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v
T
(t)
R
T
C
+
_
v
C
(t)
i (t)
v
C
(0)=V
O
Lesson 29 –
RL
and
RC
Circuits (Step Response) (Sections 72 and 73) (CLO 71)
This lesson starts out challenging but fortunately becomes easy for the students to use once the derivations
are done and they can apply solutions to a template. That this analysis becomes relatively “plugandchug”
is a mixed blessing.
It makes students capable of designing simple timing circuits but often disguises
understanding of what is really occurring.
At least part of the secret to increasing understanding is to have
students find parameters other than v
C
(
t
)
or i
L
(
t
)
.
Start the lesson by continuing from the last lesson. Quickly repeat the derivation of the firstorder
differential equation of an
RC
circuit.
Here it is again:
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
v
dt
t
dv
RC
t
v
t
v
t
Ri
t
v
t
v
t
v
t
v
C
C
T
C
T
C
R
T
+
=
+
=
+
=
Substitute for
i
(
t
)
=Cdv
C
(
t
)
/dt
Remind the students that unlike dc circuits with only sources
and resistors
RL
and
RC
circuits can store energy.
This
energy, we saw last time, gives rise to a response even after
the power is turned off.
Therefore, while this feature
complicates things it makes wonderful, practical circuits possible. Going back to our equation we now need
to solve our circuit for cases where there is an input,
v
T
(t)
. To solve
RL
and
RC
circuits under these
conditions one needs to know three things:
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 Spring '08
 MAURICIODEOLIVERIA

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