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