ECE2260F09_HW1p3soln

The exponential terms decay as t leaving only a3 we

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Unformatted text preview: e−αt + A2 te−αt + 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 source and resistor on the left. Since the L acts like a wire, we have A3 = v(t->∞) = 0V. Third, we find the initial values of energy variables: iL(0+) = iL(0–) and vC(0+) = vC(0–). At t = 0–, we assume circuit values are constant, causing the L to act like a wire and the C to act like an open circuit. The switch is closed, connecting the parallel RLC to the voltage source and resistor on the left. The L, acting like a wire, shorts the 100 mΩ resistor and the open C. Thus, the initial C voltage is zero: vC(0+) = vC(0–) = 0V Also, all the current will flow through the L and will be limited only by the 1 kΩ resistor. iL (0+ ) = iL (0−...
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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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