ECE2260F09_HW1p3soln

3 ma vt vc t c 460 vs dt dt c 5 f t 0 t 0 we

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Unformatted text preview: , this is a simple matter: v ( t ) = vC ( t ) Then we differentiate, and use the component equations involving d/dt for € L and/or C: d d i (0+ ) −2.3 mA v(t) = vC ( t ) =C = = −460 V/s + + dt dt C 5 µF t =0 t =0 We equate this to the symbolic derivative: € d v(t) = −αA1 + A2 = A2 = −460 V/s dt t =0+ Plugging in values gives the solution for v(t > 0): € −1+ v ( t ) = −257µV ⋅ e 2 2 Mr/s⋅t −1− Mr/s⋅t 5 5 + 257µV ⋅ e v ( t ) = −460 te−1Mt V/s € NOTE: Although A 2 is large, it is multiplied by t and an exponential € decay. The voltage remains small because the t is small at first, and the exponential decay becomes small quite quickly....
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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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