Unit 9. Electrostatic
Bil: Idea
FOITCS
1: Ohjl'ets
and
and
systems
Name:
Cirenits
have
pnlperties
internal
strnetnre.
Essential Knowledl:e
LB. 1: Electric charge is
conserved. The net charge of a system is equal
to the slim of the charges of all the ohjects in
the system.
a. An electrical current is a movement of
charge through a conductor.
b. A circuit is a closcd loop of elcctrical
current.
sneh
as mass
3: The
intentctions
of an object
eharl:e.
Systems
may
have
Learning
Ohjeetive (LB.LI):
The SltH..Icnt is able to make claims about natural phenomena
based on conservation
of electric charge.
Learning
Ohjective
(LB.1.2):
The student is able to make predictions, using the conservation
of electric charge, about the sign and relative quantity of net
charge of objects or systems allcr various charging processes.
including conservation
Essential Knowledl:e
I.B.2: Thcrc arc only two kinds of electric
charge. Neutral objects or systems contain equal quantities of
positive and negative charge, with the exception of some
fundamental particles that have no electric charge.
a. Likc-charged objects and systcms rcpel, and unlikc chargcd
objects and systems attract.
Essential Knowledge
I.B.3: Thc smallcst observed unit of charge
that can be isolated is the electron charge. also known as the
elementary charge.
19
a. The maguitude of thc elementary charge is equal to 1.6 x 10
coulombs.
b. Electrons have a negative elementary charge; protons have a
positive elementary charge of eqllalmagnitllde.
although the mass of
a protoll is much larger than the lllass of an electron.
Big Idea
and
-----------------
with
other
objects
of chan~e in simnlc circuits.
Learning
Obil'etin
(LB.2.1):
Thc student is able to construct an
cxplanation of the two-chargc model of
electric charge based 011 evidence produced
through scienlilic practices.
Learning OhjeetiH'
(1.11.3.1):
The student is able to challenge thc claim
that an electric charge smaller than the
elementary charge has been isolated.
can
he deserihed
by forces.
Learning
ObjeetiH'
(3.C2.t):
Essential Knowledge
3.C2: Electric force results from the
The student is able to usc Coulomb's
law
interaction of one ohject that has an electric charge with another
qualitatively
and
quantitatively
to
make
object that has an electric charge.
predictions about the intcraction between
a. Elcctric forces dominate the propel1ics of the objects in our
two electric noint charges.
everyday experiences.
However. the large number of particle
Learning
Objectin
(3.C2.2):
interactions that occur make it more convenient to treat everyday
The student is ablc to connect thc concepts
tClrces in terms ofnonfundamcntal
forces called contact forces, such
of gravitational
force and electric force to
as normal liJrce. n.iction. and tension.
compare similarities and differences
b. Electric forces may be attractive or repulsive, depending upon the
between the forces.
charges on the objects involved.
Big Idea 5: Changes
that occur as a result of interactions
arc constrained
by consen'ation
laws.
Esscntial Knowll'''ge
5.B.9: Kirchhoff's
loop
rule describes conservation
of energy in
electrical circuits.
3. Energy changes in simple electrical
circuits
arc conveniently
represented in terms of energy
change per charge moving through a battery and
a resistor.
b. Sincc electric potcntial dinercncc timcs
charge is energy, and energy is conserved, the
stun of the potcntial dinercnces
about any
closed loop must add to zero.
c. Tile electric potential ditlcrence across a
Learninl: Objective
(5.B.9.1):
The student is able to construct or interprct a graph of the
energy changes within an electrical circuit with only a single
battery and resistors in series and/or in, at most, one parallel
branch as an application of the conservation
of energy
(Kirchhotrs
loon nile).
Learning
Ohjective (5.B.9.2):
The student is able to apply conservation of cnergy concepts to
the design of an experiment that will demonstrate the validity of
Kirchholls
loop rule (LV; 0) in a circuit with only a battery
and resistors either in series or in, at most. one pair of parallel
branches.
Prol~
icient
Unit 9. Elcctl"Ostatic
ForTcs
and
Namc:
Circuits
Learning
Ohjective (S.B.9.3):
The student is able to apply conservation of encrgy (Kirchhoffs
loop rule) in ealeulations involving the total electric potential
dilTcrence for complete circuit loops with only a single battery
and resistors in series and/or in, at most, olle parallel branch.
resistor is given by the product of the currcnt
and the resistance.
d. The rate at which energy is transferred from a
resistor is equal to the product of the electric
potential difference across the resistor and the
currcnt through the resistor
ESSl'ntial Knowledge 5.C.3:
Ki rch hoff s junction rule
describes the conservation
of
electric charge in electrical
circuits. Since charge is
Learning
Ohjective (S.C.3.1):
The student is able to apply conservation of electric charge (Kirchhoffs
junction
rulc) to the comparison of electric current in various segments of an electrical
circuit with a single battery and resistors in series and in. at most, Olle parallel
branch and predict how those vaiues would change ifconfigurations
of the circuit
conserved. current must be
conserved at eachjullctioll
ill
are changed.
the circuit.
The student is able to design an investigation
Examples
should
include circuits that combine
resistors
parallel
in series and
-----------------
Learning
Ohjeeth.e
(S.C.J.2):
more resistors ill which cvidence
collected and analyzed.
of an electrical circuit with one or
of conscrvation
of electric charge can be
Lea •.••ing Ohjeetive (5.C.J.3):
Thc studcnt is able to use a description or schematic diagram of an clectrical circuit
to calculate unknown values of current in various segments or branches of the
circuit.
Electrostatics
Reading Assignment:
Read Chapter
20 sections 1 - 3 (the rest of the chapter and chapter 21 is HIGHLY recommended
continue in future physics class but not required for AI' Physics I)
As you read answer all Stop to Think ,!uestions (Cheek your answers on page 664) and work
problems.
I.
J.
thmugh
if you will
all example
Below is a list of what you necd to t.Ollieaway frol11 )'our I.eading.
Deline:
a.
conductor
b.
charge conscrvation
c.
electrostat;c
d.
electrically
e.
electric
"2.
reading
and insulator
equilibrium
neutral
f(m~c
Coulomb's
Law
Know:
a.
the direction
of electric
forces I,)r objects
b,
thc magnitude
c,
the unit lor charge
ci,
why mctals are conductors
e,
the equation
of charge on an electron,
for Coulomb's
with like charge,
unlike charge
proton
law in terms of magnitude
and direction
Ill' ahle to:
n.
explain
what happens
to the negative
charges
in a conductor
when a positively
charged object is held nearby.
h.
cxp1:lin what happens
to the negative
charges
in an insulator
when a positively
charged object is held nearby.
c.
how objects acquire
d.
in terms of f()rces. why the glass bead accelerates
a positive
charge
if the protons
are fixed ill the nucleus of the atoms.
up toward the plastic bead in example
20.5.
Unit 9. Electrostatic
Circuits
Forces
Name:
and Circuits
_
Rt.'ading Assignment:
Read Chapter 22 (all sectioos) and Chapter
your answers
23 st'ctions I - 5. As you rcad answer all Stop to Thiok 'Ioestions (Check
011 pag<.~726~7(3) ~lIId wurli: thnHlgh
all example
prohlems.
Below is a list or what you need to talit.'
away frolll your reading.
I.
Defioe/Know
h.
terminal voltage
b. direction of current
J.
the meaning
c.
.I.
series connection
k.
I.
m.
n.
parallel coooection
a.
electric current
junction
d. emf
e. resistance (& units)
f. resistivity
g.
2.
ohm's
law
used
ill
a circuit diagram
ammeter
voltmeter
kilowall hour
Explain:
a.
What creates current in a wire
b.
why current entering
c.
The I:lctors that affect resistance
d.
what type of energy is dissipatcd
e.
Kirehhoffs
Junction
f.
Kirchhofr
s loop law
g.
what happens to the magnitude
of current when it flows through a resistor
h.
what happens
of the potential
I.
why the bulbs are equally bright in example
J.
why the bulbs in ligure 23.5 are all equally bright
k.
why balteries
1.
how a ammeter
a light bulb = current leaving a light bulb
at a resistor and why that results in a potential
drop at a resistor
law
to the magnitude
when it !lows through a resistor
23.2, but in figure 23.8 bulbs I3&C are dimmer than bulb A.
drain faster in a parallel circuit than in a series circuit
and voltmeter
nl. the steps for analyzing
3.
of symbols
should be connccted
a complcx
in a circuit
circuit
Be able to:
a.
calculate
current (in tcrms of charge and timc)
b.
calculate
current (in terms of voltage and current)
c.
calculatc
resistancc
(in tcrms of voltage and current)
d.
calculate
resistance
(in terms of resistivity,
e.
caleulate
power
f.
calculate
the cquivalcnt
(total) resistance
ofscries
g.
calculate
the equivalent
(total) resistance
of parallel resistors
h.
draw a circuit with an ammeter
I.
analyze a complete
length and area)
and voltmeter
resistors
connected
properly
circuit and solve for currcn!' voltage and resistance
J.
calculate
the equivalent
(total) capacitance
of series capacitors
k.
calculate
the equivalent
(tolal) capacitance
of parallel capacitors
at any point
Electrostatics
1.
Problems
Two lightweight
balls hang straight down when both are neutral. They are close enough together
to interact, but not close enough to touch.
a.
Both are touched with a plastic rod that was
T"
rubbed with wool.
@
b.
Draw pictures showing how the balls hang if:
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@
~
~
~
t>':WJ}.
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A
Ball A is touched by a plastic rod that was
rubbed with wool and ball B is touched by a
eO\...C\r....o~
glass rod that was rubbed with silk.
~ if
c.
1w'OXd.
ynove
Both are charged by a plastic rod, but ball A is
T""'\.
charged more than ball B.
YY\S:)Vi(
@
d.
~
S~
l~
ClVV\.~
bv-k~fl<%l1<-)
Ball A is charged by a plastic rod. Ball B is
neutral.
7
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pO.lM"-~~
@~
2.
~
(tII\I~
..to..c..h ~
~
r\J2M.~
-m
~
Io~.
After combing your hair briskly, the comb will pick up small pieces of paper.
a.
b.
rl?~ ~~~ ~
Is the comb charged?
How do you know?
How can you be sure that it isn't the paper that is charged?
~-ur5
VULNtrecQ
-~
c.
,?\~~
V-{)
Is your hair charged after being combed?
~,
d.
~
12'1,w-&
Io.A--r
'}
lorv\b.
Propose an experiment
c.C'v\A-~
'?~'
to test this.
.e.-l-e.c)-ric frwc-e.
wl~
~~'!.u-r.
What evidence do you have for your answer?
crppu ~tk ~
LOrv\--b.
What kind of charge is the comb likely to have? Why?
YV\.<XN?
1- - 3.
A negatively charged electroscope
a.
Suppose you bring a negatively charged rod close to the top of the electroscope,
touching.
b.
has separated leaves.
How will the leaves respond?
but not
Use diagrams and words to explain.
How will the leaves respond if you bring a positive charged rod close to the top of the
electroscope,
but not touching?
~cuJt)
Use both charge diagrams and words to explain.
(,\jll ( ~
c1o~('
B
Elcctrostatics
4.
Problcms
Metal sphere A is initially neutral.
A positively charges rod is brought near, but not touching.
Is a now positive, negative or neutral?
5.
Metal spheres A and B are initially neutral and are touching.
brought near A, but not touching.
6.
Explain
Is A now positive, negative, or neutral?
Metal sphere A is initially neutral. It is connected
7.
Explain.
by a metal wire to the ground.
positively charged rod is brought near, but not touching.
neutral?
A positively charged rod is
A
A
Is A now positive, negative, or
Explain.
A lightweight,
positively charged ball and a neutral metal rod hang by threads.
close but not touching.
They are
A positively charged rod is held close to, but not touching, the
hanging rod on the end opposite the ball.
a.
+
+
Drawa picture of the final positions of the hanging rod and the ball. Explain your
reasoning.
b.
Suppose the positively charged rod is replaced with a negatively charged rod. Draw a picture of the final
positions of the hanging rod and the ball. Explain your reasoning.
:t- ..-----------.--/'
7;; f, J
8.
B
For each pair of charges, draw a force vector on each charge to show the electric force acting on that charge.
The length of each vector should be proportional
represents the same quantity
of charge.
<-0
8--"
~O
e~++
~
++
to the magnitude
L
(]
e-
T
of the force.
Each + and - symbol
Elcctmstatics
9.
Problems
What change in the number electrons would give an object the following
a. + H?
b. -2~C
c.
+8 ~C
d.
\o!rt-.
lJ>.1.'5).
\\JIS
-3.2~C
:It"
.1\
\.1-6'1:\o'~ '3~
S ~\O'~ to!rt7.lC.\0'~
charge?
e\-e(.,~~ -=
0~cl..
~c.When
10. A marble is given a charge of +2.1~C, and a super-ball is given a charge of .7.0
they are separated by
52 mm, what is the electrical force between them?
't,~ +2.\~~~"C
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+~
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(C;;'l..)qD~)""
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---
(' :: 6'2.)C \0 r'"
\<-.",q'f-\Oil.
In a Coulomb style experiment
~c.
2 pith balls of the same mass are given equal but opposite charges of 0.014
When separated by a distance of lO-cm, what is the electrical force between them?
C
°.
'l -:..ol't,110" C
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=
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is rubbed vigorously through someone's hair, pulling electrons from the hair and depositing them
upon the balloon. If the balloon's charge is .2.00-~C, what is the electrical force between the balloon and THE
'1 _
'""e.erson's
'it --,,~:~:- "c
'l.
head when they are separated by a distance of 3.0'cm?
t:~f:-l :f.'t7l
y.;::'I l'ID 'l:L4.
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,,~=--q)(..:...JO_~\_l_'2_l' 1_0_- "'_X_"2.X_ _ -_")_
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r:: -: ")15. Two 25.0 g spheres are hanging from lightweight
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lSlc~\D") 'l...-= ~
-
\'61<0
strings that are each 35.0 cm in length.
r
r=
-=-F
1
'3~'l
Each has the
same charge. They repel each other and make an angle of 5.00° to the vertical.
a.
Drawa free body diagram of each sphere below.~?
e-
'tl\..<.p '3,: •.d, \ {'\Cj .fV~HS
ic~ )( c.if'~LHIfY'~o\,,-(,
'1.'
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N
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Find the distance (in cm) between 2 positively charged spheres (+56~C) if the electrical force between them is
\= =- \ ~~N 186 N.
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'f:-or~IO
-=-
'(3~IO-1.)"2.
-'1.
y--:. '3~ID rY'
to<-
4
(p X 16
of the second charge?
~~I""
,~l'2..'/{'i.\P
..- -::: 2.'2., r; rJ
r "'q~IO"il3. A balloon
""
I
\
-=- I , I
of 15.5 flC is placed 12.8 cm from a second charge. If the force between the charges is 22.5 N, what
i~ the magnitude
1
.OI'i~(Ov)(.OIIi)l:IO-II)
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----(_"')'1.
'(
1"\
\(." q 'f.l~\.A charge
'1. -= 1'5.'5'1\0
_1'1'1:10")'
-- \..
b.
.t='e
'r"
:
'i'
r'
"'1':
<D+: = to"2.S ]( '1. ~,') =
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fiN:!HY\\\~
forte \Ai"") ~t>rt~.0" y- d.i<"< lh"",
~t::'. -= 0 :: 'n, ---\", j
'J r
0
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•
r:...
-l-j -= f'1'.j -::-. .2.45 - ToT (q;5
'J
-= .1."5 - • 'ZH5'l N
+;
~
..
What IS the magl1ltude of the charge on each sphere?~?
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1""y.
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Elee!l'ostatics Problems
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--.
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16. Two small objects, each with a charge of .4.0 nC, are held together by a 0.020 III length of insulating string as
shown in the diagram above. The objects are initially at rest on a horizontal, nonconducting frictionless surfacc.
The effect of gravity on each object due to the other is negligible.
(a) Calculate the tension in the string.
-r -:.re
-= \<- q I 'l2-::
#)
I'The masses of the objects are
(
~)( \0 ) ,,1.'1'1(\0
G) _ \
0.030 kg and
=
1Il2
=
'2 .
lJ,<O'llO-~ N
loO'2.)2-
III I
-1
\'l.
-,
J
0.060 kg. The string is now cut.
(c) Calculate thc magnitude of the initial acceleration of each object.
7..f--;. '0"'0-..
~.to )(10- '1
r~
= (..p:'> ""~
--o-.--::-.-()-\ l...-m-2.-------]
S
.t>~
~
'3. U>'flO -'1
::. ~
:0 fY\ ()..
(, OLo)
ex.
\--fA.--=--. -D-O-l&>-~--1
~
57.
J
(d) On the axes below, qualitatively sketch a graph of the acceleration a of the object of mass
versus the distance d between the objects after the string has been cut.
1Il2
,I
I
J
.0'2..
(e) Describe qualitatively what happens to the speeds of the objects as time increases, assuming that
the objects remain on the horizontal, nonconducting frictionless surface.
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be CVWt-ej
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Current
11doesn't maller !low fJluc!lyou
Worksheet
Problems
wanl. ~.Vhalrea/~r malters is hm~ t11uchyoll Wpnl it. The e).:lent and complex;')' of the problem does
not mailer U'GSmuch as does (he willingness to solve il. -- Ralph ~arston
17.7.45
X
'1~= :l
I~tfiiie
r
-= l'-11F\ \
..~~~~,"')(\.v~\OV)
current in a ctcuit is 0.250 A, how many el ctrons are flowing past a set point in 0.155 second?
q:-\,
-=:.
G~\:.=
-=- ')
'I: -t ""l'2.s')GI'5
~
wi~\:
:tot ~ .~~~~ t
1017 electrons take 0.810 seconds to flow past a point in the circuit. What is the current?
) '" . D 3~'~CJjj: :::
~~~;
'1 -=
t> \ ~
-
'" \-"
-
Q\:1>.....
1.1<>
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19. A wire carries a 4 A current. What is the current n a secon~ire
half the time?
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T::~A.
vVi('~'l.: 1:.9-
-
-b
4 -=
Y'I
.L.
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-
t
20. A''hair drver draws 1.12 A when plugged into a 1
o V circuit.
~ ~ ~
~
,"1
-&- 1..4 2.x.\O e\e~
that delivers tv;' "s1TlUdrchargc III
.
\
What is its resistance?
:: l~
::
[0-,_\ l.t_...cL_---...~
1:..::: \.ILA
21. A light bulb has stamped upon it the Ii.JlIowing in ormation, "60 W 120 V". How much current will flow
through the bulb?
y -==- \'2..0
y
V ='"I:- '/1_
,?:::(c0
w
~
-y; ~
'? _ ~
~
1: - Y -
I=?
22. A hot plate has an internal resistance of22.0
(a) 1.low much current did it draw?
-i.-=-V
1<.::."2.'2J1V=:\ 1...0 y'
1:;:: ~
Q.
\'20
_ l-
1-
-=\.•.....__S P<. ~_\
I operates on 120 V household AC electricity.
::\ S.y
A
2'2
12.
(b) How much power did it develop?
?::: \ V
::: (S.4'S'j( \ 2..0):: LP0~'1.
(c) If it operated for IS minutes. how much heat d d it develop (hint: work done by fr,::ic::t:::io:.:.:n!;.)?:..-_--,
-t~lS"",,('\
0<
v.J'=b -t;;,- _-:;J 1•
,?-::
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9cos
?=
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If a kWh costs 4.5 cents. how much did it cost
y. CO c.eY\..\-S
X • '2.'5
V
X.1t>
0
run the thing?
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23. Is 12 greater than, less than or cqual to II? Explail.
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v.p0-9::.
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Current
Worksheet
Problems
is holt' 1I111ch}'OlllVGllI
nof malle,. was I11l1chas does the willingness 10 sn/l'e it, -- Ralph Marston
II dOeSn'lmoller
hou'lIllich
you want.
What rea/(r
maflcrs
il. The
extent
and complexity of/he prohlell1 does
24. All wires in this figurc are made of the same material and have the same diameter.
Rank in order, tj'omlargest to smallest thc currents II to 14
rt..~~Le
C3~
25. What is thc size of the current in the flHlrth wire? Is the current into or out of
the junction? Explain.
26. What is the resistance of a copper wire, diameter of 1.50 mm and length 25.0 m? (Pc," = I. 72x 1O's Om)
\.5)',lO-;",
A-: ~
= ,t>ooOOl1lP1
L
_ ('1-13
\
c\-:::
L -=- Z. '5
TV')
.•
IZ:: P A -= (1.12.1': I()
1.-\
<i~\
0 I) ClOO II
~--i)
~ :: \ .1'2..)( \0 'l'..o-YY'o
~:
~
27. You have a long wire with resistance R. You would like to ~;;-,~ir~:fIt~an
e length but with a
resistance 2R. Should you (a) changc to a wire of the same diameter but made ofa matcrial having twice
the reisistivity. or (b) change to a wirc made of the same material but with halfthc diameter? Or will
either do? Explain.
A "0:Q.'2..
fl.,: ~
=-) ~ -=-p L+> L
J<,d::.1P <isO ~ ~
p L.- (p(\~~
Y
~
'lTV1~
f> ,~
!::
R:;=
Po
( ~A.Ni<v\
\..
1-
A =
~\
'i\ ( D 1"1.
~. -:. 1\
"~
-tr
L-
~
!V: 2-9 Ii'
~"" x'-l
1<..
A
0h... .
'LE':'WiI'e I a'ij;1wire-~ arc made of the same m'etal and al~lh~ same length. Wire I has tWIce the diameter and
halfthc voltage across its ends. What is thc ratio of ll/h?
l. V
V
tC -::0 ~ :: ~~
~
p
"l...,
T
\ -::: - (2,
__ v,
1:-J2.
_?9. A grap
10
particular
a.
f"
~
\D
'2-
2.
_
••
-=-
f'
0
I
..
f'
vo tage ISglvcn or a
\
111'"""1.
'-t
wire seglllcnt.
1:\
1(1\)
4
What is the resistance of the wire
o-Y...-
"-'
-
I.
3
-
2
b. Sketch and label on the same graph what I vs. L'I V would
look like Illr a wire made of the same material but twice
as long as the wire in part a.
Vi
21<,::.
c.
2.
-VI1-
f \.
CUl'l"elllas a unction
=
I
JL
o
o
II \' (V)
2
4
6
8
10
12
Sketch and label on the same graph what I vs. L'I V would look like for a wire made of the same
material but with twice the cross-sectional area or thc wire in part a.
(7
>-z
Currcnt
Workshcct
Problcms
II doesn'IIIJaller how much you want. tYhat really mailers ;.'1 how much you want if. The ex/e11land complexity (ithe proh/em does
nol mulfer was lI1uch as does fhe willingness to solve if. -- Ralph Marston
30. Rank in order, from largest to smallest, the currents I I to I 4 through these four resistors.
2V
!
-{
+
IV
Q-I --c:=J
2 il
I'\;.~~"i::!\~
+
G--t
Q.
-(
T'2.c~=.S"~,
2V
I
tV
.j-
(1---t -{
Q
J;.-=f-=2I'''
(1---t
IU
I~..,t"l":'
j
I'?, >"1:, :: 1:"'1 >-..t'Z.
31. Two resistors of equal lengths are connected to a battery by ideal wires. The
resistors have the same radii but are made ofdilferent materials and have different
resistivity's p with PI>P2.
a. Is the current II in resistor I larger than, smaller than~e
sam\bls h in resistor
1lJx5Itt~-.+l'\e'i\'61-oY'S
J~
oY\,('D.Ml
~
\r\ ~
lJ'ii~
(.C\\~{J,,)~
C'l\
~
+
2
Y\O
~
')
b. Which of the two resistors diss~)ates the larger amount of power? Explain.
?~1:'JO'i-r:.2.«.
c.
1: M.j.{,o
~~,
k71.P1-(Z, >~2.
~. r<"digb\~
Is the voltage LlV I across resistor I larger than, smaller than, or the same as LlV 2 across res~
Explain.
6V1
'G--t~
,>1::>\/1.
~I
)\<.-2: I ~
~.
%e ~
V=T.t2
32. Redraw the circuits below using standard circuit symbols with only right angle connections.
~."'-_J '"
'~~i@)
-
~\.
2. ~"=~,
-~
~~~"~
~
L"
C;;
: ''rf
~
,~~~~
~"=~==-
~
33. A Ilashlight bulb is connected between two 1.5 V batteries as shown. Does
the bulb light? Why or why not'?
No
I
bR. (A C,ovJ-\ ("'\~
V\.X'c.1M* ~
\.A.CLR.
-'P
C»'t1 ~C".l5I \M
b. Rank in order, tromlargest
RJ.
V=
re.
to s~e~
~
resistances R1, R2, and
_. _
~{1LJ- ''''+1,
~crop-.__
34. Current lin !lows into the three resistor connect togeher one after the other.
The graph shown the value ofthc voltage as a funciton of distance.
a. Is 1Onlgreater than, less than, or cqual to lin? Explain.
ecc
~
V
H,
f,.-~/~A
f' \
~
\
~
CUI'rent Worksheet
It doesn't
Problems
how much YOll want. What really mailers is how much )'Olt \',.'antit. 7'l1e extent and complexity of/he proh/em
n01lJlafler was much as does the willingness to soh:e if. -- Ralph Marston
35. Examine this circuit.
V -::~
malleI'
'«..
a.
Write the Kirchhoff's Loop Rule equation for this circuit.
V€, -
1: I l2., - -:t2.~'Z.- "t:'!>
Ve, ." U.2.)tICC»
b.
e~= t:>
-t~.'2X15)
(\.'2.).'00")
~
l<r~')
What is the total current.
\.1.. A
c.
.
What is the voltage drop at each re.sistor?
(\.2)(
vlOO
100) -:: \20v'
0.'2.)( 'Stij' -::.(pO
Vso
v
'joy
~.'2..Jl.'_S_~_-_-\( ~ -= '2,..-, 0 V
v'S
36. Draw a circ~; for whili.h the Rirchhoff loop rul;'e.a;-'ation is:
n.
6v-ll.2n)-~1.4b)=o
~
Y"
lPV~
(2.,
h.
12 V
Q.1.
-0,. 4n)=
12 V -(I,. 6n~= a
Q,
c.
9V~,.
12..V-
e1.
lZ.,
121.
~~
3q= 9V -tt, . sq.t, . 3'9= a
S~Q2'
Yo
rn
v..
'i",
Yo
'1v.-
lZ,
~
la3
37. For the circuit to the right
a.
Write the Kirchhoffs Loop Rule equation.
1'2.- L.I (2.'5) ~ \'2. -1:1..( 1'5)." 11. b.
Determine current through the circuit
r bCU<::\ =
l?::-
I, t
+
2'5
c.
r~(4'6) = 11. -1:..., (os"'J = 0 12.() V ~
1:2, -\' 1:~l'
J1=..
-t 1'2-
IS
Determine the currenrthat
I_V
-
,,~
I"
12, -
12..
'2..'5 -
= ~2 = -\~
I,,::
-:: [~
--
1'2..
05
goes throu
•
T:::
R
12.(.L
-t
'2.'0
h each resistor
'i 00 A
~-A ~
::::L '" !1- -= \. 2-(,,, Po]
12?,
I,s -
1:.'-1
-t-
"is
n
35.(} n
45.(}
~
V
Lf5
*y"" ~i"\"-.
?>1f A J
Ie
I"
'-+ -'
'is
-t":")
-= 1'2..(.1'51)-=
'3~
\.'1 A
does
Current Worksheet Problems
II doesn', moUer !low much YOli want. What really matters is how much you wanl il. The extent and complexity (~rtheproblem does
not maUer was much as does the willingness to solve it. -- Ralph Marst"' •..
2.-\
38. For the circuit on the right:
a.
Write the Kirchhoff loop rule equation
\1 - r:: ('2.) - 1:('1) -=. '0
I
11 V
\1.-l'2.)("2.) -t~(Lt}=0
Calcuiate the Voltage lost at the 4£1 and 2£1 resistor
b.
in this circuit.
<?
V,
4
c.
V
11 v~
(J: 12.)
V4
:
L
I
HI
~(L)
I
On the graph of voltage vs. location in circuit, graph
the Voltage changes in the circuit.
(J
39. For the circuit to the right:
a.
(p -
b.
r.('i)
-r:("2..; = 0
Calculate the current in the circuit.
lJ::: (pI.::: ';>
c.
1: ::.~
=8
L:
6V
:
-IQ
Calculate the voltage drop at each resistor
V If
:::
r r< .:. (nut) = fYV\
v1. ::. 1: 12 ::
d.
? A
Write the Kirchhoff loop rule equation.
0) ("2.) -=~
On the graph of voltage vs. location in circuit,
graph the Voltage changes in the circuit.
"
"vW
20
}
CU'Tent Worksheet
If doesn',
no/mafla
Problems
malleI' holl' /1/lich YOlf want. What really malleI's
Ivas much as does the willingness 10 solve it. --
40. What is the equivalent
is how much you want il. 71u!e;r/ent and c011lplf!xify
Ralph Marston
resistance of each group of resistors?
I
_
~
t
\JL
-,
i
T-
-
-= ~
:'::'3"
.~
..
""-
(~rthe problem
~\
does
\
l.,
1"?::.
t,
ts>
~t~ \
r.:r;~\~
~l.
.' II!
,.
.t:..f'I
,"',1':
:1.1'I
..
0:"... -;. 1: -t -l.2.2
--,.
2.
\
~'"
~:
I
I
".
-1
I"
'3
L-J
'V'.V.'2Jl
v.,'':''
.;- -t..!..
"'-V~;"-I-.
I'\"'1- 71:.,.,
~'.,.";'::2,,
.~...
::-:" :;:;::)"
j
-~'r
1..~.L
~=.5'
~
'3
.2 +
-=: 1:: ~
'3
2
t
+
emf is large enough that both bulbs are glowing.
brightly? Exp~ain.
\h..
~~
blAibS
Pc:II,V-er.ike b~S
OJ e't.~ \)()I~
cl l' =
:I:'1.~
.../,~
'I.
T
(M)"
C710
oUk1~
titu.
(;UI.e
~
A;
> 13 = C
~
~S
o...x-e
\~tp...{l
~
9=r2.~ \\tv
~
6qC
~
.
60 IV
-1-=-
I
e8
J
100IVj
J
the brightness of the
~
r:GA=
~~
}h~
~ .M-.M b~.
43. Initially bulbs A and B are glowing.
~
'2.
_' ..._ .....
_ ....
'iM'\(.-e:t ~ ~
S~
q.A'OV:>~ ~.
42. Bulbs A, Band C are identical. Rank in order, from most ttteast,
three bulbs. Explain.
.
_~
> 12'00
~V()
~.,o ~ [ ~D VV
\/<.00 )
e:t.*::::r::h:>
~
+
Which one glows more
-ervJe
"2-
-=- :.
I
2..
241V.A 60'1N light bulb and a 100 W light bulb are placed one after the other in a circuit.
The battery's
'2.
1,""';-=3
:Ie:/5
l
•.•
tes
A
=
.M
Rc
c
~
Then the switch is Qlosed. What happens to each
bulb? Does it get brighter, stay the same, get dimmer or go out? Explain.
A ~~
CLD~
I.RCL
b",,~
~
Uu?0~1&v
3 ~crG& ovU- ~c~
~h
C51NfL3lP~
+
j
re~n-(;U"\.L.e) .
B
'C1
.
44. What happens to the light intensity of a set of identical lamps in series when you add an additional
c~
'6'0
45. What happens to the light
lamp? How comc?
\10
intensity
of a set of identical
ii--
'O{.C.~
iV\
~j(\
il)c.r-ec.....~
~~
cN.~.
Q..,v-X'~
C~
CtM"Y'u-vt
0M""reAA-k
'oeC~
ol,C,rY'\~
~
lamp? How
to-.lh-
A p~
b"'0vv\.Lh.,
~
lamps in parallel
when you add an additional
,'D ~
&<PCU"'0vK
atoM
~~).
'.j..
lo-r;p ~
~L
(~
!
tl".CY'e
'2.
3
Current Worksheet Problems
II doesn'lmaffer
not mafle,. was
how much you wan!. What really mailers is how much you want if. The e.;'(lentand complexity (?flhe proh/em does
much as does (he willingness to solve it. -- Ralph Marston
(q -:r( 10)-T(20) -:I~3<::>J
46. Fill out the table for the circuit diagramed at the right
Circuit
Position
R]
R2
R3
Total
(p
Resistance
Voltage (V)
(n)
.10.0
20.0
30.0
Current (A)
• 1 t>.
\ V
100.0
-1: l(,o)~
l.V
.
'2.,"';
• \ f>"
y ~"!:e.
f><
\
,,~
6.00
=(:.1)(10')::\
47. Fill. out the table for the circuit diagramed at the right
\0 - ~,(IO) -::0
Circuit
Position
R]
R2
R3
Total
~
Resistance
10.0
20.0
30.0
(, Y
1.
.3
f.fY
6.00
1)-'
-= (.!!-
-+ '20 -t 00
.'-.LQo
T
I
.lPA
V
(0
'5. Y6..n..
(\
t -- \.
\0
J:=
Voltage (V) . Current (A)
(n)
"1:2.:'
Pr
\.\ A
CoO
(pO
io:.. 3
lp - I:'3 ('61» =-0
2:.)"' _ \1
of
IP_
IP
0 - .
(p- II. ('2...t:) -:::.
0
P<-
. "l2.
\
'"
... -
(.Do
.t ::
..••
-\.p-1.
.L", - - •
"
~o
48. Fill out the table for the circuit diagramed at the right
Circuit
Position
R]
R2
R3
Total
Resistance
Voltage (V)
(n)
10.0
20.0
30.0
1
!<-R't -
-
\
2.0
rZ #t -=
-t
'2.1 v'
."2-7
3.:'
.110", ~
• II A
?:J .!:>
£.. J-.n.
V
V
6.00
L :.
?:>"D
Current (A)
.2lt10
• "2.'"
A
A
'2...
T
(go
(,:,- (.2i)lIC)-I2(u»
LP- 2.,-=.1:2.("2.0)
1 0 -+ !"2.. -=- 2. 2. ...rL
v - r,(IO)
L. - 1: ,(10) - "T.~7..o)~ a
- I3l'6")"-c
~ - 2..1 " r 3('61:»
3.~ 30
1:'",,<fi)
-:;r-
1:3"=.1 I
~D
Current Worksheet Problems
II duesn't maller hoH' much you want. What really matters is how much yuu 'want il. The e.r:lenland complexil)' a/rhe prohlem does
1101muller was much as does {he wdlingness to so/\'e it. -- Ralph Marston
s
J.n n
-\
Hulf".A
-=.
9(JV
(Ut
(d)
n
Bulo IJ
1.
3.0.n
1
OulbC
light bulbs of fixed resistance 3.0 Q and 6.0 Q, a 9.0 V battery, and a switch 5 are connected as shown in the
schematic diagram above. The switch 5 is closed.
(a)
Calculate the current in bulb A.
~~::
1+2. -:. '5..n.
V~
(b)
=. 1:'Oo.>'t
~O<t
Calculate the current in bulb B and bulb C.
'j -
rA(~)
-1:6(t.»
q - (\~')(~)
-=
q -X/>o(3) -l:.c.("3):.c
'=1)
(p:t',
3.\# -:::
"~'S.,-\ -:::
\.Q:t:a
b 1:,
fIe.'"
l.lA
J
~.I1-:=(P~~
r1: ::. i;19
.
(c) Which light bulb is brighftis" .Iusily your answer by calculating the power for each bulb.
~~~j
~
fl~1.12. = O.<6J
__
~
C-
~:: r'2..j2.
-::Q.'2.)"Z.(~)
~ ~,,1:"2.12
\
-=(.lP)"l.(U)V"W
C~):'f\.12."'1
~f:~'l..W
(c)
Switch S is then opened. By checking the appropriate spaces below, indicate whether the brightness or
each light bulb increases, decreases, or remains the same. Explain your reasoning for each light bulb.
i. Bulb A: The brightness
__ increases ~deereases
__ remains the same
Explanation: tirCv1.4- i'::> no.,.:> ~.eQ
~
~
c;lQ.~
f>=-I.~
II.
Bulb B: The brightness
Explanation: C\,VV'r~
Ill.
Bulb C: The brightness
Explanation:
c
#-inereases
+h ~
decreases
e,
remains the same
..A.b ~
__ increases $deereases
__
~
remains the same
'ole
V\,W)
\_-
e..u-cW-t ~::
:.T~
3t (p -:: q n.
= Tn. -=I6-~
Current Worksheet Problems
II doesn', maller huw much you wan!. What really matters is how much YOlf wan! it. The extent (1mlcomplexity (~rlheproblem does
no! molter ira.\"much as does the willingness 10 so/t'c it. -- Ralph Marston
2. Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits.
(a) The two bulbs are first connected in parallel to a 120 V source.
i. Determine the resistanc.c-ofthe bulb rated 30 Wand the current in it when it is connected in this
circuit.
,,'L..
V"'L
:p -=: f.2. "1<.,-=15"
-=
r '\ '2-0)"1-.
l.!
at>
~
-.:: l<:::
4 ~2(
I = ~ -= ~
~
L.ffsD
~
0'S
l'cj
•
II. Determine the resistance of the bulb rated 40 Wand the current in it when it is connected in this
,,2..
circuit.?
~
~
-=-")
V'
U'1..D)"2.. ~
Rr \3::;;
'-to
y
1'2.0
~-::\
r::: te-:: ~
~
-:.~
(b) The bulbs are now connected in series with each other and a 120 V source.
i. Detelll1ine the resistance of the bulb rated 30 Wand the current in it when it is connected in this
circuit.
S~
y~o
n.
if',
~~
~~::
4%c "'0(,,0 :: %l-\D..el-
=G)'-tA \
L-:: ~
II. Detel:rnine the resistance of the bulb rated 40 W and th~ecurrent in it whe~t
CIrcUIt. c ~
'DloO.n..
o
.
~~
is connected in this
.
(c) In the spaces below, number the bulbs in each situation described, in order of their brightness.
(I = brightest, 4 = dimmest)
Z
30 W bulb in the parallel circuit
_, 40 W bulb in the parallel circuit
2> 30 W bulb'in
the series circuit
~ 40 W bulb in the series circuit
(d) Calculate the total power dissipated by the two bulbs in each of the following cases.
i. The parallel circuit
ii. The series circuit
'V=-TL..Q
-= C:.\'-01.- ("H
~
Cl ')
-=- 9 .t--\{)~ \;'J
~t:>
?'1 0
-=- (. \ '-\)'2- ( 2>(0,:;) .-=: I.
05 \0
V'l
n;
Current Worksheet Problems
It doesn't matter how much you want. What rea/~l' rnal/ers is how much you want it. The extent and complexity (?fthe problem does
nvtmatler was much as does the willingness to solve it. -- Ralph Marston
.'
3. The circuit above contains a battery with negligible internal resistance, a closed switch S, and three resistors, each
with a resistance of R or 2R.
(a)
(i) Rank the currents in the three resistors from greatest to least. with number 1 being greatest. If two
resistors have the same current, give them the same ranking.
\
IA
~
2-
III
Ie
(ii) Justify your answers.
\W-.U~ ~oJd~
~
~
<Z:0,-ts
CA.k-j\A."f. c...\-1\JY\.
'\ZC
-hR1J~b +'vv~h
'I[\~
0.. \~
~
'(~\~e"1Jo
6'1't
(b)
(i) Rank the voltages across the three resistors lI'om greatest to least, with number I being greatest. I
two resistors have the same voltage across them, give them the same ranking.
~
2..
\
VA
(ii) Justify your answers.
\oe.c.~'K- C-\.A-X'r~
'6 q C .
2
VB
~~
. .
U
'1ro -IT-u:ii\ \~
f<-A -:.1-g
~
Ve
~'.l
.
U.
T'tb
For parts (c) through (e), usc € = 12 V and R = 200 n, .
(c) Calculate the equivalent resistance of the circuit.
l<.~1=
2.-(£.00) +-
(l.~Df-1./ooJ'
=\'5~~.JI-
(d) Calculate the current in resistor Re.
\'2. - IA(2.\Z.) - L(.C~) ~
\'2. - (.O'"2-'26)('-tOO)
\ '2. -
'C
-
Lc. (l ...oo)-=:O
9 -::1..-0'() Tc.
Ie
-= .OI15P< OJ
1
.
~
r. '"
'-t'~
V c\Ko-p.
'
"..
e. .
AP Physics 1: Electrostatics and Circuits Answer Key
--""
:I,..cv) "4ovt..
2.c~.~:.i'"
r.r~,~
..,
'l
~l,.)(;.J
':' .t'~,-,=.I".
b. 3,\1l /\. i~
tOud,~ by a pb,lic 1('1(1thul
;::Ja~s!(lOjlila' wn.~ rubbt:d wi:h ••ill.
\\ia.~n.lhhcd
with wool acdball R j:. Illuched h~'II
.,
O,+-:••~..•...:
'\7
!'rO d~
Co
H<jlh ,<J'C dw~~d
by <l pl:ll<tiC m.1, bul haJI /\ i., o.:haT~oofllme thall ball n .
f.", ..•; •.:'1~:':
•....l.,..;-!
J. BIlII ~\ j, dlillS •.d hY:J pla ••tic r;.x1.Hall
.;
-<:fl'::'!..-..
!..)
H.....
< •..
n is Jleutral.
,
-.-,'
; &..t ..••
;...••.;)-.,Jf!.
~
.j....
'0:.
r~o.....
~
!r->
,
.
,1? .••.:.c:'!A
~l.:. .::':~~
~.;.,.,
,?t:I'~:'-l:::~T
.•:.'\
':."
-}'~.•."
2. a. yes b. neutral object doesn't cause force c. yes (equal but opposite of comb) d. negative
3. a. move farther apart b. leaves will come closer together.
<---B
4. neutral
5. negative
9. a) 6.25 x 1018Lost
6. negative
b) 1.25 x 1013gained
10.48.9 N 11. 1.76 x 10-4 N
12. 2.64 ~IC
c) 5 x 1013Lost
d) 2 x 1013gained
13.40 N
14.39 cm
Fq
r.~o /
1
r,:,
Fe;
4
15.a.
b. 9.26 x lOBC
16 a. 3.6xlO. N c) 0.012 m/s' & 0.006 m/s' d)
16 e. speed increases at a decreasing rate until it become constant at an infinite distance away.
17.0.147 A
18.2.42xlO17
19. 16 A
23. same
20.107 ohms
21. 0.5 A
26. 0.24 ohms
25.1 A out
22.a.5.45A
b. 655 W c. 589 kJ d. 74 cents
27. A (b wont work)
28.2:1
-
.1----"
..1-.
31a. Same b. R, c. V,>V,
33. No 34. a. same b. R3>R,>R,
(pi
t"Sf' t'lll
36.a.
37. a. Vb." -1,(25)
35 a. Vb'" -I,R,
- I,R,- I,R3 =
,;lVG?] ~11
b.
Cfv
c.
=. Vb." - 1,(15) = Vb.,,-13(45) = Vb.,,-I,(35)
a
32.
T
,
L
I
..•
r'
---..J
b. 1.2 A c. 120 V, 60 V, 90 V
~Jf_
~
=
a
b. 1.9 A c. 0.48 A, 0.8 A, 0.27 A, 0.343 A
•
AP Physics 1: Electrostatics and Circuits Answer Key
".':~:[j"'ifii
i
,.,."..Ii .•... i-~r
:
I
! •...
38. a. Vb'" -I,R,
- I,R,= 0 b. 8V, 4 V c.
40. a. 11 0
b. 9 0
41. 60 W
42.A>B=C
c. 1 0
d. 0.5 0
'--
-'
e. 7.5 0
f. 2.7 0
43. A gest brighter and B goes out.
44. dimmer
45. no change
46.
Circuit
Position
Resistance
(0)
Voltage (V)
Current (A)
R,
10.0
1
0.1
R,
20.0
-:zr:' .()
2
0.1
3
0.1
R3
Total
G.OO
60
0.1
47.
Circuit
Resistance
Position
(0)
R,
Iv.1)
6
0.6
R,
200
6
0.3
30.0
6
R3
Total
Voltage (V)
5.45
Current (A)
0.2
6.00
1.1
48.
Circuit
Position
Resistance
(0)
R,
".:).:.1
2.7
.27
R,
2U.O
3.3
.165
R3
30.1l
3.3
.11
Total
22
Voltage (V)
5.00
Current (A)
.27
49 (1) a) 1.8 A, b) 0.6A, 1.2 A c) Bulb A d) A decreases, B increases, C decreases
50. (2) a) i. 480 0, 0.25 A ii. 360 0, 0.33 A b) i. 480 0, 0.14 A ii) 360 0, 0.14 A c) 2, 1, 3,4 d) i. 70 W ii. 16.5 W
51. (3) a) i. 1,3,2
b) i. 1, 2, 2 c) 533 0
d) 0.015A