Physics 21
Fall, 2007
Solution, Practice Exam #2
Problem 1.
For the following circuit,
R
=8
.
0Ω
,
L
=
2
.
0mH
,and
C
= 500
µ
F, and the frequency is 700 Hz.
R
L
C
V
rms
I
rms
/
ω
C
I
rms
R
V
rms
φ
ω
LI
rms
(a) (5 pts.) Write the loop equation for this circuit.
V
−
IR
−
L
dI
dt
−
Q
C
=0
(b) (10 pts.)
Draw a phasor diagram for the voltages in
this circuit.
What is the rms value of the current if
V
rms
=6V?
For the phasor diagram shown above, use
ωL
=2
π
×
700
×
0
.
002 H = 8
.
7965 Ω;
R
=8Ω
1
/ωC
=
(
2
π
×
700
×
500
×
10
−
6
F
)
−
1
.
4547 Ω
The resultant vector of
ωLI
rms
and 1
/
(
ωC
)
I
rms
is 8.3418
I
rms
, which points upward.
Adding that resultant to
I
rms
R
gives
V
rms
=
p
8
.
3418
2
+8
2
I
rms
=11
.
5579
I
rms
Then
V
rms
=6V=11
.
5579
I
rms
, so that
I
rms
.
519 A
(c) (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?
The phase
φ
is given by
tan
φ
=
8
.
3418
8
⇒
φ
=46
.
2
◦
.
806 rad
.
The current lags the applied voltage by 46
.
2
◦
.
Problem 2.
A single rectangular loop of wire with the di
mensions shown in the ±gure is inside a region of magnetic
±eld
B
(
t
) directed into the page. The magnitude
B
(
t
)ofthe
±eld is given by
B
(
t
)=0
.
02
t
T, where
t
is in seconds.
x
x
xxxxxxx
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0.4 m
0.8 m
(a) (14 pts.) What is the current in the loop at time
t
=1s
if the resistance of the loop is 0.1 Ω?
From Faraday’s Law,
E
=
−
d
Φ
dt
=
−
d
dt
³
B
(
t
)
×
0
.
4m
×
0
.
8m
´
=
−
d
dt
³
0
.
02
t
×
0
.
×
0
.
´
=
−
0
.
02
×
0
.
4
×
0
.
8=0
.
0064 V
Then
I
=
E
/R
.
0064
/
0
.
1=0
.
064 A
(b) (6 pts.) In what direction does the current in the loop
ﬂow? (Specify clockwise or counterclockwise.) Brieﬂy
explain your answer.
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 Spring '08
 Hickman
 Physics, Magnetic Field, IMAX, Irms

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