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Solutions to Homework #6
Chapter
23
50.
Picture the Problem
: A solenoid has 640 turns, is 24 cm long, and has a radius of 4.3 cm.
Strategy:
Solve equation 2314 for the inductance.
Solution:
Calculate the inductance:
(
29
(
29
2
2
2
7
0
640
4
10 T m/A
0.043 m
12 mH
0.25 m
N
L
A
μ
π

=
=
=
l
Insight:
To double the inductance, you could increase either the radius or the number of turns by
2
, or you
could cut the length in half while keeping the number of turns the same.
54.
Picture the Problem
: The four electrical circuits
shown in the figure at the right have identical
batteries, resistors, and inductors.
Strategy:
A long time after the switch is closed
each inductor will act like an ideal wire.
Use this
principle and the rules of adding resistors in series
and in parallel to determine the ranking of the
currents supplied by the batteries.
Solution:
Let each battery have emf
ε
and each
resistor have resistance
R
. For circuit A the
inductor will act like an ideal wire when the
switch has been closed for a long time, and the
current supplied by the battery will be
.
R
For
circuits B and C the resistors in parallel with the
inductor are shorted out, and make no contribution
to the current in the circuit. The current supplied
by the battery in those circuits is also
.
R
For
circuit D the equivalent resistance of the two
resistors in parallel is
2,
R
so the current
supplied by the
battery after a long time, when the inductor acts as an ideal wire, is
2
.
R
The ranking of the currents,
therefore, is
A = B = C < D.
Insight:
While inductors act like ideal wires in DC circuits, capacitors act like open switches (see Chapter 21).
If each inductor were replaced by a capacitor, the currents in each circuit would be A, zero; B,
2 ;
R
C,
2
3 ;
R
and D, zero.
58.
Picture the Problem
: The number of turns per meter in a solenoid of fixed length is doubled. At the same time,
the current in the solenoid is halved.
Strategy:
Use equations 2314 and 2319 to determine the effect of the described changes on the energy stored
in the solenoid.
Solution:
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This note was uploaded on 02/10/2012 for the course PHY 102 taught by Professor Korotkova during the Spring '09 term at University of Miami.
 Spring '09
 KOROTKOVA
 Physics, Inductance, Work

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