ECE2260F09_HW6p23soln

# ECE2260F09_HW6p23soln - 2260 F 09 HOMEWORK#6 probs 2 and 3...

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Unformatted text preview: 2260 F 09 HOMEWORK #6 probs 2 and 3 solutions E X : + – v g ( t ) = 6V + 3 e − t cos(2 t ) u ( t )V C = 200 mF L = 200 mH R = 1.2 Ω v o ( t ) + – Note: The 6 V in the v g ( t ) source is always on. a) Write the Laplace transform, V g ( s ), of v g ( t ). b) Draw the s-domain equivalent circuit, including source V g ( s ), components, initial conditions for L and/or C , and terminals for V o ( s ). c) Write an expression for V o ( s ). d) Apply the final value theorem to find lim t →∞ v o ( t ) . S OL ' N : a) We consider only the value of v g ( t ) for t > 0 when finding the Laplace transform: L v g ( t ) { } = L 6 u ( t ) + 3 e − t cos(2 t ) u ( t ) { } V = 6 s + 3( s + 1) ( s + 1) 2 + 2 2 V b) To find initial conditions, we assume that, since the circuit input is a constant 6 V, the circuit has reached a constant state where derivatives of voltages and currents are zero. Thus, we treat inductors as wires and capacitors as open circuits. We then find the energy variables, i L ( t ) and v C ( t ): +...
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ECE2260F09_HW6p23soln - 2260 F 09 HOMEWORK#6 probs 2 and 3...

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