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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring 2008
Conflict Exam Three: Solution
Section I: (25 points) Five Concept Questions. Please circle your
answers.
Question 1 (5 points):
In an LC circuit, the electric and magnetic fields are shown in the
figure. At the moment depicted in the figure, the energy in the circuit is stored in
1.
The electric field and is decreasing
2.
The electric field and is constant
3.
The magnetic field and is decreasing
4.
The magnetic field and is constant
5.
In both the electric and magnetic field and is constant
6.
In both the electric and magnetic field and is decreasing
Solution:
(b). At the instant in question the energy is only stored in the electric field. The
energy is constant because there is no energy dissipation through a resistor. Note that
because the charge on the capacitor decreases and the current increases, the energy stored
in the electric field is decreasing and the energy stored in the magnetic field increases.
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Question 2 (5 points):
A very long solenoid consisting of
N
turns has radius
R
and
length
d
(
d
>>
R
).
Suppose the number of turns is doubled keeping all the other
parameters fixed. The self inductance
a)
remains the same.
b)
doubles.
c)
is halved.
d)
is four times as large.
e)
is four times as small.
Solution: (d).
The self inductance is proportional to the number of turns times the
magnetic flux through each turn. The magnetic flux through each turn is proportional tot
eh magnetic field which is proportional to the number of turns as well. Therefore the self
induction is proportional to the square of the number of turns. Hence, if the number of
turns is doubles the self inductance is four times as large.
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Question 3 (5 points):
Consider the
RLC
circuit below, where at time
0
t
=
the switch
is closed to apply the emf from a battery. The capacitor is initially uncharged.
Which of the curves below best approximates the time dependence of the current?
(a)
(b)
(
c
)
(
d
)
Solution (c):
The current begins at zero due to the inductance
L
and ends at zero due
to the capacitance
C
.
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Question 4 (5 points):
Consider the plot of the natural logarithm of
i
(
t
) versus
t
for a
discharging capacitor in an
RC
circuit.
The slope of the line is equal to
(a) the time constant
(b) minus the time constant
(c) the inverse of the time constant
(d) minus the inverse of the time constant.
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This note was uploaded on 04/27/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.
 Spring '07
 Hudson

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