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v
T
(t)
R
T
C
+
_
v
C
(t)
i (t)
v
C
(0)=V
O
i
N
(t)
R
T
L
i
L
(t)
i
L
(0)=I
O
Lesson 28 –
RL
and
RC
Circuits (Natural Response)
(Section 71) (CLO 71)
The next three lessons on FirstOrder Circuits can be a bit challenging for the students because they involve
calculus. The first looks at deriving the equations that describe firstorder circuits and their natural response
while the second looks at the circuits’ step responses.
An excellent example of duality and be found by
comparing the RC and RL differential equations and their solutions.
The third looks at firstorder response to
other than a step.
Suggest starting the lesson by analyzing a series
RC
circuit.
It is important to remind students that any linear
circuit can be replaced by its Thévenin equivalent. This is useful because it generalizes any firstorder circuit
to a voltage source,
v
T
(
t
) in series with a resistor
R
T
. Simply
connect a capacitor across the Thévenin equivalent circuit and do
a series analysis.
Begin with writing a KVL equation:
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This note was uploaded on 10/12/2010 for the course MAE 140 taught by Professor Mauriciodeoliveria during the Spring '08 term at UCSD.
 Spring '08
 MAURICIODEOLIVERIA

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