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PHY2054 Spring 2008
1
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Exam 3 Solutions
1. (
Ch. 20
) In the circuit shown,
L
= 56 mH,
R
= 4.6
Ω
and
V
= 12.0 V. The switch
S
has been
open for a long time then is suddenly closed at
t
= 0. At what value of
t
(in msec) will the current
in the inductor reach 1.1 A?
(1) 6.67
(2) 10.5
(3) 2.88
(4) 19.0
(5) None of these
The current in an RL circuit, starting at 0, is
( )
/
max
1
t
ii
e
τ
−
=−
, where
/
LR
=
and
max
/
iV
R
=
and V is the voltage. Here i
max
= 12.0 / 4.6 = 2.609 and
= 0.056 / 4.6 = 12.17
msec.
The solution is
()
max
ln 1
/
6.67
ti
i
−
=
msec.
2. Refer to the previous problem. What is the total energy stored in the inductor a long time after
the switch is closed?
(1) 0.19 J
(2) 0.048 J
(3) 0.76 J
(4) 0.034 J
(5) None of these
After a long time, the inductor can be ignored and the current in the inductor is i
∞
= 12.0/4.6 =
2.61 A.
The energy in the inductor is
2
1
2
0.19
L
UL
i
∞
==
J.
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View Full Document PHY2054 Spring 2008
2
3. (
Prob. 20.6
) A solenoid 6.00 cm in diameter and 10.0 cm long has 500 turns and carries a
current of 15.0 A. Calculate the magnetic flux (in webers) through a circular crosssectional area
in the middle of the solenoid.
(1) 2.7
×
10
−
4
(2) 5.1
×
10
−
2
(3) 4.7
×
10
−
4
(4) 7.5
×
10
−
4
(5) None of these
The magnetic flux through the area is
22
0
B
rB
r
n
i
φπ
π
μ
==
, where i is the current, r is the
radius of the coil and n is the number of windings/meter.
This yields
φ
B
=
2.7
×
10
−
4
webers
.
4. (
Prob. 21.47
) A microwave oven generates electromagnetic waves of frequency 2.4 GHz that
are reflected by the walls and form standing waves that heat food as the energy of the waves are
absorbed. The standingwave pattern causes food to be heated unevenly, with burn marks at the
wave peaks. If the distance between the burn marks is 4.8 cm, what is the speed of the
microwaves inside the food in km/s?
(1) 2.3
×
10
5
(2) 4.7
×
10
5
(3) 2.9
×
10
5
(4) 1.2
×
10
5
(5) None of these
The points of highest intensity occur every half wavelength, thus
λ
= 9.6 cm.
The velocity is thus
v =
f = 0.096
×
2.4
10
9
= 2.3
10
8
m/s =
2.3
×
10
5
km/s.
5. (
Prob. 21.57
) A real inductor has resistance because it is composed of a coil of wire with non
zero resistivity. To measure the inductance of a coil, a student places it across a 12.0V battery
and measures a current of 0.72 A. The student then connects the coil to a 30.0V (rms) 60 Hz
generator and measures an rms current of 0.86 A. What is the inductance of the coil?
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This test prep was uploaded on 04/17/2008 for the course PHY 2054 taught by Professor Avery during the Spring '08 term at University of Florida.
 Spring '08
 Avery
 Physics

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