Unformatted text preview: will go to 0. V f = 0 We find that the circuit is overdamped, as Î± 2 â‰¥ Ï‰ 2 . Thus, the equation takes on the form: Âµ = Â¶ â€² 1 ? âˆ’ 40 Â· + Â¶ â€² 2 ? âˆ’ 160 Â· We also know that since the switch was closed for a long time, no current is flowing through the capacitor, and we can assume the voltage across the capacitor at time 0 = 30V. V (0) = 30 = Aâ€™ 1 +Aâ€™ 2 Solving the system of equations with the following, Â¸Âµ Â¸Â· Â¹ Âº = 0 = âˆ’ 40 Â¶ â€² 1 âˆ’ 160 Â¶â€² 2 We get: Aâ€™ 1 = 40V, Aâ€™ 2 = 10V Finally, we can state v (t) as: Âµ Â¹Â·Âº = 40 ? âˆ’ 40 Â· âˆ’ 10 ? âˆ’ 160 Â· Â» , Â· > 0 +...
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 Spring '05
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 Electrical Engineering, Equations, Frequency, Quadratic equation, Elementary algebra, 40 rad

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