FinalExam2009spring - Final
Exam
2049H
 
 
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Unformatted text preview: Final
Exam
2049H
 
 
 Name:
 
 
 
 
 
 1
 2
 
 3
 
 4
 
 5
 
 6
 
 7
 
 8
 
 
 Complex
Impedance
 
 1 
 Capacitor:
 ,
Inductor:
 iω L iω C Problem
1
 
 True
or
False
Questions
 
 (a) Flux
of
Magnetic
field
through
any
closed
surface
is
zero.
 
 
 
 (b) Magnetic
field
can
be
used
to
change
the
energy
of
charged
particles.
 
 
 
 (c) A
straight
current‐carrying
wire
has
a
finite
inductance.
 
 
 
 (d) Inductors
can
store
energy.
 
 
 
 (e) Electric
field
inside
an
ohmic
resistor
wire
is
directly
proportional
to
current
 through
it.
 
 
 
 Problem
2
 
 At
t
=
0,
a
charged
particle
with
charge
of
q
sits
at
(0,0,0)=(x,y,z).

At
this
point,
an
 electric
field
pointing
in
x
direction
is
turned
on.

The
magnitude
of
electric
field
is
E.

 [
 E = ( E, 0, 0 ) ]
 
 (a) Write
force
on
the
particle
in
the
vector
form
 (b) Find
acceleration
in
vector
form
 (c) Find
the
location
of
the
particle
at
t=tf
 
 
 
 
 Problem
3
 
 A
charged
particle
with
charge
of
q
has
been
accelerated
through
a
potential
drop
of
 1000
V.

After
this
initial
potential
drop,
the
particle
does
not
experience
any
force
 due
to
electric
field.

You
may
assume
that
the
particle
is
moving
from
left
to
right.
 
 (a)
Calculate
the
energy
of
the
particle.

1
eV
=
1.6×10‐19
J.

 (b)
Calculate
its
velocity
if
the
mass
of
the
particle
is
given
by
m.


 
 After
a
while,
the
charged
particle
enters
a
space
with
magnetic
field,
which
is
 pointed
perpendicular
to
the
direction
of
its
motion.

The
magnitude
of
magnetic
 field
is
1
Tesla
and
is
pointed
out
of
the
paper.
 
 (c)
Calculate
the
force
on
the
particle
due
to
magnetic
field.
 (d)
Calculate
the
magnitude
of
velocity
of
the
particle
in
this
magnetic
field.
 (e)
Draw
the
motion
of
the
particle
in
magnetic
field.
 (f)
Does
the
magnetic
field
change
the
energy
of
the
particle?
 
 Problem
4

 
 Uniformly
Charged
Solid
Sphere
(note
it
is
not
metallic)
has
radius
R
and
volume
 charge
density
ρ.


 
 Calculate
electric
field
(its
dependence
on
 r)
 (a) for
outside
the
sphere

 (b) for
inside
the
sphere

 
 Calculate
potential
(its
dependence
on
r)
 (c)
for
outside
the
sphere

 (d) for
inside
the
sphere

 
 (e) Does
potential
vary
inside
the
 sphere?


 
 
 Problem
5
 
 A
parallel
plate
capacitor
has
been
charged
so
that
one
plate
 has
a
charge
of
1
coulomb
and
the
other
plate
has
a
charge
of
 ‐1
coulomb.


The
distance
between
the
plates
is
1m
and
the
 area
of
each
plate
is
1
m2.



 
 (a) Calculate
the
electric
field
inside
the
capacitor
 assuming
that
there
is
no
fringe
field.


 (b) Calculate
the
potential
difference
between
the
plates
 (c) Calculate
the
capacitance
of
the
parallel
plate
capacitor
 (d) What
is
the
energy
stored
in
the
capacitor?
 (e) 
What
happens
to
the
voltage
difference
if
the
distance
between
the
plates
is
 reduced
to
0.1
m.
 (f) If
the
space
between
the
plates
are
filled
(completely)
by
a
material
with
 dielectric
constant
of
4.
 
 Problem
6
 
 Given
a
series
RLC
circuit
as
drawn
and
an
oscillating
driving
voltage
answer
 following
questions.

 V (t ) = Vmax cos(ω t ) 
 
 (a) Calculate
the
total
impedance
of
the
circuit
 (b) What
is
the
expression
for
the
phase
of
the
current
through
the
circuit
with
 respect
to
the
driving
voltage?

You
can
assume
 I (t ) = I max cos(ω t − φ ) .
 (c) Draw
a
graph
for
power
delivered
versus
driving
frequency
for
the
circuit.

 Be
sure
to
define
x
axis
as
frequency,
y
axis
as
power
delivered
and
clearly
 indicate
the
maximum
power
delivered.
 (d) Draw
a
graph
for
the
phase
of
the
current
with
respect
to
the
voltage.
 (e) Calculate
the
frequency
at
which
power
delivered
to
the
circuit
is
maximized.
 
 
 Problem
7
 
 A
solenoid
has
a
length
l,
N
total
coils
and
cross
sectional
area
of
A
(πR2)
 
 (a) Calculate
the
inductance
of
this
solenoid
 (b) If
a
current,
I,
flows
through
the
solenoid,
how
much
energy
is
stored
in
the
 solenoid?
 (c) What
is
the
voltage
drop
across
the
inductor
when
there
is
no
change
in
 current?
 (d) What
happens
to
the
voltage
drop
across
the
inductor
when
the
current
is
 changed
at
a
pace
of
α
amperes
per
second?
 
 
 
 
 
 Problem
8
 Calculate
I1
and
I2
in
the
circuit
 shown
left.
 
 
 
 ...
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