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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.
 Fall '08
 Cotter,N

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