expansion and Inverse Transform to time-domain  2 10 ( ) 5 2 () 5 2 2 ( 3 ) 2 2 10 10 (3 2 ) out Zs Vs s sZ s s s s s s s ss s s       (1 ) ( 2 ) 10 ) V out ( s ) s 10 5 s 2 3 s
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ExampleProb1 - Example S-Domain Problem(A2.1 1H t=0 For t <...

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