ECE2260F09_HW6p45soln

# ECE2260F09_HW6p45soln - 2260 F 09 HOMEWORK#6 probs 4 and 5...

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2260 F 09 HOMEWORK #6 probs 4 and 5 solutions E X : + v g ( t ) = 2 V t < 0 e t V t 0 R 1 = 2 Ω R 2 = 4 Ω L = 3 H v o ( t ) + a) Write the Laplace transform V g ( s ) of v g ( t ). b) Write the Laplace transform V o ( s ) of v o ( t ). Be sure to include the effects of initial conditions, if they are nonzero. c) Write a numerical time-domain expression for v o ( t ) where t 0. S OL ' N : a) The Laplace transform depends only on what the input signal is from time 0 to . L v g ( t ) { } = L e t { } V = 1 s + 1 V b) We find initial conditions by considering circuit at t = 0 . The circuit has a 2 V input and has reached equilibrium. Thus, the L acts like a wire. + v g ( t ) = 2V R 1 = 2 Ω R 2 = 4 Ω L = 3 H i L (0 ) We use Ohm's Law to obtain the initial inductor current: i L (0 ) = 2 V 2 Ω + 4 Ω = 1 3 A Our circuit model includes initial conditions for the L :

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+ V g ( s ) = 1 s + 1 R 1 = 2 Ω R 2 = 4 Ω sL = 3 s V o (
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ECE2260F09_HW6p45soln - 2260 F 09 HOMEWORK#6 probs 4 and 5...

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