Capacitance and Circuits Questions I have a homework that I need in 1 day Name: Lab Day/Time: Homework 5 Capacitance and Circuits Homework is due at the be

Capacitance and Circuits Questions I have a homework that I need in 1 day Name:
Lab Day/Time:
Homework 5 Capacitance and Circuits
Homework is due at the beginning of the Wednesday lecture. It must be handwritten, not typeset. The multiplechoice answers must be circled. In the space after the problem, a short justification of each multiple-choice the
answer must be included. The open-response answers must be worked out clearly using good physics presentation
and will be graded on correctness and how carefully the work is explained. The problems should be worked in
the space after the problem on the assignment printout; additional paper may be used if needed. No credit will
be given for answers without appropriate supporting work. Minimum good presentation requires the following:
(1) Symbolic expression for any formula, (2) Manipulation of symbolic expressions, not numeric expressions, (3)
Substitution of numbers with units, (4) Reporting final answers with correct units and vector expressions, (5)
Enough English description to allow the reader to have some idea what you are doing without looking at the
math.
Multiple Choice Problems
The questions in this section are to be answered by circling the correct multiple-choice answer AND
providing a short justification of your answer in the space after the problem..
Homework Problem 5.1 A capacitor has capacitance C with air filling the space between the capacitor plates. If
a dielectric with dielectric constant ? = 2 is inserted between the plates so that the dielectric material completely
fills the space between the plates, what is the new capacitance of the capacitor?
Select One of the Following:
(a) C
(b) 2C
(c) 4C
(d) C/2
(e) C/4
Homework Problem 5.2 You build a parallel plate capacitor with aluminum foil and plastic wrap (guess ? = 1.5
and thickness d = 0.05mm) as the dielectric. You charge the capacitor to 100V. How much plate area is required
to store 50J of energy?
Select One of the Following:
(a) 7 × 107 m2
(b) 3 × 105 m2
(c) 4 × 104 m2
(d) 2 × 102 m2
(e) 3 × 10?2 m2
1
Homework Problem 5.3 A carbon nanotube is a cylindrical tube formed of carbon atoms bonded into a hollow
circular cylinder. The typical cross-sectional radius of a carbon nanotube is 0.7nm = 7×10?10 m. A typical length
for a carbon nanotube is 50µm = 5 × 10?5 m. The resistivity of a carbon nanotube is 1 × 10?6 ?m. Compute
the resistance of a carbon nanotube along it long dimension.
Select One of the Following:
(a) 8 × 106 ?
(b) 1 × 108 ?
(c) 8 × 102 ?
(d) 2 × 105 ?
(e) 3 × 107 ?
Homework Problem 5.4 The figure to the right shows three
points in an electric field. The potentials of the points obey the
relationship VA > VB > VC . The potential decreases uniformly
from points A to C. A positively charged particle is constrained
to move along the line drawn. If the particle is released from rest
at point B, which of the following best describes its motion?
A
Select One of the Following:
(a) The particle stays at rest at point B.
(b) The particle moves toward point A with constant speed.
(c) The particle moves toward point A with decreasing speed.
(d) The particle moves toward point A with increasing speed.
(e) The particle moves toward point C at a constant speed.
(f) The particle moves toward point C with decreasing speed.
(g) The particle moves toward point C with increasing speed.
2
B
C
Homework Problem 5.5 The electric potential in a region of space has the value
V (z) = ?z + ? cos(kz)
where ?, k, and ? are constants. Compute the electric field in this region.
Select One of the Following:
2
~ = ?( ?z + ? sin(kz))z?
(a) E
2
k
~
(b) E = ?(?z + ? cos(kz))z?
~ = ?z(?z + ? sin(kz))z?
(c) E
~ = ?(? ? ?k sin(kz))z?
(d) E
~ = ?(? ? ? sin(kz))z?
(e) E
2
~ = ?( ?z + ? sin(kz))z?
(f) E
2
Homework Problem 5.6 The capacitors in a coilgun found on the internet are 600µF with maximum voltage
800V. What is the maximum energy one of these capacitors can contain? Assume two significant figures.
Select One of the Following:
(a) 96J
(b) 190J
(c) 0.12J
(d) 0.24J
Homework Problem 5.7 The world’s largest Van de Graaff generator, on display at Boston’s Museum of Science,
has a radius of 2.25m and can produce a voltage of 2.0MV = 2.0 × 106 V. Modeling the generator as an isolated
conducting sphere, compute the energy stored in the Van de Graaff. It is probably easiest to compute the energy
from the capacitance.
Select One of the Following:
(a) 300J
(b) 10J
(c) 2000J
(d) 1000J
(e) 500J
3
Homework Problem 5.8 A 2.0µF parallel plate capacitor of separation 2.0mm is connected to a 6.0V battery.
A dielectric slab of dielectric constant ? = 3.0 is inserted between the plates (with the battery still connected)
so as to fill the space between the plates. How much energy is stored on the capacitor plates when the dielectric
slab is in place?
(a) 36µJ
(b) 12µJ
(c) 110µJ
(d) 24µJ
(e) 48µJ
Homework Problem 5.9 A parallel-plate capacitor with circular plates of radius r and separation d has capacitance
C. If the radius of the plates is doubled to 2r and the separation of the plates is doubled to 2d, what is the new
capacitance in terms of the original capacitance C?
Select One of the Following:
(a) C
(b) 2C
(c) 4C
(d) 8C
(e) C/2
(f) C/4
4
Homework Problem 5.10 A positive point charge with charge
+Q is placed and held inside a cavity in a neutral conductor as
drawn. No charge is transferred to the conductor as the point
charge is placed. The conductor is then grounded. Is there a
non-zero electric field outside the conductor after grounding? If
there is, what is the direction of the electric field outside of the
conductor after grounding?
conductor
Select One of the Following:
(a) The electric field outside the conductor is zero.
(b) The electric field points generally away from the conductor.
(c) The electric field points generally toward the conductor.
5
+Q
Open Response Questions
Homework Problem 5.11 A parallel plate capacitor is shown to the right. The capacitor is formed by
two conducting plates connected to terminals a and
b. The plates have plate area A. Between the two
plates is a dielectric with dielectric constant ? and
thickness d? and a third conductor with thickness
dc . There is an airspace of thickness da between the
conductor and plate b. Compute the capacitance of
the system. Carefully show all intermediate steps
in the calculation and provide appropriate English
description of the calculation. Label the sign of the
charges you introduce and draw the electric field
with ? = 2. Leave ? symbolic in your calculation.
plate b
plate a
a
dielectric
d?
6
conductor
dc
air
b
da
Homework Problem 5.12 A spherical capacitor is formed
from an inner conducting sphere of radius a = 10cm, a dielectric shell with inner radius b = 15cm and outer radius
c = 20cm, and an outer conducting shell with inner radius
d = 25cm. The dielectric shell has dielectric constant ? = 3.
For the computation of the capacitance, assume an arbitrary
charge of Q on the inner conductor and ?Q on the outer
conductor.
(a)Compute the potential difference across region I,
?VI , in terms of Q.
Conductor
Air
Dielectric
Air
Conductor
(b)Compute the potential difference across region II,
?VII , in terms of Q.
I
(c)Compute the potential difference across region III,
?VIII , in terms of Q.
II
III
(d)Compute the capacitance between the inner and
outer conductor, both symbolically and numerically.
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