ECE2260F07_HW1p3soln

ECE2260F07_HW1p3soln

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Unformatted text preview: of the product of L and C: ω2 = o 1 1 2 = = 0.2 M 2 (r/s) LC 1 µH ⋅ 5 µF Substituting into the equation for the roots yields the following: € s1,2 = −1 Mr/s ± € € 1 − 0.2 Mr/s = −1 ± 2 Mr/s 5 The roots are real, so the circuit is overdamped, and we use the exponential form of general solution: v ( t ) = A1e s1t + A2e s2 t + A3 Second, we find the A 3 value from v(t) as t->∞. (The exponential terms decay as t->∞, leaving only A3.) We assume the circuit values become constant as t->∞, causing the L to act like a wire and the C to act like an open circuit. The switch is also open, detaching the voltage so...
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This document was uploaded on 03/17/2014 for the course ECE 2260 at University of Utah.

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