midterm 03 – VARELA, CHRISTOPHER – Due: Nov 15 2007, 11:00 pm
1
Question 1, chap 32, sect 5.
part 1 of 1
10 points
In a series
RLC
ac circuit, the resistance is
8 Ω, the inductance is 25 mH, and the capac
itance is 24
μ
F. The maximum potential is
219 V, and the angular frequency is 100 rad
/
s.
Calculate the maximum current in the cir
cuit.
Correct answer: 0
.
528674 (choice number
8).
Explanation:
Let :
R
= 8 Ω
,
L
= 25 mH = 0
.
025 H
,
C
= 24
μ
F = 2
.
4
×
10

5
F
,
V
max
= 219 V
,
and
ω
= 100 rad
/
s
.
The capacitive reactance is
X
C
=
1
ω C
=
1
(100 rad
/
s) (2
.
4
×
10

5
F)
= 416
.
667 Ω
.
The inductive reactance is
X
L
=
ω L
= (100 rad
/
s) (0
.
025 H)
=2
.
5 Ω
.
The maximum current is
I
max
=
V
max
Z
=
V
max
±
R
2
+(
X
L

X
C
)
2
=
219 V
±
(8 Ω)
2
+ (2
.

416
.
667 Ω)
2
=
0
.
528674 A
.
Question 2, chap 31, sect 2.
part 1 of 1
10 points
A coil is wrapped with 375 turns of wire on
the perimeter of a circular frame (of radius
82 cm). Each turn has the same area, equal
to that of the frame.
A uniform magnetic
±eld is directed perpendicular to the plane of
the coil. This ±eld changes at a constant rate
from 26 mT to 69 mT in 50 ms.
What is the magnitude of the induced
E
in
the coil at the instant the magnetic ±eld has
a magnitude of 36 mT?
Correct answer: 681
.
251 (choice number
10).
Explanation:
Basic Concepts:
E
=

N
d
Φ
B
dt
Φ
B
≡
²
+
B
·
d
+
A
=
B
·
A
Solution:
E
=

N
d
Φ
B
dt
=

NA
Δ
B
Δ
t
=

N π r
2
(
B
2

B
1
)
Δ
t
=

(375)
π
(82 cm)
2
×
(69 mT)

(26 mT)
50 ms
=

681
.
251 V
E
= 681
.
251 V
.
Question 3, chap 33, sect 5.
part 1 of 1
10 points
Consider an electromagnetic wave pattern
as shown in the ±gure below.
E
B
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View Full Documentmidterm 03 – VARELA, CHRISTOPHER – Due: Nov 15 2007, 11:00 pm
2
The wave is
1.
traveling right to left.
2.
traveling left to right.
correct
3.
a standing wave and is stationary.
Explanation:
The
+
E
vector and
+
B
vector are not at the
same point on the velocity axis.
Pick an instant in time, where the
E
and
B
Felds are at the same point on the velocity
axis.
z
v
x
y
E
B
±or instance, let us choose the point where
the
+
E
vector is along the
x
axis, as shown in
the above Fgures. At this same instant, the
+
B
vector is along the negative
y
axis (at a point
with a phase di²erence of 360
◦
from the place
on the velocity (
z
) axis where the
+
E
vector is
drawn).
Then
+
E
×
+
B
is along the negative
z
axis.
Therefore, the electromagnetic wave is
traveling left to right.
Question 4, chap 31, sect 3.
part 1 of 2
10 points
A horizontal circular wire loop of radius
0
.
7 m lies in a plane perpendicular to a uni
form magnetic Feld pointing from above into
the plane of the loop, has a magnitude of
0
.
52 T.
If in 0
.
14 s the wire is reshaped from a circle
into a square, but remains in the same plane,
what is the magnitude of the average induced
emf in the wire during this time?
Correct answer: 1
.
22703 (choice number 4).
Explanation:
Let :
r
=0
.
7m
,
b
.
52 T
,
and
Δ
t
.
14 s
.
The average induced emf
E
is given by
±E²
=
N
±
ΔΦ
Δ
t
²
=
ΔΦ
Δ
t
since
N
= 1, and
ΔΦ =
B
(
A
circle

A
square
)
=
B
(
π r
2

A
square
)
.
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 Spring '10
 Turner
 Magnetic Field, Correct Answer, Choice number, – VARELA

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