Name:
Lab Day/Time:
Monday Homework 6 Capacitance
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..
Monday Homework Problem 6.1 Consider a capacitor with capacitance C charged with a battery so that one
of the capacitor plates has a charge Q. After charging, the battery is disconnected. The capacitor has potential
energy U . If the capacitance is increased to 2C while the charge on the plates is undisturbed, what is the new
energy of the capacitor in terms of the original energy U ?
Select One of the Following:
(a) U
(b) 2U
(c) 4U
(d) U/2
(e) U/4
Monday Homework Problem 6.2 A parallel-plate capacitor with plate area A and plate spacing d is charged to
a potential difference ∆V by a connection to a battery. If the plate area is increased to 2A while the potential
difference and the separation stay the same, what happens to the charge stored on one capacitor plate as the area
is increased?
Select One of the Following:
(a) The charge increases.
(b) The charge decreases.
(c) The charge charge stays the same.
Monday Homework Problem 6.3 You build a parallel plate capacitor with aluminum foil and plastic wrap (guess
κ = 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
Monday Homework Problem 6.4 A positively charged particle is
placed at the point A in the figure to the right. Select the direction
the particle will move if released at point A. Equipotential lines
are drawn and the potential of each is labelled. The potential
changes smoothly between the equipotentials.
10V
Select One of the Following:
(a) +x̂
A
(b) −x̂
3V
y
(c) +ŷ
(d) −ŷ
(e) The charge will not move.
1V
x
(f) The direction of motion cannot be determined.
Monday Homework Problem 6.5 The European High Magnetic Field Laboratory claims to have the world’s
largest capacitor bank. The bank can hold 50MJ = 5.0 × 107 J of energy when charged to a voltage of 24, 000V.
What is the capacitance of the capacitor bank?
Select One of the Following:
(a) 3.6 × 10−3 F
(b) 0.088F
(c) 0.17F
(d) 23F
(e) 4, 200F
Monday Homework Problem 6.6 A 2µF parallel-plate capacitor with plate separation 2.0mm is connected to
a 6V battery. What is the electric field between the plates when the system is in equilibrium?
Select One of the Following:
(a) 1 × 10−2 N
C
(b) 1 N
C
(c) 50N/C
(d) 3000N/C
(e) 6000N/C
2
Monday Homework Problem 6.7 To exploit the properties
of different dielectric materials, a capacitor is made out of
three layers of dielectric as shown to the right. The two
outer layers have the same thickness, ℓ1 = 1.0 × 10−4 m. The
central layer has thicknes ℓ2 = 5.0×10−5 m. The total area of
one of the conducting plates which surround the dielectric is
3.0m2 . Each layer has a different dielectric constant κ1 = 3.2,
κ2 = 9.0, and κ3 = 5.5. What is the capacitance, Cab of the
system?
Select One of the Following:
a
Conductor
κ1
κ2
(a) 0.48µF
κ3
(b) 1.6µF
(c) 4.9µF
Conductor
b
(d) 43µF
(e) 310µF
Monday Homework Problem 6.8 In a region of space, the electric potential is constant and positive. What can
be inferred about the electric field in the region?
Select One of the Following:
(a) The electric field is zero.
(b) The electric field is positive.
(c) The electric field is negative.
(d) Nothing can be inferred about the electric field.
Monday Homework Problem 6.9 The electric field points to
Select One of the Following:
(a) lower
(b) higher
(c) equal
(d) There is no relation between field direction and the change in potential.
3
electric potential.
Monday Homework Problem 6.10 Select the inequality for
the potential at the points A, B, C, and D based on the
electric field map.
A
Select One of the Following:
(a) VC > VB > VA > VD
(b) VC = VD > VB > VA
D
(c) VB > VA > VD > VC
(d) VD > VA > VB > VC
B
(e) VB > VC > VD > VA
(f) VC > VB > VD > VA
(g) VC = VD > VA = VB
(h) VA = VB = VC = VD
4
C
Name:
Lab Day/Time:
Wednesday Homework 6 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..
Wednesday Homework Problem 6.1 An iron beam is 20m long and has rectangular cross-section of width
10cm and height 20cm. Iron has a resistivity of 9.7 × 10−8 Ωm. How much current would flow through the beam
if 120V were applied across the 20m length of the beam?
Select One of the Following:
(a) 8.1 × 10−7 A
(b) 2.5 × 107 A
(c) .5 × 10−7 A
(d) 6.2 × 106 A
(e) 1.2 × 106 A
Wednesday Homework Problem 6.2 In the resistance network
to the right, all resistors are 2Ω and the battery is 6V. Calculate
the potential difference across R3 .
R1
Select One of the Following:
(a) 65 V
(b) 85 V
R2
(c) 3V
(d) 2V
(e) 6V
R4
1
R3
Wednesday Homework Problem 6.3 When a light bulb burns out, current can no longer pass through the light
bulb. If you have a string of Christmas tree lights, and all the lights go out when one light burns out, which of
the following most likely describes how the lights are wired?
Select One of the Following:
(a) series
(b) parallel
Wednesday Homework Problem 6.4 The figure below shows a circuit containing identical light bulbs. When
the switch is closed, how does the brightness of bulb BA change? Assume a perfect battery.
Select One of the Following:
(a) The brightness of BA increases.
(b) The brightness of BA decreases.
(c) The brightness of BA stays the same.
BA
2
Wednesday Homework Problem 6.5 The circuit to the right
contains a battery, an ammeter, and a collection of resistors.
What happens to the potential difference across R2 if R5 is increased?
R4
Select One of the Following:
R5
c
d
R6
(a) The potential difference increases.
(b) The potential difference decreases.
(c) The potential difference stays the same.
R2
R3
R7
b
R1
a
3
A
+
_
V
e
Open Response Questions
Wednesday Homework Problem 6.6 For the circuit below, R1 = 3.0Ω, R2 = 6.0Ω, R3 = 6.0Ω, R4 = 3.0Ω,
and R5 = 3.0Ω, and ∆V0 = 9.0V. To receive any IBC for this problem, your symbolic work must clearly express
your method.
(a)What is the equivalent resistance of the network?
(b)What is the voltage across R5 ?
(c)What is the current through R1 ?
(d)How much power is dissipated in R3 ?
R1
R2
R3
R5
R4
∆V0
4
Wednesday Homework Problem 6.7 In the circuit at the right,
∆V = 12V, R1 = 1Ω, R2 = 3Ω, R3 = 6Ω, R4 = 2Ω, and
R5 = 2Ω.
R1
(a)Compute the equivalent resistance of the circuit.
R5
∆V
(b)Compute the current delivered by the battery.
(c)Compute the power consumed by R1 .
R4
(d)Compute the current through R3 .
(e)Compute the voltage across R4 .
5
R2
R3
Wednesday Homework Problem 6.8 A conducting sphere of
radius a = 5cm is surrounded by a dielectric shell, with constant
dielectric κ = 5, inner radius b = 10cm, and outer radius c =
15cm. The system is shown to the right.
Dielectric
(a)Compute the capacitance between the conductor and
ground. Report both the symbolic value and a numeric
value. Clearly report and label any intermediate quantities used to get your result and carefully show your work.
(b)If the conductor has a potential difference of 100V with
the ground, what charge is on the conductor?
(c)What is the energy of the system if the potential difference between the inner conductor and ground is 100V?
6
Conductor
a
c
b
7
air
conductor
conductor
a
dielectric
plate b
plate a
dielectric
Wednesday Homework Problem 6.9 A parallelplate 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 = 25m2 . Between the two plates are two layers
of dielectric with dielectric constant κ = 3.2 and
two layers of conductor. There is an airspace between the two conducting layers. Both conducting
layers, dielectric layers, and the airspace have thicknesses d = 1.0mm. Compute the capacitance of
the system. Carefully show all intermediate steps
in the calculation and provide appropriate English
description of the calculation. Report both a full
symbolic formula for the capacitance and a numeric
value. There is no need to draw the field map unless
it would help you in the calculation. This problem
must be worked starting with the fields; a solution
involving some combination of capacitors will not
be accepted.
b
...

Purchase answer to see full
attachment