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Physics 21
Fall, 2007
Hour Exam #2
1
2
3
4
5
Total
Name:
Recitation Time
Recitation Leader
This exam is closed notes and closed book. You must show enough work on all problems to convince the grader
you understand how to solve the problem. You may use a calculator. Give units. There is an equation sheet on
the last page. All problems count 20 points.
Problem 1.
For the following circuit,
R
=5
.
0Ω
,
L
=40
.
0 mH, and
C
= 300 nF, and the frequency is
1000 Hz.
R
L
C
V
rms
(a) (5 pts.) Draw a phasor diagram for the voltages
in this circuit. What is the rms value of the cur
rent if
V
rms
=6V?
(b) (5 pts.) What is the phase relationship between
the current and the applied ac voltage? In other
words, does the current lag or lead the applied
voltage? by how much?
(c) (5 pts.) What is the power delivered to the circuit
by the power supply?
(d) (5 pts.) At what frequency would the rms cur
rent be the maximum for the given
V
rms
? (It is
not necessary to derive this result; just show the
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Consider a straight segment of wire of
length
a
carrying a current
I
. (The rest of the wire
need not be considered and is not shown.)
P
=(
x,
0,0)
(0,

a
/2,0)
(0
,+a
/2,0)
x
y
I
d
l
(a) (5 pts.) Use the BiotSavart law to write an ex
pression for the magnetic Feld
d
B
at the point
P
on the
x
axis due to the current
I
in the inFnites
imal segment of wire
d
l
locatedat(0
,y,
0). Sim
pliﬂy your expression by working out the cross
product. Be careful to distinguish between the
coordinate
x
and the cross product symbol
×
.
(b) (10 pts.) ±ind the magnetic Feld at
P
due to the
current in the Fnite length of wire from
y
=
−
a/
2
to
y
=+
a/
2. Your answer should be in terms of
a
,
I
, and fundamental constants. Remember that
B
is a vector; include necessary unit vectors.
(c) (5 pts.) Verify that your result approaches the
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This note was uploaded on 02/29/2008 for the course PHYSICS 21 taught by Professor Hickman during the Spring '08 term at Lehigh University .
 Spring '08
 Hickman
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