MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
8.02
Spring 2008
Problem Set 9
Due: Wednesday, April 16 at 11 am.
Hand in your problem set in your section slot in the boxes outside the door of 32-
082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3
Group A)
Problem 1: Read
Experiment 6: Inductance and RL Circuits
Pre-Lab Questions (10
points)
1.
RL Circuits (3 points)
Consider the circuit at left, consisting of a battery (emf
ε
), an inductor
L
, resistor
R
and switch
S
.
For times
t
< 0 the switch is open and there is no
current in the circuit.
At
t
= 0 the switch is closed.
(a)
Using Kirchhoff’s loop rules (really Faraday’s
law now), write a differential equation relating the emf
on the battery, the current in the circuit and the time
derivative of the current in the circuit.
(b)
The solution to your differential equation should look:
/
( )
(
)
t
I t
A X
e
τ
−
=
−
where
A
,
X
, and
τ
are constants. Plug this expression into the differential
equation you obtained in (a) in order to confirm that it indeed is a solution and to
determine what the time constant
τ
and the constants
A
, and
X
are.
What
would be a better label for
A
?
(HINT:
You will also need to use the initial
condition for current.
What is
(
0)
I t
=
?)
(c)
Now that you know the time dependence for the current
I
in the circuit you can
also determine the voltage drop
V
R
across resistor and the EMF generated by the
inductor.
Do so, and confirm that your expressions match the plots in Fig. 6a or
6b in Experiment 6.

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