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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Fall 2007
Turn in at your table during class labeled with your name and group (e.g. L01 4A)
Problem Set 12
Due: Wednesday, November 28
th
at class beginning (before 10:15/12:15)
This problem set focuses on material from week 12.
Textbook references can be found at
the top of the summaries from these days.
Warm Up
Problem 1:
LC
Circuit
(a) Initially, the capacitor in a series
LC
circuit is charged.
A switch is closed, allowing
the capacitor to discharge, and after time
T
the energy stored in the capacitor is one
quarter its initial value.
Determine
L
if
C
and
T
are known.
(b) A capacitor in a series
LC
circuit has an initial charge
and is being discharged.
Find, in terms of
L
and
C
, the flux through each of the
N
turns in the coil at time
t
, when
the charge on the capacitor is
Q
(
t
).
0
Q
(c) An
LC
circuit consists of a 90.0mH inductor and a
1.000 F
μ
capacitor.
If the
maximum instantaneous current is 0.100 A, what is the greatest potential difference
across the capacitor?
Sample Exam Problem…
Problem 2: Solenoid
Consider a long solenoid of length
D
and radius
a
with
N
turns, placed along the zaxis (it
is centered at z=0).
It is hooked in series with a capacitor
C
, a resistor
R
, and a power
supply that is driving the circuit on resonance.
At time t = 0 the current flowing through
the solenoid is a maximum,
I
0
.
(a) At this moment (t = 0), calculate the magnetic field
B
0
everywhere inside the
solenoid.
Show your work.
(b) Calculate the self inductance
L
of the solenoid.
Show your work.
(c) Write an equation for the time dependence of the magnetic field
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 Fall '07
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