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This is a Practice Exam from Summer 2006
SHOW YOUR WORK,
Document your reasoning, showing algebra,
conversion factors and diagrams.
Constants you don't have to remember are k = 9.0x109Nm2/C2
and e = 1.6x10-19C. Relationships we have not
derived in class are the potential due to a point charge, V=kq/r
and the energy stored in a capacitor W=
˝Vq
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18-C2 (Sister
using most of the same numbers.)
As a classroom demonstration of electrostatic repulsive
forces, a plastic cup is hung by a light thread from a support
directly above an insulated metal sphere. In our mind we
contrive a situation with larger charges than we actually
encountered this summer.
Given: The mass of the cup was 2.5 g. Imagine that we
could give it a positive charge of 8 µC. Further imagine
that the thread is 50 cm long and tied to a support 40
cm above the center of the sphere, and cup is in equilibrium
30 cm horizontally from the center of the sphere.
Find: (a) How great is the electrostatic force between the
sphere and the cup? [18 mN]
(b) What is the charge on the sphere? [23 nC] |
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19-B11 (Sister
using most of the same numbers.)
An electron somehow gets loose from the negative terminal
of your automobile battery and heads fro the positive terminal.
Given: The voltage of the battery is 12 V and the
electron starts from rest. Electrons all have the same mass, and
it is 9.1095x10-31 kg, just as they all have
the same charge, and that is 1.6022x10-19 C
Find: (a) What is the potential energy of the electron when it
starts out on its journey to the positive terminal? [1.92 x 10-19
J]
(b) How fast is it going when it gets there? [ 2.05 x 106
m/s]
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20-B10 (Inspired
by)
An electron beam strikes a
target electrode in a diagnostic x-ray machine used to take
pictures of broken bones. Very little of the energy of the
electron beam forms penetrating radiation; most is wasted as
heat so that anode heating is a problem. A common solution to
this problem for a short burst of x-rays is to spin the anode
about an axis parallel to but offset from the electron beam.
Given: One tube manufacturer suggests a 2.5 A beam at
75 kV and says that average heat dissipation over a minute
is 870 W.
Find: (a) What is the power consumed by the x-ray tube while the
beam current is on? [ 188 kW]
(b) If all of the energy were to converted to heat, what would
be the average current over a minute that could be tolerated by
this tube.[ 124 mA]
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-21-A8 (Rewritten
with a part added.)
A inexpensive string of Christmas tree lights uses only
one wire to connect each bulb to the next. Unfortunately, since
they are connected in series, if one bulb goes out, they all go
out.
Given: There are 12 bulbs in series connected to a 120 V source.
When lit, each bulb consumes 7.5 W of power.
Find: (a) When lit, what is the voltage across each bulb? [ 10
V]
(b) When lit, what is the resistance of each bulb? [ 13.3 Ω]
(c) If one bulb goes out, what is the voltage across that bulb?
[ 120 V]
(d) With one bulb burned out, what is the voltage across each of
the remaining bulbs? [ 0 V ]
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-B10 (Sister.)
Consider a circuit that consists of a battery and four
resistors connected as shown at the left.
Given: The battery has an emf of 150 V and an internal
resistance of 3 Ω. The resistors have values of R1=
5 Ω, R2= 6 Ω, R3= 12 Ω,
and R4= 4 Ω.
Find: (a) What is the current that passes through R1?
[ 15 A ]
(b) What is the terminal voltage of the battery? [ 105 V ]
(c) What is the power dissipated by R2? [ 150 W ]
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21-B17
(Sister.)
The most commonly used
analog electrical meter is based on the electromechanical
D’Arsonval meter movement. Invented in 1882 by Jaques-Arsčne
d'Arsonval, a French biologist, it is based on a coil
very fine wire that is placed in a magnetic field. As we shall
see in the next chapter after the exam, it only takes tiny
current in the coil to make the pointer rotate against a pair of
tiny little coil springs. The angle of rotation is then
proportional to the current in the coil. Too much current,
however, will burn out the coil. Used as a voltmeter, the
d’Arsonval meter coil is connected in series with a current
limiting resistor. Used as an ammeter, the meter coil is
connected parallel with a shunt resistor.
Given: Full scale deflection of the meter is caused by a current
of 350 µA. Used as a voltmeter, it needs to measure
10 V. Used as an ammeter with 0.0450 Ω shunt
resistor, it will read full scale at 5 A,
Find: (a) What value of current limiting resistor is needed?
[ 28 kΩ ]
(b) How much resistance does the coil have? [ 640 Ω ] |
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