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EE202
HOMEWORK PROBLEMS
SPRING 10
DUE WEDNESDAY APRIL 14
65.
Solve each of the indicated questions.
(a)
In the circuit below,
L
1
=
0.8 H,
L
2
=
0.45 H,
M
=
0.175 H,
R
s
=
R
=
12
!
.
If
v
s
(
t
)
=
30cos(10
t
)
V, find the maximum instantaneous steady state power delivered to R when
(i) a dot is in position A, and
(ii) a dot is in position B.
(b)
For the circuit shown below with
i
L
(0
!
)
=
0
and
v
C
(0
!
)
=
2V
, the current,
i
L
(
t
)
, in amps for
t
!
0
.
(c)
Find the input impedance
Z
in
(
s
)
for the circuit below.
66.
In the circuit below, the coupling coefficient
k
has been adjusted so that the exact resonant
frequency is
!
=
200
rad/sec given that
C
=
0.35
mF,
R
=
2
Ω
,
L
1
=
L
2
=
0.1
H.
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Spring 10
2
(a)
Find the equivalent inductance,
L
eq
, of the coupled inductors, the mutual inductance
M
,
and the coupling coefficient
k
.
(i)
Step 1:
replace the coupled coils by an inductor labeled
L
eq
.
Find the value of
L
eq
that meets the resonance condition specified in the problem statement.
Are there two values?
If
so pick the largest.
(ii)
Step 2:
For circuit (aa) below,
L
eq
=
L
1
L
2
!
M
2
L
1
+
L
2
!
2
M
and for circuit (bb) below
L
eq
=
L
1
L
2
!
M
2
L
1
+
L
2
+
2
M
.
Nice trick formulas.
Determine M using your answer from step 1.
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 Spring '06

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