Sample problems
Topic: RC and RL circuits
Statement of problem
In the circuit shown in the figure, the switch has been in position a for a long time.
At t=0, it moves instantaneously from a to b.
(a) Find
0
()
vt
for
0
t
≥
.
(b) What is the total energy delivered to the 1
k
Ω
resistor?
(c) How many time constants does it take to deliver 95% of the energy found in (b)?
Solution
(a) At t=0, the steady state of the circuit is
2.5
mA
16
k
Ω
4
k
Ω
(0)
L
i
The steady current
(0)
L
i
is also the initial current for t>0. By KCL, it is
16
(0)
2.5
2
16
4
L
k
im
A
m
A
kk
Ω
=−
×
Ω+
Ω
At t=0, the switch turns to position b, so the circuit is like
120
mH
0
v
+
−
1
k
Ω
60
mH
(0)
L
i
The PARALLEL inductance in this circuit is
120
60
120
/ /60
40
120
60
mH
mH
mH
mH
mH
mH
mH
×
==
+
Therefore the time constant for this RL circuit is
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '05
 Unknown
 Electrical Engineering, Inductor, RC circuit, 1K, 4k, 16k

Click to edit the document details