Lab Manual
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School
Moorpark College *
*We aren’t endorsed by this school
Course
M20
Subject
Physics
Date
Jan 9, 2024
Type
Pages
85
Uploaded by MasterStrawLoris22
1
M
OO
RPAR
K
C
OLLEGE
P
H
Y
SI
C
S
M
20B L
A
B
M
ANUA
L
B
Y
PR
O
F
ESSO
R
H.
FR
E
D
M
E
Y
E
R
WITH
C
O
N
T
R
IB
U
TIO
N
S
FR
O
M
PR
O
F
ESSO
R
B
A
L
A
ZS BE
C
HT
R
E
V
ISE
D
S
PR
I
N
G 2020
NO
TE
T
O
T
H
E
IN
S
T
RUC
T
IOR:
S
ome of t
h
e ex
p
er
i
me
n
ts
p
rese
n
te
d
h
ere
in
d
o
n
ot
re
qui
re t
h
e w
h
o
l
e
l
a
b
p
er
i
o
d
to ta
k
e t
h
e
d
ata.
O
n
ce t
h
e st
ud
e
n
ts
h
ave
p
erforme
d
t
h
e
ex
p
er
i
me
n
t a
nd
recor
d
e
d
t
h
e ex
p
er
i
me
n
ta
l
d
ata, t
h
ey are ex
p
ecte
d
to a
n
a
l
yze t
h
e
d
ata a
nd
com
pl
ete (
n
eat
l
y) a
ll
ca
l
c
ul
at
i
o
n
s
du
r
in
g c
l
ass t
i
me.
If t
h
ere
i
s st
ill
c
l
ass
t
i
me
l
eft after eac
h
st
ud
e
n
t
h
as com
pl
ete
d
t
h
e a
n
a
l
ys
i
s,
h
ave t
h
em wr
i
te
up
a
s
u
mmary a
nd
co
n
c
lu
s
i
o
n
u
s
in
g t
h
e
d
e
p
artme
n
t-
p
rov
id
e
d
l
a
p
to
p
s.
It
i
s s
u
ggeste
d
t
h
at t
h
e
in
str
u
ctor s
i
g
n
a
nd
d
ate t
h
e
d
ata s
h
eet o
nl
y after t
h
e st
ud
e
n
t
h
as com
pl
ete
d
t
h
e a
b
ove.
NO
TE
T
O
T
H
E
S
T
UD
E
N
T
:
T
hi
s Ma
nu
a
l
i
s
p
rov
id
e
d
free of c
h
arge.
It
i
s yo
u
r
res
p
o
n
s
ibili
ty to
p
r
in
t t
h
e ma
nu
a
l
(co
l
or
i
s
b
est)
p
r
i
or to t
h
e
b
eg
innin
g of t
h
e
semester a
nd
pu
t t
h
e ma
nu
a
l
in
a
bind
er.
S
ome of t
h
e
l
a
b
s
h
ave
p
re-
l
a
b
ass
i
g
n
me
n
ts
in
vo
l
v
in
g ca
l
c
ul
at
i
o
n
s or
d
er
i
vat
i
o
n
s.
I
n
t
h
e
d
ays
l
ea
din
g
up
to eac
h
l
a
b
-
l
a
b
exerc
i
ses
n
eat
l
y we
ll
b
efore c
l
ass.
Have yo
u
r
in
str
u
ctor s
i
g
n
t
h
e
p
re-
l
a
b
d
er
i
vat
i
o
n
a
nd
ca
l
c
ul
at
i
o
n
s
h
eets
p
r
i
or to start
in
g t
h
e act
u
a
l
ex
p
er
i
me
n
t.
2
F
O
R
EWO
RD
The exper
i
men
t
s and exerc
i
ses
i
n
t
h
i
s vo
l
ume are
i
n
t
ended
t
o demons
t
ra
t
e
t
he Laws of
P
hys
i
cs
t
ha
t
you have s
t
ud
i
ed
t
hrough a
t
heore
ti
ca
l
approach
i
n
t
he
l
ec
t
ure por
ti
on of
t
he
course.
In some cases,
t
hese Laws have been demons
t
ra
t
ed by
t
he
i
ns
t
ruc
t
or
i
n
t
he
l
ec
t
ure por
ti
on of
t
he course.
B
u
t
i
n
t
he
l
abora
t
ory course, you (a
l
ong w
it
h your
l
ab
par
t
ners) w
ill
cons
t
ruc
t
and perform
t
he exper
i
men
t
s w
it
h coach
i
ng from
t
he
l
ab
i
ns
t
ruc
t
or, and
t
hereby, you w
ill
demons
t
ra
t
e
t
he app
li
cab
l
e phys
i
ca
l
pr
i
nc
i
p
l
es for
yourse
l
f. The pr
i
mary ob
j
ec
ti
ve of your
l
ab effor
t
s
i
s
t
o ga
i
n prac
ti
ca
l
unders
t
and
i
ng of
t
he
t
heory, so
t
ha
t
your exper
i
en
ti
a
l
know
l
edge w
ill
beg
i
n
t
o comp
l
emen
t
your
unders
t
and
i
ng of
t
heory.
In add
iti
on
t
o ga
i
n
i
ng
t
h
i
s prac
ti
ca
l
exposure
t
o
t
he Laws of
P
hys
i
cs,
t
he
l
abora
t
ory
per
i
ods compr
i
s
i
ng
t
h
i
s course w
ill
s
t
ar
t
you on your way
t
o becom
i
ng a sk
ill
ed
l
ab
prac
titi
oner.
Your
l
ab sk
ill
s w
ill
become an
i
mpor
t
an
t
componen
t
of your overa
ll
sc
i
en
ti
f
i
c and
t
echn
i
ca
l
compe
t
ency
i
n
t
he fu
t
ure. As you con
ti
nue
t
o
t
ake more advanced
sc
i
ence and
/
or eng
i
neer
i
ng courses and
t
hen pursue emp
l
oymen
t
oppor
t
un
iti
es,
it
may
surpr
i
se you
t
o f
i
nd
t
ha
t
you are sure
t
o re
t
urn frequen
tl
y
t
o
t
he
l
abora
t
ory or
t
o
t
he
e
l
ec
t
r
i
c
it
y, e
l
ec
t
ron
i
cs, mach
i
nery, or ma
t
er
i
a
l
s shop.
You w
ill
emp
l
oy
t
he know
l
edge
you have ga
i
ned from your co
ll
ege courses
i
n
t
hese venues.
Your
i
ns
t
ruc
t
ors are we
ll
aware of
t
he
i
mpor
t
ance for you
t
o deve
l
op effec
ti
ve and
compe
t
en
t
l
ab sk
ill
s, and
t
hey w
ill
ass
i
s
t
you
i
n
t
h
i
s deve
l
opmen
t
. Of
t
en,
t
h
i
s w
ill
mean
t
ha
t
t
hey w
ill
i
ns
i
s
t
on a h
i
gh s
t
andard of nea
t
ness,
t
horoughness, and a
tt
en
ti
on
t
o de
t
a
il
i
n your
l
ab work. In many cases,
t
he
l
ab equ
i
pmen
t
prov
i
ded for your use
i
s soph
i
s
ti
ca
t
ed
and expens
i
ve
t
o rep
l
ace.
Your
i
ns
t
ruc
t
ors w
ill
demons
t
ra
t
e
t
he correc
t
way
t
o se
t
up
t
he
exper
i
men
t
a
l
appara
t
uses and execu
t
e
t
he
l
ab procedures.
Incorrec
t
use of
t
he equ
i
pmen
t
can
l
ead
t
o
i
nva
li
d resu
lt
s and may a
l
so
l
ead
t
o equ
i
pmen
t
damage.
A
t
Moorpark
C
o
ll
ege, you w
ill
no
t
be he
l
d respons
i
b
l
e f
i
nanc
i
a
ll
y for
i
mproper use of
l
ab equ
i
pmen
t
.
B
u
t
you are asked
t
o be recep
ti
ve
t
o gu
i
dance, re
i
nforcemen
t
of correc
t
use of
l
ab
equ
i
pmen
t
, and pruden
t
l
ab prac
ti
ces.
You w
ill
no
t
be pena
li
zed for poor
l
ab prac
ti
ces,
bu
t
poor
l
ab prac
ti
ces w
ill
l
ead
t
o poor exper
i
men
t
a
l
resu
lt
s and may
l
ead
t
o safe
t
y
v
i
o
l
a
ti
ons.
Ins
t
ruc
t
ors are human
;
when
t
hey observe poor
l
ab prac
ti
ce, care
l
essness, and
i
na
tt
en
ti
veness,
it
makes an
i
mpress
i
on.
When your
i
ns
t
ruc
t
ors observe consc
i
en
ti
ous
l
ab
prac
ti
ce, observance of safe
t
y ru
l
es, and nea
t
ness,
t
hey may be
i
nc
li
ned
t
o g
i
ve you
t
he
benef
it
of
t
he doub
t
.
In your fu
t
ure
t
echn
i
ca
l
endeavors, you w
ill
u
tili
ze documen
t
a
ti
on for sys
t
ems and
equ
i
pmen
t
, forma
tt
ed
i
n accordance w
it
h accep
t
ed
t
echn
i
ca
l
s
t
andards such as
t
hose
i
ssued by
t
he In
t
erna
ti
ona
l
Organ
i
za
ti
on for
St
andard
i
za
ti
on (I
S
O), Ins
tit
u
t
e of E
l
ec
t
r
i
ca
l
and E
l
ec
t
ron
i
cs Eng
i
neers (IEEE), Amer
i
can Na
ti
ona
l
St
andards Ins
tit
u
t
e (AN
S
I),
E
l
ec
t
ron
i
c Indus
t
r
i
es A
lli
ance (EIA), and o
t
hers.
Genera
ll
y, safe
t
y adv
i
sor
i
es re
l
a
t
ed
t
o
equ
i
pmen
t
are of
t
wo
t
ypes
:
WA
R
NING
S
app
l
y
t
o s
it
ua
ti
ons where
i
n
j
ury
t
o personne
l
may occur
i
f equ
i
pmen
t
i
s used
i
mproper
l
y
;
C
AUTION
S
app
l
y
t
o s
it
ua
ti
ons where
equ
i
pmen
t
damage or
i
neffec
ti
ve resu
lt
s may occur
i
f equ
i
pmen
t
i
s used
i
mproper
l
y.
These conven
ti
ons w
ill
be used
i
n
t
he
t
echn
i
ca
l
documen
t
a
ti
on prov
i
ded
i
n
t
h
i
s vo
l
ume.
3
THI
S
P
AGE I
S
INTENTIONALLY LE
F
T
B
LANK
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4
E
RR
O
R
S
AND
E
RR
O
R
PR
O
PA
G
A
TIO
N
IN
T
RODUC
T
ION:
Labora
t
ory exper
i
men
t
s
i
nvo
l
ve
t
ak
i
ng measuremen
t
s and us
i
ng
t
hose measuremen
t
s
i
n an equa
ti
on
t
o ca
l
cu
l
a
t
e an exper
i
men
t
a
l
resu
lt
.
I
t
i
s a
l
so
necessary
t
o know how
t
o es
ti
ma
t
e
t
he uncer
t
a
i
n
t
y, or error,
i
n phys
i
ca
l
measuremen
t
s
and
t
o know how
t
o use
t
hose uncer
t
a
i
n
ti
es
t
o ca
l
cu
l
a
t
e error marg
i
ns
i
n
t
he exper
i
men
t
a
l
resu
lt
.
R
E
AD
T
HI
S
L
A
B
BE
FOR
E
C
L
A
SS
.
T
H
E
E
X
E
RCI
S
E
S
A
T
T
H
E
E
ND OF
T
HI
S
HANDOU
T
WI
LL
BE
DON
E
DURING C
L
A
SS
T
IM
E
.
YOUR GRAD
E
WI
LL
BE
D
ETE
RMIN
E
D
B
Y HOW W
ELL
YOU DO
T
H
E
E
X
E
RCI
S
E
S
.
A
T
T
H
E
E
ND OF
T
H
E
P
E
RIOD HAND IN
T
H
E
E
X
E
RCI
S
E
S
A
L
ONG WI
T
H YOUR N
E
A
TL
Y
DON
E
CA
L
CU
L
A
T
ION
S
H
EET
S
S
HOWING A
LL
OF YOUR WORK.
T
YP
E
S
OF
E
XP
E
RIM
E
N
T
A
L
E
RROR
S
Exper
i
men
t
a
l
errors can genera
ll
y be c
l
ass
i
f
i
ed
i
n
t
o
t
hree
t
ypes
:
persona
l
, sys
t
ema
ti
c,
and random.
Perso
n
a
l
E
rrors
These errors ar
i
se from persona
l
b
i
as of care
l
essness
i
n read
i
ng an
i
ns
t
rumen
t
,
i
n
record
i
ng da
t
a, or
i
n ca
l
cu
l
a
ti
ons, and para
ll
ax
i
n read
i
ng a me
t
er.
Of
t
hese, on
l
y para
ll
ax
errors can be es
ti
ma
t
ed and used
i
n error propaga
ti
on.
Effor
t
shou
l
d be made
t
o e
li
m
i
na
t
e
exper
i
men
t
a
l
errors.
(When
l
ook
i
ng a
t
non-d
i
g
it
a
l
me
t
er,
t
here
i
s a sma
ll
d
i
s
t
ance be
t
ween
t
he need
l
e and
t
he
s
i
de
t
o s
i
de.
Th
i
s apparen
t
change
i
n read
i
ng, due
t
o
t
he change
i
n pos
iti
on of
t
he
S
ystemat
i
c
E
rrors
Errors of
t
h
i
s
t
ype resu
lt
i
n measured va
l
ues wh
i
ch are cons
i
s
t
en
tl
y
t
oo h
i
gh or
t
oo
l
ow.
C
ond
iti
ons wh
i
ch
l
ead
t
o sys
t
ema
ti
c errors are as fo
ll
ows
:
1.
An
i
mproper
l
y ca
li
bra
t
ed
i
ns
t
rumen
t
such as a
t
hermome
t
er wh
i
ch cons
i
s
t
en
tl
y
reads 99º
C
i
n bo
ili
ng wa
t
er
i
ns
t
ead of 100º
C
.
2.
A me
t
er, m
i
crome
t
er, vern
i
er ca
li
per, or o
t
her
i
ns
t
rumen
t
, wh
i
ch was no
t
proper
l
y zeroed or for wh
i
ch
t
he zero correc
ti
on fac
t
or was no
t
cons
i
dered.
3.
Theore
ti
ca
l
errors due
t
o a s
i
mp
li
f
i
ed ma
t
hema
ti
ca
l
mode
l
for
t
he sys
t
em, wh
i
ch
cons
i
s
t
en
tl
y g
i
ves a ca
l
cu
l
a
t
ed va
l
ue d
i
fferen
t
from
t
he ca
l
cu
l
a
t
ed va
l
ue pred
i
c
t
ed
from a more accura
t
e ma
t
hema
ti
ca
l
mode
l
.
5
Ra
nd
om
E
rrors
R
andom errors resu
lt
from unknown and unpred
i
c
t
ab
l
e var
i
a
ti
ons
i
n exper
i
men
t
a
l
measuremen
t
s.
P
oss
i
b
l
e sources of random errors
i
nc
l
ude
:
1.
Observa
ti
ona
l
e.g., errors when read
i
ng
t
he sca
l
e of a measur
i
ng dev
i
ce
t
o
t
he
sma
ll
es
t
d
i
v
i
s
i
on.
2.
Env
i
ronmen
con
t
ro
l
.
S
uch errors can be de
t
erm
i
ned s
t
a
ti
s
ti
ca
ll
y or can be es
ti
ma
t
ed by
t
he
exper
i
men
t
er.
S
TATI
S
TI
C
AL DETE
R
MINATION O
F
R
ANDOM E
RR
O
R
S
When
t
here are many measuremen
t
s of
t
he same quan
tit
y,
t
he average or mean va
l
ue
i
s
def
i
ned by
where
i
s
t
he
i
t
h
measured va
l
ue and
N
i
s
t
he
t
o
t
a
l
number of
measuremen
t
s.
There are
t
wo ways
t
o s
t
a
ti
s
ti
ca
ll
y ca
l
cu
l
a
t
e
t
he uncer
t
a
i
n
t
y
i
n
t
he measured va
l
ue.
One
me
t
hod
i
s
t
o ca
l
cu
l
a
t
e
t
he
mea
n
d
ev
i
at
i
o
n
d
I
t
i
s common
t
o express
t
he exper
i
men
t
a
l
va
l
ue of
t
he measuremen
t
as
:
Measured va
l
ue of x =
where
d
a s
t
a
ti
s
ti
ca
l
es
ti
ma
t
e of
t
he uncer
t
a
i
n
t
y
i
n
t
he measured va
l
ue.
As can be
observed,
t
he mean dev
i
a
ti
on
i
s a measure of
t
he spread on
t
he da
t
a.
Ano
t
her me
t
hod used
t
o ca
l
cu
l
a
t
e
t
he random error
i
s by ca
l
cu
l
a
ti
ng
t
he
The measured va
l
ue of x can
t
hen be expressed as
:
Measured va
l
ue of
N
i
i
x
N
x
1
_
1
i
x
N
x
x
d
N
i
i
1
d
x
N
x
x
d
s
N
i
i
2
1
.
.
.
.
d
s
x
x
6
The s
t
a
ti
s
ti
ca
l
me
t
hods above w
ill
be used
i
n se
l
ec
t
ed
l
ab exerc
i
ses
t
o fo
ll
ow, such as
measuremen
t
s of
ti
me are needed and an average or mean
i
s ca
l
cu
l
a
t
ed.
E
S
TIMATION O
F
R
ANDOM E
RR
O
R
S
An eas
i
er me
t
hod
t
o de
t
erm
i
ne random error
i
s
t
o es
ti
ma
t
e
t
he random error by u
tili
z
i
ng
t
he accuracy of
t
he
i
ns
t
rumen
t
and
t
he
j
udgmen
t
of
t
he exper
i
men
t
er.
The error
i
n a
g
i
ven
i
ns
t
rumen
t
i
s de
t
erm
i
ned by
t
he sma
ll
es
t
d
i
v
i
s
i
on on
t
ha
t
i
ns
t
rumen
t
or
F
or examp
l
e,
t
he sma
ll
es
t
d
i
v
i
s
i
on on a me
t
er s
ti
ck
i
s 1mm or 0.1cm.
Th
i
s
i
s
t
he
l
eas
t
coun
t
for
t
he me
t
er s
ti
ck.
In mos
t
measuremen
t
s
t
he sma
ll
es
t
d
i
v
i
s
i
on represen
t
s
t
he
r
i
gh
t
mos
t
d
i
g
it
i
n
t
he va
l
ue of
t
ha
t
measuremen
t
, and
t
he es
ti
ma
t
ed measuremen
t
error
i
s
t
he
l
eas
t
coun
t
.
F
or examp
l
e, a measured va
l
ue may be 78.2cm
0.1cm.
S
ome
ti
mes a measuremen
t
may be made w
it
h an es
ti
ma
t
ed error
l
ess
t
han
t
he
l
eas
t
coun
t
.
F
or examp
l
e, an exper
i
men
t
er may es
ti
ma
t
e read
i
ng on a me
t
er s
ti
ck as 78.25cm by
no
ti
ng
t
ha
t
t
he read
i
ng was abou
t
ha
l
fway be
t
ween 78.2cm and 78.3cm.
The
exper
i
men
t
er may represen
t
t
he va
l
ue as 78.25cm
0.05cm.
Keep
i
n m
i
nd
t
ha
t
t
he
r
i
gh
t
mos
t
d
i
g
it
mus
t
be es
ti
ma
t
ed by
t
he exper
i
men
t
er and
i
s
t
hus doub
t
fu
l
.
S
ome
ti
mes
t
he es
ti
ma
t
ed error
i
s
l
arger
t
han
t
he
l
eas
t
coun
t
.
F
or examp
l
e, when
measur
i
ng
t
he d
i
s
t
ance be
t
ween
t
he
t
wo spo
t
s be
l
ow,
t
he exper
i
men
t
er wou
l
d need
t
o
es
ti
ma
t
e where
t
he cen
t
er of each spo
t
wou
l
d be
l
oca
t
ed.
The error
i
n
t
he measured
d
i
s
t
ance wou
l
d be
l
arger
t
han
t
he
l
eas
t
coun
t
and
t
he amoun
t
of
t
he es
ti
ma
t
ed error wou
l
d
be up
t
o
t
he
j
udgmen
t
of
t
he exper
i
men
t
er.
No
t
e how much
t
he error es
ti
ma
t
es depend on
t
he
j
udgmen
t
of
t
he exper
i
men
t
er.
There
may be errors
i
n
j
udgmen
t;
however,
t
o avo
i
d s
t
a
ti
ng a resu
lt
more accura
t
e
l
y
t
han you
probab
l
y measured
it
, one shou
l
d
t
ry
t
o avo
i
d be
i
ng
t
oo conserva
ti
ve
i
n es
ti
ma
ti
ng errors.
E
RROR PROPAGA
T
ION
P
A
R
TIAL DE
R
IVITIVE
S
B
efore we can perform error propaga
ti
on ca
l
cu
l
a
ti
ons, we mus
t
know how
t
o
t
ake wha
t
know
how
t
o do
t
h
i
s, p
l
ease use your know
l
edge
t
o he
l
p your c
l
assma
t
es who have no
t
ye
t
been
t
augh
t
how.
S
uppose we have a func
ti
on
f
where
f
=
f
(x,y,z).
The par
ti
a
l
der
i
va
ti
ve of
f
w
it
h respec
t
t
o
x
i
s found by
t
ak
i
ng
t
he ord
i
nary der
i
va
ti
ve wh
il
e
t
rea
ti
ng
y
and
z
as cons
t
an
t
s.
The
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7
no
t
a
ti
on for
t
h
i
s der
i
va
ti
ve
i
s
.
L
i
kew
i
se,
t
he par
ti
a
l
der
i
va
ti
ve of
f
w
it
h respec
t
t
o
y
i
s
found by
t
ak
i
ng
t
he ord
i
nary der
i
va
ti
ve wh
il
e
t
rea
ti
ng
x
and
z
as cons
t
an
t
s and
i
s wr
itt
en
as
and
t
he par
ti
a
l
der
i
va
ti
ve of
f
w
it
h respec
t
t
o
z
i
s found by
t
ak
i
ng
t
he ord
i
nary
der
i
va
ti
ve wh
il
e
t
rea
ti
ng
x
and
y
as cons
t
an
t
s and
i
s wr
itt
en as
.
As an examp
l
e,
l
e
t
. Then
=
C
onv
i
nce yourse
l
f
t
ha
t
and
t
ha
t
.
A
B
S
OLUTE AND
R
ELATIVE E
RR
O
R
S
Abso
l
u
t
e Error
:
When an error
i
s es
ti
ma
t
ed
i
n a measured va
l
ue of x
it
w
ill
be des
i
gna
t
ed
as
(
d
e
l
ta
x
).
has
t
he same un
it
s as
x
and
i
s ca
ll
ed
t
he
a
b
so
lu
te error
i
n
x
.
F
or
examp
l
e,
i
f
,
t
he abso
l
u
t
e error
i
s
.
R
e
l
a
ti
ve Error
:
The ra
ti
o of
t
he abso
l
u
t
e error
t
o
t
he measured va
l
ue
x,
,
i
s ca
ll
ed
t
he
re
l
at
i
ve error
.
I
t
i
s usua
ll
y represen
t
ed as a percen
t
.
F
or examp
l
e,
t
he re
l
a
ti
ve error
i
n
t
he above examp
l
e
i
s
.
No
t
e
:
There are
ti
mes when
it
i
s necessary
t
o form
re
l
at
i
ve error
back from
a
b
so
lu
te
error
:
.
C
OM
P
UTATION O
F
E
RR
O
R
F
or a func
ti
on
,
t
he abso
l
u
t
e error
i
n
f
,
,
i
s def
i
ned as
:
The re
l
a
ti
ve error
i
n f wou
l
d
t
hus be
x
f
y
f
z
f
3
2
5
y
z
x
f
3
2
5
yz
x
x
x
f
3
2
3
10
5
xyz
x
x
yz
3
2
5
z
x
y
f
2
2
15
y
z
x
z
f
x
x
cm
cm
x
1
.
0
0
.
2
cm
x
1
.
0
x
x
x
%
5
05
.
0
0
.
2
1
.
0
0
.
2
1
.
0
cm
cm
x
error
x
r
e
l
a
ti
ve
z
y
x
f
f
,
,
f
2
2
2
z
z
f
y
y
f
x
x
f
f
2
2
2
1
z
z
f
y
y
f
x
x
f
f
f
f
8
EXAM
P
LE
Us
i
ng
t
he func
ti
on we used as an examp
l
e for par
ti
a
l
der
i
va
ti
ves, we wou
l
d have
t
hus
wh
i
ch when s
i
mp
li
f
i
ed
becomes
No
t
e
t
ha
t
t
he quan
titi
es
i
n
t
he paren
t
heses are
j
us
t
t
he percen
t
errors mu
lti
p
li
ed by
t
he
exponen
t
for
t
ha
t
par
ti
cu
l
ar var
i
ab
l
e.
S
uppose we have
t
he exper
i
men
t
a
l
va
l
ues for
x,
y
, and
z
as
:
,
, and
We wou
l
d
t
hus have
t
he percen
t
error
i
n
f
as
:
No
t
e
t
ha
t
t
he
% error
i
s ro
und
e
d
up
to t
h
e
n
earest w
h
o
l
e
nu
m
b
er
.
Si
nce
it
i
s
j
us
t
an
es
ti
ma
t
e, we canno
t
j
us
ti
fy more accuracy
i
n
t
he error.
ANOTHE
R
EXAM
P
LE
S
uppose
where
,
, and
Thus
where
,
, and
;
or,
2
3
2
2
2
2
3
2
3
2
2
3
2
3
5
15
5
5
5
10
z
y
z
x
y
z
x
y
y
z
x
z
x
x
y
z
x
xy
z
f
f
2
2
2
3
2
z
z
y
y
x
x
f
f
cm
cm
x
1
.
0
0
.
3
cm
cm
y
1
.
0
2
.
5
cm
cm
z
1
.
0
4
.
2
2
2
2
4
.
2
1
.
0
3
2
.
5
1
.
0
0
.
3
1
.
0
2
f
f
c
b
a
V
2
2
5
3
cm
a
1
.
0
2
.
8
cm
b
1
.
0
5
.
6
cm
c
1
.
0
1
.
5
2
2
2
c
c
V
b
b
V
a
a
V
V
c
a
a
V
6
c
b
b
V
10
2
2
2
5
3
c
b
a
c
V
9
No
ti
ce
t
ha
t
t
he nega
ti
ve s
i
gn
i
n
does no
t
ma
tt
er s
i
nce
it
i
s squared.
Now
Or,
= 5.5%
The f
i
na
l
resu
lt
s wou
l
d be g
i
ven as
.
P
E
RC
ENT DI
S
CR
E
P
AN
C
Y
Once an exper
i
men
t
a
l
va
l
ue and
it
s percen
t
error are ca
l
cu
l
a
t
ed,
t
he
p
erce
n
t
di
scre
p
a
n
cy
i
s def
i
ned as
p
erce
n
t
di
scre
p
a
n
cy
in
X
=
There w
ill
be agreemen
t
be
t
ween
t
he accep
t
ed va
l
ue and
t
he exper
i
men
t
a
l
va
l
ue
i
f
t
he
percen
t
d
i
screpancy
i
s
l
ess
t
han
t
he pred
i
c
t
ed percen
t
error
i
n
t
he exper
i
men
t
a
l
va
l
ue as
de
t
erm
i
ned by error propaga
ti
on.
In o
t
her words,
t
he exper
i
men
t
a
l
va
l
ue
i
s w
it
h
i
n
t
he
marg
i
n of error.
T
hi
s s
h
o
uld
b
e a
dd
resse
d
in
t
h
e co
n
c
lu
s
i
o
n
of yo
u
r
l
a
b
re
p
ort.
If
t
here
i
s no
t
agreemen
t
, some sources of error may be presen
t
wh
i
ch may no
t
have been
accoun
t
ed for and some
reaso
n
a
bl
e ex
pl
a
n
at
i
o
n
shou
l
d be
i
nc
l
uded
i
n
t
he conc
l
us
i
on of
your repor
t
.
2
2
2
2
2
2
5
3
10
6
c
c
b
a
b
c
b
a
c
a
V
c
V
2
2
2
2
2
2
2
2
2
2
2
2
5
3
5
3
5
3
10
5
3
6
c
c
b
a
c
b
a
b
c
b
a
c
b
a
c
b
a
c
a
V
V
2
2
2
2
2
2
2
1
.
5
1
.
0
1
.
0
5
.
6
5
2
.
8
3
5
.
6
10
1
.
0
5
.
6
5
2
.
8
3
2
.
8
6
V
V
%
6
81
cm
V
accep
t
ed
e
r
i
men
t
a
l
accep
t
ed
X
X
X
exp
2
2
2
2
2
2
2
5
3
10
5
3
6
c
c
b
b
a
b
a
b
a
a
V
V
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10
E
RR
O
R
PR
O
PA
G
A
TIO
N
E
X
E
RC
ISES
De
t
erm
i
ne
t
he ca
l
cu
l
a
t
ed va
l
ue us
i
ng
t
he g
i
ven va
l
ues
i
n
t
he g
i
ven equa
ti
ons.
B
e sure
t
o
in
c
lud
e t
h
e
uni
ts
in
yo
u
r a
n
swer
. Us
i
ng
t
he error propaga
ti
on me
t
hod descr
i
bed above,
ca
l
cu
l
a
t
e
t
he percen
t
error
i
n
t
he ca
l
cu
l
a
t
ed va
l
ue.
F
or
t
h
i
s exerc
i
se, amswers shou
l
d be
w
it
h
t
he proper number of s
i
gn
i
f
i
can
t
f
i
gures and
yo
u
r
p
erce
n
t error
i
s to
b
e g
i
ve
n
to
two s
i
g
ni
f
i
ca
n
t f
i
g
u
res.
Ha
nd
in
t
hi
s a
n
swer s
h
eet.
Wor
k
t
h
e
p
ro
bl
ems
n
eat
l
y
o
n
scratc
h
p
a
p
er
and s
t
ap
l
e
your work
t
o
t
h
i
s shee
t
.
1.
A=xy
,
,
______________
_______%
2.
f
=x+y,
for x and y g
i
ven
i
n prob
l
em # 1
______________
_______%
3.
f
=x-y,
for x and y g
i
ven
i
n prob
l
em # 1
______________
_______%
4.
z=3x+2y,
for x and y g
i
ven
i
n prob
l
em # 1
______________
______%
5.
for
,
______________
______%
6.
,
,
______________
______%
7.
,
,
___________
______%
8.
,
,
______________
______%
9.
,
,
,
______________
______%
10.
,
,
______________
______%
H
i
n
t:
C
onver
t
1°
t
o rad
i
ans
cm
cm
x
1
.
0
0
.
3
cm
cm
y
1
.
0
0
.
4
2
2
t
h
g
%
3
00
.
2
m
h
%
4
630
.
0
s
t
k
M
T
2
%
6
5
.
2
K
g
M
%
2
100
m
N
k
3
2
00
.
5
M
L
g
cm
d
%
2
0
.
30
g
M
cm
L
2
.
0
3
.
20
2
2
y
x
z
%
2
0
.
3
cm
x
%
2
0
.
4
cm
y
C
b
cm
a
z
2
3
2
5
%
1
0
.
2
cm
a
%
1
0
.
3
cm
b
%
2
0
.
11
cm
C
s
i
n
d
h
m
m
d
05
.
0
00
.
1
1
10
11
THI
S
P
AGE I
S
INTENTIONALLY LE
F
T
B
LANK
12
S
P
E
C
I
F
I
C
HE
A
T
CAPAC
IT
Y
F
O
R
M
ET
A
LS
AND
HE
A
T O
F
FU
SIO
N
F
O
R
W
A
TE
R
IN
T
RODUC
T
ION
Part 1.
Us
i
ng
t
he me
t
hod of m
i
x
t
ures,
t
he spec
i
f
i
c hea
t
capac
it
y of copper and a
l
um
i
num
w
ill
be measured.
Part 2
. The s
t
uden
t
w
ill
des
i
gn an exper
i
men
t
t
o measure
t
he
l
a
t
en
t
hea
t
of fus
i
on for
wa
t
er.
Pr
i
or to com
in
g to c
l
ass, t
h
e st
ud
e
n
t s
h
a
ll
o
u
t
lin
e
hi
s
/h
er
p
roce
du
re for Part
2.
R
E
QUIR
E
D
E
QUIPM
E
N
T
AND MA
TE
RIA
L
S
St
eam Genera
t
or (
i
nc
l
ud
i
ng cover, p
l
ugs, and bo
il
er cups)
C
a
l
or
i
me
t
er
D
i
g
it
a
l
Thermome
t
er (2)
Me
t
r
i
c
B
a
l
ance
St
ra
i
ner
P
o
t
of Ho
t
Wa
t
er
one for
t
he c
l
ass
Dra
i
n
B
ucke
t
one for
t
he c
l
ass (
i
f no s
i
nk
i
s ava
il
ab
l
e for dra
i
n
i
ng used wa
t
er)
Towe
l
s
S
o
li
d
S
pec
i
mens of
C
opper and A
l
um
i
num
De-Ion
i
zed (DI) Wa
t
er
Ice
Hea
t
- and
St
eam-
P
ro
t
ec
ti
ve G
l
oves (recommended)
S
afe
t
y G
l
asses (recommended)
T
H
E
ORY (
T
O
BE
COMP
LETE
D PRIOR
T
O C
L
A
SS
)
Part 1.
The spec
i
f
i
c hea
t
capac
it
y of a subs
t
ance
i
s def
i
ned as
t
he hea
t
energy per un
it
mass per un
it
change
i
n
t
empera
t
ure or
:
The un
it
s we w
ill
use are
F
rom
t
he def
i
n
iti
on of spec
i
f
i
c hea
t
capac
it
y, we can express
t
he change
i
n hea
t
energy,
The me
t
hod of m
i
x
t
ures cons
i
s
t
s of de
t
erm
i
n
i
ng
t
he quan
tit
y of hea
t
t
ransferred from a
g
i
ven amoun
t
of ho
t
so
li
d
t
o a g
i
ven amoun
t
of wa
t
er and ca
l
or
i
me
t
er a
t
a g
i
ven
l
ower
t
empera
t
ure.
If
it
i
s assumed
t
ha
t
t
here
i
s no hea
t
exchange be
t
ween
t
he ca
l
or
i
me
t
er and
gram
C
ca
l
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13
it
s surround
i
ngs,
t
he hea
t
l
os
t
by
t
he ho
t
so
li
d
i
s equa
l
t
o
t
he hea
t
ga
i
ned by
t
he wa
t
er and
ca
l
or
i
me
t
er.
Le
t
m
w
be
t
he mass of
t
he wa
t
er
i
n
t
he ca
l
or
i
me
t
er,
m
c
i
s
t
he mass of
t
he ca
l
or
i
me
t
er
con
t
a
i
ner (
i
nser
t
)
;
bo
t
h are a
t
an
i
n
iti
a
l
t
empera
t
ure
T
1
.
A so
li
d of mass
m
i
s hea
t
ed
t
o a
t
empera
t
ure of
T
2
.
Af
t
er
t
he so
li
d
i
s p
l
aced
i
n
t
he wa
t
er,
t
he f
i
na
l
t
empera
t
ure of
t
he
m
i
x
t
ure
i
s
T
.
The spec
i
f
i
c hea
t
capac
it
y of
t
he ca
l
or
i
me
t
er
i
nser
t
i
s g
i
ven by
c
c.
The spec
i
f
i
c hea
t
capac
it
y of
t
he so
li
d
i
s g
i
ven by
c
, and
t
he spec
i
f
i
c hea
t
of wa
t
er
i
s g
i
ven by
c
w
.
C
onserva
ti
on of energy means
t
ha
t
t
he hea
t
l
os
t
by
t
he so
li
d spec
i
men equa
l
s
t
he hea
t
ga
i
ned by
t
he ca
l
or
i
me
t
er con
t
a
i
ner (
i
nser
t
) and wa
t
er.
Thus,
As par
t
of
t
he
t
heory
i
n your repor
t
,
t
h
i
s equa
ti
on
i
s
t
o be so
l
ved for
c
.
Part 2
.
Hea
t
of fus
i
on
i
s g
i
ven by
:
, where
m
i
s
t
he amoun
t
of
i
ce me
lti
ng
t
o
wa
t
er a
t
0º
C
and
L
f
i
s
t
he
l
a
t
en
t
hea
t
of fus
i
on for
i
ce
t
o wa
t
er.
PROC
E
DUR
E
NO
TE
:
I
n
a
ll
ex
p
er
i
me
n
ts,
b
efore ta
kin
g meas
u
reme
n
ts, orga
ni
ze a
n
eat
d
ata s
h
eet
w
i
t
h
rows a
nd
co
lu
m
n
s a
ll
l
a
b
e
l
e
d
w
i
t
h
var
i
a
bl
es a
nd
uni
ts.
As
p
art of yo
u
r
d
ata,
recor
d
t
h
e est
i
mate
d
un
certa
in
ty
in
eac
h
meas
u
reme
n
t.
WARNING:
T
h
e water
in
t
h
e steam ge
n
erator
i
s
b
o
ilin
g
h
ot.
Use ca
u
t
i
o
n
a
nd
b
e
extreme
l
y caref
ul
to
n
ot t
ip
t
h
e steam ge
n
erator over.
A
l
so,
k
ee
p
yo
u
r
h
a
nd
s away
from t
h
e steam.
S
team ca
nn
ot
b
e see
n
a
nd
w
ill
bu
r
n
severe
l
y.
Wear
in
g t
h
e
p
rotect
i
ve g
l
oves
i
s recomme
nd
e
d
w
h
e
n
wor
kin
g w
i
t
h
t
h
e
h
ot water a
nd
steam
e
n
v
i
ro
n
me
n
t of t
h
e steam ge
n
erator.
w
hi
c
h
indi
cates t
h
at a
ll
or
n
ear
l
y a
ll
of t
h
e water
in
t
h
e steam ge
n
erator
h
as
b
o
il
e
d
a
dd
more water to t
h
e reservo
i
r
i
mme
di
ate
l
y, or t
u
r
n
off t
h
e e
l
ectr
i
ca
l
p
ower to t
h
e
steam ge
n
erator.
Ig
n
or
in
g t
h
e war
nin
g
li
g
h
t ca
n
l
ea
d
to e
quip
me
n
t
d
amage or a
n
e
l
ectr
i
ca
l
f
i
re.
CAU
T
ION:
B
e s
u
re to t
u
r
n
off t
h
e D
i
g
i
ta
l
T
h
ermometer w
h
e
n
d
o
n
e w
i
t
h
i
t.
B
atter
i
es for t
h
ese t
h
ermometers cost a
b
o
u
t $4.00 eac
h
a
nd
r
un
d
ow
n
qui
c
kl
y
i
f t
h
e
t
h
ermometer
i
s
l
eft o
n
.
A
l
so,
b
e s
u
re
n
ot to s
ub
merge t
h
e
b
attery e
nd
of t
h
e
t
h
ermometer
in
to a
n
y of t
h
e var
i
o
u
s water
b
at
h
s.
Do
in
g t
hi
s w
ill
d
estroy t
h
e
t
h
ermometer.
f
m
L
Q
14
Part 1 Proce
du
re:
Fill
t
he s
t
eam genera
t
or reservo
i
r
t
wo
t
h
i
rds fu
ll
, p
l
ug
it
i
n, and
t
urn
t
he power
sw
it
ch on.
De
t
erm
i
ne
t
he mass of enough of one k
i
nd of me
t
a
l
t
o f
ill
t
he bo
il
er cup abou
t
2
/
3 fu
ll
of
t
he me
t
a
l
.
Inser
t
a
t
hermome
t
er
i
n
t
o
t
he me
t
a
l
and p
l
ace
t
he bo
il
er
cup
i
n
t
o
t
he bo
il
er.
ca
l
or
i
me
t
er .
Fill
t
he ca
l
or
i
me
t
er
i
nser
t
abou
t
ha
l
f fu
ll
of d
i
s
till
ed wa
t
er, p
l
ace a few p
i
eces
of
i
ce
i
n
t
he ca
l
or
i
me
t
er
i
nser
t
t
o br
i
ng
t
he
t
empera
t
ure of
t
he wa
t
er
t
wo or
t
hree degrees be
l
ow room
t
empera
t
ure and we
i
gh
it
aga
i
n.
Us
i
ng a second
t
hermome
t
er, measure and record
t
he
t
empera
t
ure of
t
he wa
t
er
i
ns
i
de
t
he ca
l
or
i
me
t
er
i
nser
t
.
Af
t
er
t
he wa
t
er
i
n
t
he bo
il
er beg
i
ns
t
o bo
il
, wa
it
a few m
i
nu
t
es for
t
he
t
empera
t
ure of
t
he me
t
a
l
t
o s
t
ab
ili
ze, record
t
h
i
s
t
empera
t
ure.
P
our
t
he ho
t
me
t
a
l
sho
t
i
n
t
o
t
he ca
l
or
i
me
t
er
i
nser
t
.
Assemb
l
e
t
he ca
l
or
i
me
t
er, s
ti
r
t
he
m
i
x
t
ure, and record
t
he f
i
na
l
t
empera
t
ure when equ
ili
br
i
um has been reached.
(How do you know when equ
ili
br
i
um has been reached?)
R
epea
t
t
he process for ano
t
her samp
l
e of me
t
a
l
so
li
d.
I
t
i
s assumed
t
ha
t
t
he ca
l
or
i
me
t
er con
t
en
t
s are
t
herma
ll
y
i
so
l
a
t
ed from
t
he
i
r
surround
i
ngs,
i
.e.,
i
nsu
l
a
t
ed.
Th
i
s
i
s d
i
ff
i
cu
lt
t
o rea
li
ze
i
n prac
ti
ce, bu
t
t
he effec
t
due
t
he hea
t
exchange can be m
i
n
i
m
i
zed by hav
i
ng
t
he
t
empera
t
ure d
i
fference be
t
ween
t
he
i
n
iti
a
l
ca
l
or
i
me
t
er
i
nser
t
con
t
en
t
s and
t
he surround
i
ngs abou
t
t
he same as
t
he
d
i
fference be
t
ween
t
he f
i
na
l
t
empera
t
ure of
t
he ca
l
or
i
me
t
er con
t
en
t
s and
t
he
surround
i
ngs.
Part 2 Proce
du
re:
In
t
h
i
s par
t
of
t
he exper
i
men
t
, you w
ill
des
i
gn an exper
i
men
t
t
o de
t
erm
i
ne
t
he
l
a
t
en
t
hea
t
of fus
i
on for wa
t
er.
Yo
u
s
h
o
uld
come to t
h
e
l
a
b
oratory w
i
t
h
a
n
o
u
t
lin
e of t
h
e
p
roce
du
re yo
u
pl
a
n
to
u
se.
Inc
l
ude
i
n your
l
ab repor
t
t
he de
t
a
il
s of
t
he procedure
you used (recommend us
i
ng
t
he same forma
t
as
t
he
P
ar
t
I
P
rocedure above).
L
A
B
R
E
POR
T
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your wr
it
e-up sha
ll
i
nc
l
ude
t
he
fo
ll
ow
i
ng
:
(see
t
he append
i
x for W
R
ITING A
F
O
R
MAL
R
E
P
O
R
T)
15
T
h
eory
:
Der
i
ve each equa
ti
on used
i
n
t
he ana
l
ys
i
s for
P
ar
t
1 and
P
ar
t
2.
Proce
du
re
:
St
a
t
e
t
he de
t
a
il
s of how
P
ar
t
2 of
t
h
i
s exper
i
men
t
was performed.
A
n
a
l
ys
i
s
:
Type
t
he da
t
a shee
t
.
C
ompu
t
e
t
he spec
i
f
i
c hea
t
capac
iti
es of
t
he
t
wo me
t
a
l
s
samp
l
es.
C
ompu
t
e
t
he hea
t
of fus
i
on for
i
ce.
P
erform a samp
l
e ca
l
cu
l
a
ti
on of each
t
ype.
(
St
a
t
e
t
he equa
ti
on used, subs
tit
u
t
e
t
he numbers,
t
hen s
t
a
t
e
t
he answer.)
Us
i
ng Error
P
ropaga
ti
on, de
t
erm
i
ne
t
he percen
t
uncer
t
a
i
n
t
y
i
n your resu
lt
s.
Assume a 2% error
i
n a
ll
va
l
ues.
Co
n
c
lu
s
i
o
n
(
to
b
e ty
p
e
d
)
:
A conc
l
us
i
on con
t
a
i
n
i
ng a summary of resu
lt
s, and a
compar
i
son of your exper
i
men
t
a
l
va
l
ues w
it
h accep
t
ed va
l
ues sha
ll
be prov
i
ded
i
n your
repor
t
.
(Is
t
he percen
t
d
i
screpancy
l
ess
t
han pred
i
c
t
ed error?)
The conc
l
us
i
on shou
l
d a
l
so
i
nc
l
ude sources of error and how
t
he exper
i
men
t
cou
l
d be
i
mproved.
A
pp
e
ndi
x
:
The or
i
g
i
na
l
s
i
gned da
t
a shee
t
and answers
t
o ques
ti
ons shou
l
d be
i
nc
l
uded
i
n
an append
i
x
t
o your repor
t
.
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16
PURPO
S
E
Law of
C
oo
li
ng,
, and
t
o
de
t
erm
i
ne
t
he
ti
me cons
t
an
t
.
R
E
QUIR
E
D
E
QUIPM
E
N
T
(see
ph
oto o
n
t
h
e
n
ext
p
age)
Ha
l
f-
i
nch
C
opper Tube (abou
t
20cm
l
ong, s
t
oppered w
it
h a dowe
l
a
t
one end)
R
i
ng
St
and (60cm me
t
a
l
rod a
tt
ached
t
o base) (2)
Tube
C
l
amp (2)
D
i
g
it
a
l
Thermome
t
er
St
opwa
t
ch
P
ropane Torch
T
H
E
ORY
t
o
t
he
t
empera
t
ure d
i
fference be
t
ween
t
he ob
j
ec
t
and
t
he surround
i
ngs
:
(1)
Here
k
i
s a cons
t
an
t
and
T
=
T
-
T
s
where
T
s
i
s t
h
e tem
p
erat
u
re of t
h
e s
u
rro
undin
g a
i
r
.
F
rom
t
he equa
ti
on
, we have
(2)
Pr
i
or to start of t
h
e
l
a
b
c
l
ass
p
er
i
o
d
, com
bin
e e
qu
at
i
o
n
s (1) a
nd
(2), se
p
arate t
h
e
var
i
a
bl
es a
nd
s
i
m
pli
fy to o
b
ta
in
:
Where
T
0
i
s t
h
e
ini
t
i
a
l
tem
p
erat
u
re of t
h
e o
b
ject w
hi
c
h
i
s coo
lin
g
.
We sha
ll
def
i
ne
t
he
ti
me cons
t
an
t
and hence
(3)
PROC
E
DUR
E
Look a
t
t
he p
i
c
t
ure be
l
ow and se
t
up your s
t
a
ti
on as shown.
B
e sure
t
he
t
hermome
t
er
i
s
cen
t
ered
i
n
t
he copper
t
ube and
i
s no
t
t
ouch
i
ng
t
he s
i
des of
t
he
t
ube.
Us
i
ng
t
he propane
17
t
orch, hea
t
t
he p
i
pe un
i
form
l
y a
l
ong
it
s
l
eng
t
h
t
o a
t
empera
t
ure of be
t
ween 125
0
C
and
150
0
C
.
When
t
he
t
empera
t
ure has somewha
t
s
t
ab
ili
zed, record
t
he
t
empera
t
ure as
T
0.
R
ecord
t
he
t
empera
t
ure
T
a
t
15 s
i
n
t
erva
l
s for
t
he f
i
rs
t
t
wo m
i
nu
t
es and
t
hen a
t
30s
i
n
t
erva
l
s for
t
he nex
t
f
i
ve m
i
nu
t
es.
Fi
gure 1
WARNING:
T
h
ere are severa
l
ty
p
es of
b
ott
l
e
d
f
l
amma
bl
e gases store
d
in
t
h
e
L
a
b
Pre
p
Room.
For t
hi
s ex
p
er
i
me
n
t,
b
e s
u
re t
h
e
b
ott
l
e
d
gas yo
u
are
u
s
in
g
i
s
p
a
in
te
d
gas we
ldin
g, a
nd
u
s
in
g t
hi
s gas may ca
u
se over
h
eat
in
g, me
l
t
in
g of t
h
e
l
a
b
e
quip
me
n
t, a
nd/
or ex
pl
os
i
o
n
of t
h
e gas.
O
li
ve gree
n
b
ott
l
es co
n
ta
in
Nat
u
ra
l
(Met
h
a
n
e) gas, w
hi
c
h
i
s
u
se
d
in
cam
pin
g stoves a
nd
may
n
ot
p
ro
du
ce e
n
o
u
g
h
h
eat
for t
hi
s ex
p
er
i
me
n
t.
CAU
T
ION:
B
e s
u
re to t
u
r
n
off t
h
e D
i
g
i
ta
l
T
h
ermometer w
h
e
n
d
o
n
e w
i
t
h
i
t.
B
atter
i
es for t
h
ese t
h
ermometers cost a
b
o
u
t $4.00 eac
h
a
nd
wear
d
ow
n
qui
c
kl
y
i
f t
h
e
t
h
ermometer
i
s
l
eft o
n
.
18
ANA
L
Y
S
I
S
Assume m = 126g ± 2%
Us
i
ng M
i
crosof
t
M
S
Exce
l
, p
l
o
t
a sem
i
-
l
ogar
it
hm
i
c (sem
i
-
-
ba
ll
t
he max-m
i
n
li
nes, and p
l
o
t
t
hem by hand.
F
rom
t
he max and m
i
n s
l
ope
li
nes,
de
t
erm
i
ne a percen
t
error
i
n
t
he s
l
ope.
F
rom
t
he s
l
ope of
t
he graph and
t
he s
l
ope error, de
t
erm
i
ne
and
t
he % error
i
n
.
T
a
k
e t
h
e
ln
of
b
ot
h
s
id
es of t
h
e e
qu
at
i
o
n
(3) a
nd
s
h
ow t
h
e s
l
o
p
e of t
h
e gra
ph
i
s -
You do no
t
have a
t
heore
ti
ca
l
va
l
ue for
because we do no
t
know
k.
L
A
B
R
E
POR
T
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your wr
it
e-up sha
ll
i
nc
l
ude
t
he
fo
ll
ow
i
ng
:
(see
t
he append
i
x for W
R
ITING A
F
O
R
MAL
R
E
P
O
R
T)
T
h
eory:
Inc
l
ude any ma
t
hema
ti
ca
l
der
i
va
ti
ons you needed
t
o perform.
A
n
a
l
ys
i
s
:
Type
t
he da
t
a shee
t
and
i
nc
l
ude a re
l
evan
t
d
i
scuss
i
on of
t
he resu
lt
s.
Co
n
c
lu
s
i
o
n
(
to
b
e ty
p
e
d
)
:
A conc
l
us
i
on con
t
a
i
n
i
ng a summary of resu
lt
s sha
ll
be
prov
i
ded
i
n your repor
t
.
The conc
l
us
i
on shou
l
d a
l
so
i
nc
l
ude sources of error and how
t
he
exper
i
men
t
cou
l
d be
i
mproved.
A
pp
e
ndi
x
:
The or
i
g
i
na
l
s
i
gned da
t
a shee
t
and answers
t
o ques
ti
ons (see be
l
ow) shou
l
d
be p
l
aced
i
n an append
i
x
t
o your repor
t
.
QU
E
S
T
ION
S
(1)
C
a
l
cu
l
a
t
e
t
he
ti
me
it
t
akes for
t
he
t
empera
t
ure d
i
fference be
t
ween
t
he copper
t
ube
and
it
s surround
i
ngs
t
o coo
l
t
o w
it
h
i
n 1% of
t
he beg
i
nn
i
ng
t
empera
t
ure d
i
fference
be
t
ween
t
he
t
ube and
it
s surround
i
ngs.
(2)
Us
i
ng error propaga
ti
on and
t
he % error
i
n
,
de
t
erm
i
ne
t
he % uncer
t
a
i
n
t
y
i
n
t
h
i
s
ti
me.
(3)
Does
t
he
ti
me ca
l
cu
l
a
t
ed
i
n Ques
ti
on (1) depend on
t
he
i
n
iti
a
l
t
empera
t
ure?
Jus
ti
fy your answer.
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19
THI
S
P
AGE I
S
INTENTIONALLY LE
F
T
B
LANK
20
CA
LIB
RA
TI
N
G
A
THE
R
M
O
M
ETE
R
IN
T
RODUC
T
ION
When a measurab
l
e phys
i
ca
l
proper
t
y of an ob
j
ec
t
var
i
es w
it
h
t
empera
t
ure,
t
ha
t
ob
j
ec
t
can be ca
li
bra
t
ed
t
o func
ti
on as a
t
hermome
t
er.
In
t
h
i
s exper
i
men
t
,
t
he e
l
ec
t
r
i
ca
l
res
i
s
t
ance of a sem
i
-conduc
t
or, ca
ll
ed a
t
herm
i
s
t
or, w
ill
be used for
t
h
i
s purpose.
R
E
QUIR
E
D
E
QUIPM
E
N
T
AND MA
TE
RIA
L
S
St
eam Genera
t
or (
i
nc
l
ud
i
ng cover and p
l
ugs)
Therm
i
s
t
or
D
i
g
it
a
l
Thermome
t
er
D
i
g
it
a
l
Mu
lti
-Me
t
er (DMM)
Tes
t
Lead
A
lli
ga
t
or
C
li
ps
Tub of
Sl
ushy Ice (Wa
t
er
Ice m
i
x
t
ure)
Three (3) Tubs of Wa
t
er
:
R
oom Temp, 10°
C
above
R
oom, and 10°
C
be
l
ow
R
oom
Dra
i
n
B
ucke
t
one for
t
he c
l
ass (
i
f no s
i
nk
i
s ava
il
ab
l
e for dra
i
n
i
ng used wa
t
er)
Towe
l
s
T
H
E
ORY
F
rom o
t
her exper
i
men
t
s,
it
i
s found
t
ha
t
t
he res
i
s
t
ance of a
t
herm
i
s
t
or var
i
es accord
i
ng
t
o
t
he equa
ti
on
(1)
Where
R
0
and
B
are cons
t
an
t
s and
T
i
s
t
he abso
l
u
t
e
t
empera
t
ure.
F
rom
t
wo measuremen
t
s of
t
he res
i
s
t
ance a
t
t
he (known) s
t
eam po
i
n
t
s and
i
ce po
i
n
t
s,
t
he
above equa
ti
on can be used
t
o de
t
erm
i
ne
B
and
R
0
.
Tak
i
ng
t
he na
t
ura
l
l
ogar
it
hm of bo
t
h s
i
des, one can see
t
ha
t
(2)
Pr
i
or to
l
a
b
c
l
ass,
u
se
R
1
at
T
1
a
nd
R
2
at
T
2
in
e
qu
at
i
o
n
(1)
a
nd
d
er
i
ve ex
p
ress
i
o
n
s for
R
0
a
nd
B
.
Sh
ow a
ll
of t
h
e a
l
ge
b
ra a
nd
in
c
lud
e t
h
e
d
er
i
vat
i
o
n
in
t
h
e t
h
eory
p
ort
i
o
n
of yo
u
r
l
a
b
re
p
ort.
The express
i
on for
B
i
s
21
PROC
E
DUR
E
C
onnec
t
t
he
t
herm
i
s
t
or
t
o
t
he DMM w
it
h
t
he DMM se
t
t
o read OHM
S
(ohmme
t
er).
Immerse
t
he
t
herm
i
s
t
or
i
n a ba
t
h of me
lti
ng
i
ce and record
t
he res
i
s
t
ance
t
h
i
s
i
ce
po
i
n
t
i
s one of your known
t
empera
t
ures.
Immerse
t
he
t
herm
i
s
t
or
i
n a ba
t
h of bo
ili
ng wa
t
er and record
t
he res
i
s
t
ance
t
h
i
s
s
t
eam po
i
n
t
i
s your o
t
her known
t
empera
t
ure.
Three wa
t
er ba
t
hs have been prepared
:
one be
l
ow room
t
empera
t
ure, one a
t
approx
i
ma
t
e
l
y room
t
empera
t
ure, and one above room
t
empera
t
ure.
Measure
t
he
res
i
s
t
ance of
t
he
t
herm
i
s
t
or when p
l
aced
i
n each of
t
he wa
t
er ba
t
hs.
A
l
so,
measure
t
he
t
empera
t
ure of each wa
t
er ba
t
h w
it
h a d
i
g
it
a
l
t
hermome
t
er.
Assume a
±2% uncer
t
a
i
n
t
y
i
n
t
he res
i
s
t
ance for a
ll
read
i
ngs.
WARNING:
T
h
e water
in
t
h
e steam ge
n
erator ca
n
b
e
b
o
ilin
g
h
ot.
Use ca
u
t
i
o
n
a
nd
b
e extreme
l
y caref
ul
to
n
ot t
ip
t
h
e steam ge
n
erator over.
A
l
so,
k
ee
p
yo
u
r
h
a
nd
s
away from t
h
e steam.
S
team ca
nn
ot
b
e see
n
a
nd
w
ill
bu
r
n
severe
l
y.
Wear
in
g t
h
e
p
rotect
i
ve g
l
oves
i
s recomme
nd
e
d
w
h
e
n
wor
kin
g w
i
t
h
t
h
e
h
ot water a
nd
steam
e
n
v
i
ro
n
me
n
t of t
h
e steam ge
n
erator.
nin
g
li
g
h
t,
w
hi
c
h
indi
cates t
h
at a
ll
or
n
ear
l
y a
ll
of t
h
e water
in
t
h
e steam ge
n
erator
h
as
b
o
il
e
d
a
dd
more water to t
h
e reservo
i
r
i
mme
di
ate
l
y, or t
u
r
n
off t
h
e e
l
ectr
i
ca
l
p
ower to t
h
e
steam ge
n
erator.
Ig
n
or
in
g t
h
e war
nin
g
li
g
h
t ca
n
l
ea
d
to e
quip
me
n
t
d
amage or a
n
e
l
ectr
i
ca
l
f
i
re.
CAU
T
ION:
B
e s
u
re to t
u
r
n
off t
h
e D
i
g
i
ta
l
T
h
ermometer w
h
e
n
d
o
n
e w
i
t
h
i
t.
B
atter
i
es for t
h
ese t
h
ermometers cost a
b
o
u
t $4.00 eac
h
a
nd
r
un
d
ow
n
qui
c
kl
y
i
f t
h
e
t
h
ermometer
i
s
l
eft o
n
.
A
l
so,
b
e s
u
re
n
ot to s
ub
merge t
h
e
b
attery e
nd
of t
h
e
t
h
ermometer
in
to a
n
y of t
h
e var
i
o
u
s water
b
at
h
s.
Do
in
g t
hi
s w
ill
d
estroy t
h
e
t
h
ermometer.
ANA
L
Y
S
I
S
C
a
l
cu
l
a
t
e
t
he cons
t
an
t
s
B
and
R
0
us
i
ng
t
he
i
ce and s
t
eam po
i
n
t
t
herm
i
s
t
or res
i
s
t
ance da
t
a.
Us
i
ng equa
ti
on (2), ca
l
cu
l
a
t
e
t
he
t
empera
t
ures of
t
he
t
hree ba
t
hs us
i
ng
t
he
t
herm
i
s
t
or
res
i
s
t
ance da
t
a.
De
t
erm
i
ne
t
he uncer
t
a
i
n
t
y of
t
hese
t
empera
t
ures by propaga
ti
ng
t
he uncer
t
a
i
n
ti
es
i
n
equa
ti
on (2).
Assume a 2% error
i
n
B
,
R
0,
a
nd
R
.
E
rror
p
ro
p
agat
i
o
n
o
nl
y
n
ee
d
s to
b
e
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22
d
o
n
e for o
n
e tem
p
erat
u
re,
n
ot t
h
ree.
C
h
oose t
h
e va
lu
e of
R
w
hi
c
h
g
i
ves t
h
e
max
i
m
u
m
p
erce
n
t error.
C
ompare your resu
lt
s w
it
h
t
he d
i
g
it
a
l
t
hermome
t
er va
l
ues and d
i
scuss
t
he resu
lt
s.
Are
your resu
lt
s w
it
h
i
n
t
he marg
i
n of error?
If no
t
, why no
t
?
L
A
B
R
E
POR
T
W
R
ITING A
F
O
R
MAL
R
E
P
O
R
T and fo
ll
ow
t
hese gu
i
de
li
nes
i
n prepar
i
ng and
subm
itti
ng your
l
ab repor
t
.
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23
THI
S
P
AGE I
S
INTENTIONALLY LE
F
T
B
LANK
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24
THE
NA
T
UR
E O
F
ELE
C
T
R
I
CA
L
R
ESIST
ANC
E
IN
T
RODUC
T
ION
The ob
j
ec
ti
ve of
t
h
i
s exper
i
men
t
i
s
t
o s
t
udy some fundamen
t
a
l
proper
ti
es of e
l
ec
t
r
i
ca
l
res
i
s
t
ance of me
t
a
l
s.
We sha
ll
i
nves
ti
ga
t
e how
t
he res
i
s
t
ance depends on
t
he curren
t
t
hrough a w
i
re and
t
hrough a
t
ungs
t
en f
il
amen
t
li
gh
t
bu
l
b.
The res
i
s
ti
v
it
y of an unknown
me
t
a
l
w
ill
be de
t
erm
i
ned.
In
t
he course of do
i
ng
t
he exper
i
men
t
, you w
ill
l
earn how
t
o
w
i
re a s
i
mp
l
e c
i
rcu
it
and how
t
o make measuremen
t
s w
it
h vo
lt
me
t
ers, amme
t
ers, and
ohmme
t
ers, wh
i
ch are of
t
en ava
il
ab
l
e as se
l
ec
t
ab
l
e func
ti
ons on a D
i
g
it
a
l
Mu
lti
-Me
t
er
(DMM).
R
E
QUIR
E
D
E
QUIPM
E
N
T
AND MA
TE
RIA
L
S
D
i
rec
t
C
urren
t
(D
C
)
P
ower
S
upp
l
y (0
25 VD
C
)
D
i
g
it
a
l
Mu
lti
-Me
t
er (DMM) (2)
A
lli
ga
t
or
C
li
ps
M
i
crome
t
er
R
es
i
s
t
ance W
i
re (sma
ll
d
i
ame
t
er)
Tungs
t
en-
Fil
amen
t
L
i
gh
t
B
u
l
b w
it
h
S
ocke
t
S
harp Kn
i
fe or
R
azor
B
l
ade (
t
o scrape off w
i
re
i
nsu
l
a
ti
on)
Fl
ame
S
ource (cand
l
e or
li
gh
t
er) (
t
o burn off w
i
re
i
nsu
l
a
ti
on = a
lt
erna
t
e
t
o kn
i
fe)
S
IMP
LE
CIRCUI
T
S
Fi
gure 1 shows a s
i
mp
l
e c
i
rcu
it
t
ha
t
has on
l
y
t
wo
compo
n
e
nt
s
.
Fi
rs
t
,
t
he
po
w
er s
u
pp
l
y
prov
i
des
t
he
e
l
ec
t
romo
ti
ve force (emf,
V
, or
)
t
ha
t
crea
t
es
t
he e
l
ec
t
r
i
c curren
t
(
I
)
i
n
t
he
c
i
rcu
it
.
The un
it
of curren
t
i
s
t
he
A
mpere
(
A
)
.
The power supp
l
y has a
pos
iti
ve
and a
nega
ti
ve
t
erm
i
na
l
.
The arrow
i
nd
i
ca
t
es
t
ha
t
t
he curren
t
f
l
ows from
t
he pos
iti
ve
t
erm
i
na
l
t
o
t
he nega
ti
ve
t
erm
i
na
l
of
t
he power supp
l
y.
(If v
i
ewed m
i
croscop
i
ca
ll
y, e
l
ec
t
rons f
l
ow
conven
ti
ona
l
curren
t
ti
ve charge f
l
ow
i
ng from
pos
iti
ve
t
o nega
ti
ve.
We sha
ll
use conven
ti
ona
l
curren
t
i
n
t
h
i
s c
l
ass.)
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25
Fi
gure 1
The componen
t
on
t
he r
i
gh
t
i
s ca
ll
ed a
res
i
s
t
or
(
R
)
;
it
s
res
i
s
t
ance
i
s measured
i
n ohms
(
).
You can
t
h
i
nk of
t
he power supp
l
y as
t
he source of e
l
ec
t
r
i
ca
l
power wh
i
ch
i
s
d
i
ss
i
pa
t
ed by
t
he res
i
s
t
or or
l
oad
.
In o
t
her words, res
i
s
t
ance
i
s
t
he phys
i
ca
l
proper
t
y
t
ha
t
conver
t
s e
l
ec
t
r
i
ca
l
energy
t
o hea
t
(or
li
gh
t
,
i
n
t
he case of a
li
gh
t
bu
l
b).
The s
t
ra
i
gh
t
li
nes
connec
ti
ng
t
he power supp
l
y
t
o
t
he res
i
s
t
or are w
i
res (
conduc
t
ors
)
t
ha
t
serve as condu
it
s
for
t
he e
l
ec
t
r
i
ca
l
curren
t
.
They are assumed
t
o have no
summar
i
zes
t
he re
l
a
ti
onsh
i
p among
t
he c
i
rcu
it
componen
t
s d
i
scussed above
:
V
/
R
(1)
Or,
I
=
/
R
Hence,
we see
t
ha
t
curren
t
t
hrough
t
he res
i
s
t
or
i
s propor
ti
ona
l
t
o
t
he vo
lt
age across
t
he
res
i
s
t
or.
V= RI
.
F
rom
t
h
i
s equa
ti
on, we see
t
ha
t
i
f vo
lt
age
i
s p
l
o
tt
ed on
t
he y-ax
i
s and curren
t
on
t
he x-ax
i
s,
t
he graph wou
l
d be a
s
t
ra
i
gh
t
li
ne
i
f
t
he res
i
s
t
ance of
t
he c
i
rcu
it
componen
t
or dev
i
ce
i
s cons
t
an
t
and
t
he s
l
ope
of
t
he
li
ne wou
l
d be equa
l
t
o
R
.
If
t
he graph
i
s a s
t
ra
i
gh
t
li
ne,
t
he dev
i
ce
i
s sa
i
d
t
o be an
ohm
i
c
dev
i
ce.
If
t
he graph of
V
vs.
I
i
s no
t
a s
t
ra
i
gh
t
li
ne,
t
he c
i
rcu
it
componen
t
i
s sa
i
d
t
o be
non-ohm
i
c
.
F
or
t
hese o
t
her
t
ypes of componen
t
s, res
i
s
t
ance
i
s no
t
a cons
t
an
t
bu
t
may vary w
it
h
t
empera
t
ure or curren
t
t
hrough
t
he dev
i
ce.
T
H
E
U
S
E
OF AMM
ETE
R
S
AND VO
LT
M
ETE
R
S
An amme
t
er
i
s used
t
o measure
t
he curren
t
t
ha
t
passes
th
ro
u
g
h
a c
i
rcu
it
componen
t
.
The
amme
t
er
i
s a
l
ways connec
t
ed
i
n
ser
i
es
w
it
h
t
he componen
t
, so
t
he curren
t
t
ha
t
passes
I
R
+
-
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26
t
hrough
t
he componen
t
mus
t
pass
t
hrough
t
he me
t
er. Amme
t
ers have
very
li
tt
l
e
res
i
sta
n
ce
, and so
t
hey w
ill
change
t
he curren
t
i
n
t
he c
i
rcu
it
very
littl
e.
S
ee f
i
gure 2.
Fi
gure 2
A vo
lt
me
t
er
i
s used
t
o measure
t
he vo
lt
age d
i
fference
across
a componen
t
.
The
vo
lt
me
t
er
i
s a
l
ways connec
t
ed
i
n
para
ll
e
l
w
it
h
t
he componen
t
, as
i
n f
i
gure 3.
I
Fi
gure 3
Your professor w
ill
exp
l
a
i
n
t
he use of
t
he par
ti
cu
l
ar me
t
er you w
ill
be us
i
ng for
t
h
i
s
exper
i
men
t
.
I
t
i
s
i
mpor
t
an
t
t
ha
t
you an
ti
c
i
pa
t
e
t
he curren
t
or vo
lt
age magn
it
ude and
t
ha
t
you se
t
your me
t
er on a h
i
gh enough sca
l
e for
t
he read
i
ng.
B
e
tt
er
t
o se
t
it
t
oo h
i
gh
t
han
t
oo
l
ow.
Vo
lt
me
t
ers have a very h
i
gh res
i
s
t
ance, so
t
hey have very
littl
e curren
t
pass
i
ng
t
hrough
t
hem.
The amme
t
er
i
s more eas
il
y damaged
t
han
t
he vo
lt
me
t
er
;
t
herefore, pay
par
ti
cu
l
ar a
tt
en
ti
on
t
o
t
he sca
l
e se
tti
ng and make sure
it
i
s w
i
red
i
n ser
i
es.
R
+
_
A
I
+
_
+
_
R
+
_
V
+
_
Ammeter
Vo
l
tmeter
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27
CAU
T
ION:
W
h
e
n
u
s
in
g t
h
e Ammeter (f
un
ct
i
o
n
o
n
t
h
e DMM),
BE
S
UR
E
to
in
c
lud
e
t
h
at
i
s,
I
=
V
/
R.
W
i
t
h
R
=
0, t
h
e
L
aws of P
h
ys
i
cs w
ill
try to ma
k
e t
hi
s e
qu
at
i
o
n
wor
k
b
y
in
creas
in
g t
h
e c
u
rre
n
t to a
pp
roac
h
in
f
ini
ty (
),
un
t
il
t
h
e Ammeter
bl
ows
a f
u
se.
Pay atte
n
t
i
o
n
to t
h
e sett
in
gs of yo
u
r DMM
b
efore yo
u
co
nn
ect
i
t
in
to a
c
i
rc
ui
t.
If yo
u
r DMM
i
s set as a
n
Ammeter,
i
t w
ill
lik
e
l
y
bl
ow a f
u
se
i
f co
nn
ecte
d
in
n
ce).
T
H
E
ORY
Part 1.
Even good conduc
t
ors,
li
ke me
t
a
l
s, have some res
i
s
t
ance.
F
or sma
ll
curren
t
s,
t
he
res
i
s
t
ance of a me
t
a
l
i
s
i
ndependen
t
of
t
he vo
lt
age across
it
s
l
eng
t
h.
Each k
i
nd of me
t
a
l
has a charac
t
er
i
s
ti
c proper
t
y ca
ll
ed
it
s
res
i
s
ti
v
it
y
(
)
.
The res
i
s
t
ance,
R
, of a w
i
re
i
s g
i
ven
i
n
t
erms of
t
he res
i
s
ti
v
it
y
, accord
i
ng
t
o
t
he re
l
a
ti
onsh
i
p
:
(2)
Where
l
i
s
t
he
l
eng
t
h of
t
he w
i
re and
A
i
s
t
he cross-sec
ti
ona
l
area, as shown
i
n
t
he
d
i
agram above.
B
y measur
i
ng
t
he vo
lt
age from one end of
t
he w
i
re
t
o
t
he o
t
her and by
measur
i
ng
t
he curren
t
t
hrough
t
he w
i
re,
R
can be de
t
erm
i
ned.
The
l
eng
t
h
l
and
t
he
d
i
ame
t
er
d
w
ill
be measured d
i
rec
tl
y, so
t
ha
t
of an unknown me
t
a
l
can be ca
l
cu
l
a
t
ed.
We w
ill
assume
t
he
t
empera
t
ure rema
i
ns cons
t
an
t
t
hroughou
t
t
he exper
i
men
t
.
Part 2.
When
t
he
t
empera
t
ure of a me
t
a
l
changes,
t
he res
i
s
t
ance
i
ncreases accord
i
ng
t
o
t
he re
l
a
ti
onsh
i
p
:
(3)
Where
R
0
i
s
t
he res
i
s
t
ance a
t
T
0
res
i
s
t
ance and
i
s pos
iti
ve for me
t
a
l
s.
Th
i
s exper
i
men
t
w
ill
use a
t
ungs
t
en-f
il
amen
t
li
gh
t
bu
l
b.
B
y
i
ncreas
i
ng
t
he vo
lt
age across
t
he bu
l
b,
t
he curren
t
t
hru
t
he bu
l
b w
ill
i
ncrease
and so w
ill
t
he
t
empera
t
ure of
t
he f
il
amen
t
.
You w
ill
ver
i
fy qua
lit
a
ti
ve
l
y
t
ha
t
t
he
res
i
s
t
ance of
t
he
t
ungs
t
en
i
ncreases w
it
h
t
empera
t
ure.
A
l
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28
PROC
E
DUR
E
Part 1:
C
u
t
a
l
eng
t
h of approx
i
ma
t
e
l
y 1 m of
t
he unknown w
i
re.
S
crape
t
he
i
nsu
l
a
ti
on
from bo
t
h ends for good e
l
ec
t
r
i
ca
l
connec
ti
on.
W
i
re
t
he c
i
rcu
it
as shown
i
n f
i
gure 4 us
i
ng a
lli
ga
t
or c
li
ps
t
o make connec
ti
ons
w
it
h
t
he w
i
re.
WARNING:
Ma
k
e s
u
re t
h
e
p
ower s
uppl
y
i
s t
u
r
n
e
d
OFF, a
nd
DO NO
T
t
u
r
n
i
t o
n
un
t
il
yo
u
r c
i
rc
ui
t
i
s a
pp
rove
d
b
y yo
u
r
in
str
u
ctor.
I
Fi
gure 4
Turn
t
he power supp
l
y knobs
t
o m
i
n
i
mum se
tti
ngs and
t
urn
t
he power supp
l
y ON.
Gradua
ll
y
t
urn
t
he power supp
l
y vo
lt
age up
t
o
i
ncrease
t
he curren
t
.
Ob
t
a
i
n a
t
l
eas
t
s
i
x da
t
a po
i
n
t
s of vo
lt
age and curren
t
, w
it
h curren
t
s be
t
ween 0 and 100 mA,
and crea
t
e a da
t
a
t
ab
l
e of your measuremen
t
s of
V
vs.
I
.
Measure
t
he
l
eng
t
h of
t
he w
i
re be
t
ween
t
he connec
ti
ons.
Us
i
ng a m
i
crome
t
er,
measure
t
he d
i
ame
t
er of
t
he w
i
re.
B
e sure
t
o record
t
he es
ti
ma
t
ed uncer
t
a
i
n
ti
es.
(One source or error
i
s
t
he
i
nsu
l
a
ti
on on
t
he w
i
re.)
B
efore d
i
sman
tli
ng your c
i
rcu
it
, make a rough graph of
V
vs.
I
.
I
t
shou
l
d be c
l
ose
t
o a s
t
ra
i
gh
t
li
ne.
Part 2
+
_
V
+
_
A
cu
t
w
i
re
power
supp
l
y
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29
Fi
gure 5
Measure
t
he res
i
s
t
ance of
t
he 6 V
li
gh
t
bu
l
b (
t
ungs
t
en f
il
amen
t
) w
it
h an
ohmme
t
er.
Use
t
h
i
s va
l
ue as
R
0
.
R
ep
l
ace
t
he cu
t
w
i
re w
it
h
t
he
6 V
li
gh
t
bu
l
b as shown
i
n f
i
gure 5.
Take curren
t
read
i
ngs w
it
h vo
lt
age se
tti
ngs from 0.5 V
t
o 6 V
i
n 0.5 vo
lt
i
ncremen
t
s, and crea
t
e a da
t
a
t
ab
l
e of your measuremen
t
s of
V
vs.
I
.
ANA
L
Y
S
I
S
AND DI
S
CU
SS
ION
Part 1
Pl
o
t
t
he vo
lt
age vs.
t
he curren
t
and from
t
he s
l
ope, de
t
erm
i
ne
t
he res
i
s
t
ance of
t
he
w
i
re.
Use error propaga
ti
on of errors,
t
o f
i
nd
t
he uncer
t
a
i
n
t
y
i
n
t
he res
i
s
ti
v
it
y.
Assume
a 2% error
i
n
R
.
St
a
t
e your f
i
na
l
resu
lt
for
t
he res
i
s
ti
v
it
y of
t
he unknown me
t
a
l
,
t
oge
t
her w
it
h
t
he
percen
t
uncer
t
a
i
n
t
y.
Part 2
Us
i
ng M
S
Exce
l
(ava
il
ab
l
e on
t
he
P
hys
i
ca
l
S
c
i
ences Depar
t
men
t
l
ap
t
op
compu
t
ers),
Pl
o
t
a graph of
V
vs.
I
.
Wha
t
does
t
h
i
s graph
t
e
ll
you abou
t
t
he
res
i
s
t
ance of
t
he f
il
amen
t
as a func
ti
on of
t
he
t
empera
t
ure?
Es
ti
ma
t
e
t
he
l
owes
t
and h
i
ghes
t
res
i
s
t
ance by es
ti
ma
ti
ng
t
he max and m
i
n s
l
opes
of
t
he graph by draw
i
ng
t
angen
t
li
nes and de
t
erm
i
n
i
ng
t
he
i
r s
l
ope. Th
i
s can be
done w
it
h M
S
Exce
l
.
I
+
_
V
+
_
A
li
gh
t
bu
l
b
power
supp
l
y
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30
Assum
i
ng
t
ha
t
t
he
t
empera
t
ure of
t
he ho
t
f
il
amen
t
i
s abou
t
5,000
0
C
, use
t
he
res
i
s
t
ance of
t
he ho
t
f
il
amen
t
a
t
6 V and equa
ti
on (3)
t
o ca
l
cu
l
a
t
e
for
t
he
f
il
amen
t
.
C
ompare your va
l
ue
t
o
t
he accep
t
ed va
l
ue of
= 0.0045
/
0
C
for
t
ungs
t
en.
L
A
B
R
E
POR
T
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your wr
it
e-up sha
ll
i
nc
l
ude
t
he
fo
ll
ow
i
ng
:
(see
t
he append
i
x for W
R
ITING A
F
O
R
MAL
R
E
P
O
R
T)
T
h
eory:
Inc
l
ude any ma
t
hema
ti
ca
l
der
i
va
ti
ons you needed
t
o perform.
A
n
a
l
ys
i
s
:
Type
t
he da
t
a shee
t
(s) and
i
nc
l
ude a re
l
evan
t
d
i
scuss
i
on of
t
he resu
lt
s.
Co
n
c
lu
s
i
o
n
(
to
b
e ty
p
e
d
)
:
A conc
l
us
i
on con
t
a
i
n
i
ng a summary of resu
lt
s sha
ll
be
prov
i
ded
i
n your repor
t
.
The conc
l
us
i
on shou
l
d a
l
so
i
nc
l
ude sources of error and how
t
he
exper
i
men
t
cou
l
d be
i
mproved.
A
pp
e
ndi
x
:
The or
i
g
i
na
l
s
i
gned da
t
a shee
t
(s) and answers
t
o ques
ti
ons (see be
l
ow)
shou
l
d be
i
nc
l
uded
i
n an append
i
x
t
o your repor
t
.
W
h
e
n
wr
i
t
in
g
up
t
h
e a
n
swers to t
h
e
qu
est
i
o
n
s, s
h
ow mat
h
emat
i
ca
l
ste
p
s
p
erforme
d
w
h
ere a
pp
ro
p
r
i
ate.
QU
E
S
T
ION
S
1.
S
uppose
t
ha
t
you cou
l
d s
t
re
t
ch your w
i
re and
it
s dens
it
y rema
i
ned
t
he same.
If
it
i
s now s
t
re
t
ched
t
o
t
w
i
ce
it
s or
i
g
i
na
l
l
eng
t
h, wha
t
i
s
t
he ra
ti
o of
t
he new
res
i
s
t
ance
t
o
t
he or
i
g
i
na
l
res
i
s
t
ance?
(No
t
e
t
ha
t
t
he area and
l
eng
t
h bo
t
h
change.)
2.
B
y wha
t
fac
t
or wou
l
d
t
he res
i
s
t
ance of your w
i
re change
i
f
it
were cu
t
i
n ha
l
f,
w
it
h bo
t
h ends scraped and
t
w
i
s
t
ed
t
oge
t
her so
t
ha
t
you now had
t
wo w
i
res
s
i
de-by-s
i
de w
it
h
t
he o
t
her ends
t
w
i
s
t
ed
t
oge
t
her a
l
so?
(H
i
n
t:
Use
t
he ra
ti
o
me
t
hod.)
3.
If
t
he amme
t
er and
t
he vo
lt
me
t
er were m
i
s
t
aken
l
y
i
n
t
erchanged
i
n
t
he c
i
rcu
it
of par
t
1, and
t
he power
i
s
t
urned on, wou
l
d e
it
her of
t
hese me
t
ers be
damaged?
4.
S
uppose
t
he ends of
t
he w
i
re were no
t
proper
l
y scraped
;
how wou
l
d
t
h
i
s affec
t
t
he resu
lt
s,
i
f a
t
a
ll
? Wou
l
d
t
h
i
s
li
ke
l
y cause sys
t
ema
ti
c, or random error
i
n
t
he
resu
lt
s?
5.
You are asked
t
o des
i
gn a c
i
rcu
it
componen
t
w
it
h zero
t
empera
t
ure coeff
i
c
i
en
t
of res
i
s
t
ance.
C
ons
i
der
i
ng
t
h
i
s exper
i
men
t
, how m
i
gh
t
t
h
i
s be accomp
li
shed?
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31
6.
Wha
t
i
s
t
he benef
it
t
o
t
he bu
l
b
i
f
t
he res
i
s
t
ance
i
ncreases w
it
h
t
empera
t
ure?
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32
ELE
C
T
R
I
C
F
IEL
D
P
LOTTI
N
G
IN
T
RODUC
T
ION
The e
l
ec
t
r
i
c f
i
e
l
d or
i
g
i
na
t
es on pos
iti
ve charge and ends on nega
ti
ve charge.
The f
i
e
l
d
d
i
rec
ti
on
i
s
t
herefore from pos
iti
ve
t
o nega
ti
ve.
Jus
t
as
t
he grav
it
a
ti
ona
l
f
i
e
l
d
li
nes are
perpend
i
cu
l
ar
t
o an equ
i
po
t
en
ti
a
l
surface, such as a
t
ab
l
e
t
op, e
l
ec
t
r
i
c f
i
e
l
d
li
nes (
E
f
i
e
l
d
li
nes) are perpend
i
cu
l
ar
t
o equ
i
po
t
en
ti
a
l
li
nes.
E
l
ec
t
r
i
c po
t
en
ti
a
l
i
s measured
i
n
vo
lt
s
,
t
hus equ
i
po
t
en
ti
a
l
li
nes are equa
l
vo
lt
age
li
nes.
B
y p
l
o
tti
ng equ
i
po
t
en
ti
a
l
li
nes and
draw
i
ng
li
nes perpend
i
cu
l
ar
t
o
t
hem,
t
he
E
f
i
e
l
d can be mapped.
In
t
h
i
s exper
i
men
t
, a vo
lt
me
t
er
i
s used
t
o de
t
erm
i
ne po
i
n
t
s of equa
l
po
t
en
ti
a
l
on a
carbon
i
zed conduc
ti
ng paper.
Us
i
ng a power supp
l
y, a po
t
en
ti
a
l
d
i
fference, or vo
lt
age
d
i
fference,
i
s es
t
ab
li
shed be
t
ween
t
wo me
t
a
li
zed areas.
The curren
t
t
hrough
t
he paper
causes
t
he po
t
en
ti
a
l
t
o smoo
t
h
l
y change be
t
ween
t
he pos
iti
ve and nega
ti
ve
t
erm
i
na
l
s. The
vo
lt
age
i
n d
i
fferen
t
reg
i
ons can be measured w
it
h a probe and vo
lt
me
t
er and equa
l
vo
lt
age reg
i
ons can be mapped.
+
C
A
RB
ONIZED
P
A
P
E
R
V
_
_
P
R
O
B
E
DI
P
OLE
20 V
+
+
Fi
gure 1
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33
E
QUIPM
E
N
T
AND MA
TE
RIA
L
S
C
arbon
i
zed (conduc
ti
ve)
P
aper w
it
h
Sil
ver-
P
a
i
n
t
ed E
l
ec
t
rodes
C
ork-
B
acked
Pl
ywood
B
oard
Pl
a
i
n Wh
it
e
P
r
i
n
t
er
P
aper
D
i
g
it
a
l
Mu
lti
-Me
t
er (DMM)
0-25V D
C
P
ower
S
upp
l
y
P
unch
Pi
ns
St
ra
i
gh
t
Pi
nes
Thumb
t
acks w
it
h
S
o
l
dered Loops (for A
lli
ga
t
or
C
li
p connec
ti
on)
Tes
t
Lead (w
it
h
P
robe End)
A
lli
ga
t
or
C
li
ps
F
rench
C
urve (draw
i
ng
t
oo
l
)
Fl
ex
i
b
l
e
R
u
l
er (draw
i
ng
t
oo
l
)
S
c
i
ssors
PROC
E
DUR
E
(
P
r
i
or
t
o s
t
ar
ti
ng
t
he
l
ab c
l
ass, rev
i
ew d
i
po
l
es, f
i
e
l
ds, and e
l
ec
t
r
i
c f
i
e
l
d mapp
i
ngs
i
n your
t
ex
t
book.)
Part 1
Pl
ace
t
he cork board, cork s
i
de up, on your
l
ab
t
ab
l
e.
P
u
t
shee
t
s of p
l
a
i
n wh
it
e
paper
(one for each
l
ab par
t
ner) on
t
he board and
t
hen p
l
ace
t
he carbon
i
zed paper
on
t
he board, on
t
op of
t
he wh
it
e paper.
A
li
gn
t
he paper s
t
ack w
it
h
t
he edges of
t
he board, and secure
t
he paper
t
o
t
he board by us
i
ng a push p
i
n a
t
each corner.
Use
t
he spec
i
a
ll
y-bu
ilt
t
humb
t
acks and a
lli
ga
t
or c
li
ps
t
o connec
t
t
he pa
t
ch cords
t
o
t
he me
t
a
li
zed d
i
po
l
e areas.
W
i
re
t
he c
i
rcu
it
as shown
i
n f
i
gure 1.
Turn on
t
he power supp
l
y and es
t
ab
li
sh 20 V be
t
ween
t
he d
i
po
l
es.
Good con
t
ac
t
i
s cr
iti
ca
l
.
If good con
t
ac
t
i
s made, when
t
he probe
i
s p
l
aced abou
t
ha
l
f-way
be
t
ween
t
he
t
wo po
l
es,
t
he read
i
ng shou
l
d be c
l
ose
t
o 10 V
;
and, when
t
he probe
i
s p
l
aced
i
n
t
he +20 V me
t
a
li
zed po
l
e area (no
t
t
he
t
ack)
t
he vo
lt
age shou
l
d read
abou
t
20 V. Once you have es
t
ab
li
shed good con
t
ac
t
, do no
t
d
i
s
t
urb
t
he
t
humb
t
acks
i
n any way.
Now
l
oca
t
e equ
i
po
t
en
ti
a
l
s a
t
3 V, 6 V, 10 V, 14 V, and 17 V.
You w
ill
need
seven po
i
n
t
s for each equ
i
po
t
en
ti
a
l
, one a
t
t
he
li
ne of symme
t
ry, and
t
hree on each
s
i
de of
t
he
li
ne of symme
t
ry.
C
arefu
ll
y move
t
he probe around (w
it
hou
t
d
i
s
t
urb
i
ng
t
he
t
humb
t
ack connec
ti
ons)
t
o f
i
nd
t
he
l
oca
ti
on of
t
he equ
i
po
t
en
ti
a
l
po
i
n
t
s.
C
arefu
ll
y mark
t
he equ
i
po
t
en
ti
a
l
po
i
n
t
w
it
h a penc
il
.
Do no
t
damage
t
he
paper
i
n any way.
Do no
t
t
ake da
t
a po
i
n
t
s nex
t
t
o
t
he edge of
t
he paper.
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34
Part 2
D
i
sconnec
t
t
he a
lli
ga
t
or c
li
p from
t
he pos
iti
ve po
l
e
t
humb
t
ack and connec
t
it
t
o a
t
humb
t
ack
l
oca
t
ed a
t
t
he cen
t
er of
t
he me
t
a
li
zed
li
ne.
Make sure
t
he power
supp
l
y
i
s s
till
a
t
20 V.
Loca
t
e
t
he 5 V, 10 V, and 15 V equ
i
po
t
en
ti
a
l
.
Aga
i
n, you
w
ill
need seven po
i
n
t
s for each equ
i
po
t
en
ti
a
l
, one a
t
t
he
li
ne of symme
t
ry, and
t
hree on each s
i
de of
t
he
li
ne of symme
t
ry.
C
arefu
ll
y move
t
he probe around
(w
it
hou
t
d
i
s
t
urb
i
ng
t
he
t
humb
t
ack connec
ti
ons)
t
o f
i
nd
t
he
l
oca
ti
on of
t
he
equ
i
po
t
en
ti
a
l
po
i
n
t
s.
C
arefu
ll
y mark
t
he equ
i
po
t
en
ti
a
l
po
i
n
t
w
it
h a penc
il
.
Do no
t
damage
t
he paper
i
n any way.
Do no
t
t
ake da
t
a po
i
n
t
s nex
t
t
o
t
he edge of
t
he
paper.
Af
t
er a
ll
equ
i
po
t
en
ti
a
l
da
t
a po
i
n
t
s for bo
t
h par
t
s have been
l
oca
t
ed, use a p
i
n
t
ack
t
o punch a ho
l
e a
t
each da
t
a po
i
n
t
t
hru a
ll
t
hree
l
ayers of paper.
A
l
so, perfora
t
e
around
t
he per
i
me
t
ers of each me
t
a
li
zed area.
The perfora
t
ed wh
it
e shee
t
s are
your da
t
a shee
t
s for
t
h
i
s exper
i
men
t
.
T
H
E
E
XP
E
RIM
E
N
T
1.
P
repare
t
wo e
l
ec
t
r
i
c f
i
e
l
d p
l
o
t
s, one for
t
he d
i
po
l
e and
t
he o
t
her for
t
he po
i
n
t
and
li
ne charge.
Lay
t
he perfora
t
ed shee
t
on
t
op of ano
t
her shee
t
of wh
it
e paper.
C
opy
t
he perfora
t
ed da
t
a po
i
n
t
s on
t
o
t
he wh
it
e paper by mark
i
ng each perfora
ti
on
on
t
o
t
he wh
it
e paper be
l
ow w
it
h penc
il
.
2.
c
i
rc
l
e.
Nex
t
, draw
t
he equ
i
po
t
en
ti
a
l
li
nes us
i
ng a f
l
ex
i
curve ru
l
er or
F
rench curve.
Do no
t
draw
t
he curve from po
i
n
t
t
o po
i
n
t;
some po
i
n
t
s may
li
e on one s
i
de of
t
he
po
i
n
t
, as feas
i
b
l
e.
3.
Draw
t
he e
l
ec
t
r
i
c f
i
e
l
d
li
nes as smoo
t
h, so
li
d curves, perpend
i
cu
l
ar
t
o
t
he
equ
i
po
t
en
ti
a
l
curves where
t
hey
i
n
t
ersec
t
.
The me
t
a
li
zed areas are a
l
so
equ
i
po
t
en
ti
a
l
s
;
t
herefore, make sure
t
he E-f
i
e
l
d
li
nes
i
n
t
ersec
t
perpend
i
cu
l
ar
t
o
t
he
me
t
a
li
zed area.
Draw
t
he f
i
e
l
d
li
ne a
l
ong
t
he
li
ne of symme
t
ry and
t
hree
add
iti
ona
l
li
nes on each s
i
de.
S
ymme
t
ry of
t
he f
i
e
l
d
li
nes w
ill
be a fac
t
or
i
n
grad
i
ng your draw
i
ng.
Th
i
nk of
t
he
li
ne of symme
t
ry as a m
i
rror and draw
t
he
f
i
e
l
d
li
nes accord
i
ng
l
y.
4.
The equ
i
po
t
en
ti
a
l
vo
lt
ages shou
l
d be
l
abe
l
ed, and
t
he E-f
i
e
l
d
li
nes shou
l
d have
arrows
i
n
t
he proper d
i
rec
ti
on on your draw
i
ng.
L
A
B
R
E
POR
T
Hand
i
n your draw
i
ng a
l
ong w
it
h
t
he answers
t
o
t
he ques
ti
ons be
l
ow.
Type up your
answers and
i
nc
l
ude
t
hem an append
i
x
t
o your
l
ab repor
t
.
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35
QU
E
S
T
ION
S
(j
u
st
i
fy yo
u
r a
n
swers)
(1)
C
ons
i
der
i
ng
t
he d
i
po
l
e f
i
e
l
d, where
i
s
it
t
he s
t
ronges
t
?
The weakes
t
?
(2)
F
or each par
t
,
t
he edge of
t
he cen
t
er po
l
e of
t
he d
i
po
l
e was a
t
zero po
t
en
ti
a
l;
i
s
t
he
E
-f
i
e
l
d zero
t
here a
l
so?
(3)
Us
i
ng
, ca
l
cu
l
a
t
e
t
he average
E
-f
i
e
l
d a
l
ong
t
he
li
ne of symme
t
ry
be
t
ween 6V and 14V po
t
en
ti
a
l
s and be
t
ween
t
he 3V and 6V po
t
en
ti
a
l
s for
t
he
d
i
po
l
e f
i
e
l
d.
(4)
How do
t
he
E
-f
i
e
l
ds found
i
n ques
ti
on (3) compare, and are
t
he resu
lt
s as
expec
t
ed?
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36
CAPAC
IT
ANC
E and
CAPAC
ITO
R
S
PURPO
S
E
Part 1
.
To bu
il
d a capac
it
or us
i
ng paper sandw
i
ched be
t
ween
t
wo a
l
um
i
num shee
t
s
;
To
measure
t
he d
i
e
l
ec
t
r
i
c cons
t
an
t
of
t
he paper
;
and, To observe how capac
it
ance depends on
t
he geome
t
ry of
t
he capac
it
or.
(No
t
e
:
The d
i
e
l
ec
t
r
i
c ma
t
er
i
a
l
i
n a capac
it
or
i
s
t
he
subs
t
ance or ma
t
er
i
a
l
t
ha
t
ma
i
n
t
a
i
ns separa
ti
on of
t
he charge p
l
a
t
es.)
Part 2
.
F
rom
t
he capac
it
or d
i
scharge curve, de
t
erm
i
ne
t
he
R
es
i
s
t
ance
C
apac
it
ance
(
RC
)
ti
me cons
t
an
t
of a ser
i
es
RC
c
i
rcu
it
and compare
it
t
o
t
he ca
l
cu
l
a
t
ed
RC
va
l
ue.
T
H
E
ORY
Part 1
.
The capac
it
ance
C
i
s def
i
ned as
t
he quan
tit
y of charge d
i
v
i
ded by vo
lt
age (
Q
/
V
).
C
apac
it
ance
i
s de
t
erm
i
ned by
t
he separa
ti
on
d
be
t
ween
t
he p
l
a
t
es and
A
,
t
he area of
t
he
p
l
a
t
es accord
i
ng
t
o
t
he equa
ti
on
(1)
where
i
s
t
he d
i
e
l
ec
t
r
i
c cons
t
an
t
.
The d
i
e
l
ec
t
r
i
c ma
t
er
i
a
l
i
n
t
h
i
s exper
i
men
t
i
s paper.
Part 2
.
The vo
lt
age of a d
i
scharg
i
ng capac
it
or
i
n ser
i
es w
it
h a res
i
s
t
or
i
s g
i
ven by
(2)
RC
i
s def
i
ned as
t
he
ti
me cons
t
an
t
.
P
r
i
or
t
o c
l
ass,
t
ake
t
he na
t
ura
l
l
ogar
it
hm (
l
n) of
bo
t
h s
i
des of equa
ti
on (2), pu
t
t
he resu
lt
an
t
equa
ti
on
i
n
t
he form of a s
t
ra
i
gh
t
li
ne, and
i
den
ti
fy
t
he s
l
ope of
t
he
li
ne.
E
QUIPM
E
N
T
AND MA
TE
RIA
L
S
20 cm X 28 cm a
l
um
i
num shee
t
s (2 per group)
20 cm X 14 cm a
l
um
i
num shee
t
s (2 per group)
C
ork-
B
acked
Pl
ywood
B
oard (2 per group)
P
or
t
ab
l
e DMM
1
µ
F
capac
it
or
St
opwa
t
ch
D
i
rec
t
C
urren
t
(D
C
)
P
ower
S
upp
l
y (0
25 VD
C
)
A
lli
ga
t
or
C
li
ps
C
apac
it
ance me
t
er
St
ack of p
l
a
i
n
P
r
i
n
t
er
P
aper for
t
he c
l
ass
M
i
crome
t
er
Graph paper
R
u
l
er
Assor
t
ed K
il
ogram Lab We
i
gh
t
s
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37
PROC
E
DUR
E
Part 1
.
C
ons
t
ruc
ti
ng a capac
it
or and measur
i
ng
it
s capac
it
ance
Us
i
ng a m
i
crome
t
er, measure
t
he
t
h
i
ckness of
t
en shee
t
s of paper.
Measure
t
he
l
eng
t
h and w
i
d
t
h of
t
he a
l
um
i
num p
l
a
t
es.
1.
C
ons
t
ruc
t
t
he capac
it
or by pu
tti
ng one shee
t
of paper be
t
ween
t
he
t
wo a
l
um
i
num
p
l
a
t
es as shown be
l
ow.
Pl
ace
t
he p
l
a
t
es and sandw
i
ched paper be
t
ween
t
wo cork-
backed p
l
ywood boards
;
cork-s
i
de aga
i
ns
t
t
he a
l
um
i
num p
l
a
t
es.
Le
t
t
he
t
abs on
each p
l
a
t
e s
ti
ck ou
t
of
t
he edge of
t
he boards on oppos
it
e ends.
2.
Pl
ace 4 kg of mass (s
l
o
tt
ed
l
ab we
i
gh
t
s) even
l
y d
i
s
t
r
i
bu
t
ed on
t
he
t
op board.
Us
i
ng
t
es
t
l
eads and a
lli
ga
t
or c
li
ps, a
tt
ach a capac
it
ance me
t
er
t
o
t
he
t
abs on
t
he
C
1
, as seen on
t
he me
t
er.
Add more we
i
gh
t
and
no
ti
ce
t
he var
i
a
ti
on
i
n
C
1
.
Add we
i
gh
t
s un
til
t
here
i
s very
littl
e var
i
a
ti
on
i
n
C
1
.
R
ecord
t
he capac
it
ance,
C
1
, as seen on
t
he me
t
er.
3.
C
arefu
ll
y
i
nser
t
ano
t
her shee
t
of paper and re-measure
t
he capac
it
ance
C
2
w
it
h
t
he
we
i
gh
t
s s
t
and
i
ng on
t
he
t
op cork board.
4.
Now remove
t
he
l
arge a
l
um
i
num p
l
a
t
es, rep
l
ace
t
hem w
it
h
t
he sma
ll
er a
l
um
i
num
p
l
a
t
es, and separa
t
e
t
he p
l
a
t
es w
it
h
j
us
t
one shee
t
of paper.
Aga
i
n, p
l
ace 4 kg of
mass on
t
he
t
op cork board and measure
t
he capac
it
ance
C
3
.
Part 2
.
The
RC
ti
me cons
t
an
t
.
W
i
re
t
he c
i
rcu
it
shown
i
n
t
he schema
ti
c be
l
ow (f
i
gure (1)).
No
t
e
t
ha
t
t
he
vo
lt
me
t
er
i
s a
S
e
t
t
he power
t
o
t
he max
i
mum vo
lt
age of
t
he power supp
l
y.
Do no
t
exceed 25 V.
C
l
ose
t
he sw
it
ch and charge
t
he capac
it
or.
The capac
it
or
i
s charged when
t
he
vo
lt
me
t
er reaches a s
t
eady s
t
a
t
e.
Open
t
he sw
it
ch
t
o d
i
scharge
t
he capac
it
or
t
hrough
t
he res
i
s
t
or and
t
he D
i
g
it
a
l
Vo
lt
me
t
er DVM.
Take vo
lt
age read
i
ngs for
t
hree m
i
nu
t
es.
Take
t
hese read
i
ngs frequen
tl
y dur
i
ng
t
he f
i
rs
t
m
i
nu
t
e and
t
hen
j
us
t
a few for
t
he rema
i
n
i
ng
ti
me.
a
l
um
i
num
shee
t
paper
cork-backed board
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38
Fi
gure 1
WARNING:
E
l
ectro
l
yt
i
c ca
p
ac
i
tors (
i
.e., ca
p
ac
i
tors t
h
at
u
se a
liquid
di
e
l
ectr
i
c) ca
n
b
e
d
a
n
gero
u
s
i
f
n
ot
h
a
ndl
e
d
p
ro
p
er
l
y.
T
hi
s ty
p
e of ca
p
ac
i
tor
i
s very se
n
s
i
t
i
ve to
reverse
p
o
l
ar
i
ty vo
l
tages a
nd
may
p
o
p
or ex
pl
o
d
e
i
f co
nn
ecte
d
i
m
p
ro
p
er
l
y,
p
oss
ibl
y
scatter
in
g
h
ot e
l
ectro
l
yte.
B
e s
u
re to co
nn
ect t
h
e
p
os
i
t
i
ve vo
l
tage
l
ea
d
to t
h
e
term
in
a
l
).
C
h
ec
k
w
i
t
h
yo
u
r
in
str
u
ctor to ma
k
e s
u
re yo
u
h
ave
id
e
n
t
i
f
i
e
d
t
h
e
ca
p
ac
i
tor
p
os
i
t
i
ve term
in
a
l
correct
l
y.
WARNING:
We are
u
s
in
g
n
e
i
t
h
er
l
arge ca
p
ac
i
tors
n
or
hi
g
h
vo
l
tage
in
t
hi
s
l
a
b
ex
p
er
i
me
n
t.
s
h
oc
k
or
bu
r
n
hu
ma
n
t
i
ss
u
e
i
f
di
sc
h
arg
in
g across t
h
e s
kin
.
Ge
n
era
ll
y,
k
ee
pin
g t
h
e
a
ppli
e
d
vo
l
tage
b
e
l
ow 48 V
i
s co
n
s
id
ere
d
l
ow vo
l
tage.
L
ow ca
p
ac
i
ta
n
ce ca
p
ac
i
tors
are co
n
s
id
ere
d
safe at t
hi
s vo
l
tage
l
eve
l
,
bu
t t
h
ey may st
ill
d
e
li
ver a s
u
r
p
r
i
s
in
g s
h
oc
k
.
B
efore c
h
arg
in
g a ca
p
ac
i
tor a
nd
after
u
s
in
g
i
t
in
a c
i
rc
ui
t, t
h
e ca
p
ac
i
tor ca
n
b
e
l
arge ca
p
ac
i
tor, co
n
s
id
er
in
c
ludin
g a res
i
stor
in
t
h
e s
h
ort
in
g c
i
rc
ui
t, as t
h
e
in
sta
n
ta
n
eo
u
s c
u
rre
n
t
p
ro
du
ce
d
co
uld
b
e
qui
te
hi
g
h
.
ANA
L
Y
S
I
S
Part 1
.
Us
i
ng equa
ti
on (1),
t
he area
A
,
t
he separa
ti
on
d
, and capac
it
ance
C
1
, ca
l
cu
l
a
t
e
t
he va
l
ue of
+
-
C
=
1
µ
F
DVM
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39
L
A
B
R
E
POR
T
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your wr
it
e-up sha
ll
i
nc
l
ude
t
he
fo
ll
ow
i
ng
:
(see
t
he append
i
x for W
R
ITING A
F
O
R
MAL
R
E
P
O
R
T)
T
h
eory
:
Inc
l
ude any ma
t
hema
ti
ca
l
der
i
va
ti
ons you needed
t
o perform.
A
n
a
l
ys
i
s
:
D
i
scuss your resu
lt
s ob
t
a
i
ned
i
n
P
ar
t
1 and
P
ar
t
2.
B
e sure
t
o
i
nc
l
ude a pr
i
n
t
-
ou
t
of your M
S
Exce
l
graphs.
Co
n
c
lu
s
i
o
n
(
to
b
e ty
p
e
d
)
:
A conc
l
us
i
on con
t
a
i
n
i
ng a summary of resu
lt
s, and a
compar
i
son of your exper
i
men
t
a
l
va
l
ues w
it
h accep
t
ed va
l
ues sha
ll
be prov
i
ded
i
n your
repor
t
.
(Is
t
he percen
t
d
i
screpancy
l
ess
t
han pred
i
c
t
ed error?)
The conc
l
us
i
on shou
l
d a
l
so
i
nc
l
ude sources of error and how
t
he exper
i
men
t
cou
l
d be
i
mproved.
A
pp
e
ndi
x
:
The or
i
g
i
na
l
s
i
gned da
t
a shee
t
s shou
l
d be
i
nc
l
uded
i
n an append
i
x
t
o your
repor
t
.
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40
V
O
LT
A
G
E
AND CURR
E
N
T
D
I
V
I
D
E
R C
I
RCU
I
T
S
I
N
T
R
O
DUC
T
IO
N
The exper
i
men
t
a
l
ob
j
ec
ti
ves
i
n
t
h
i
s
l
ab are
t
o des
i
gn vo
lt
age and curren
t
d
i
v
i
der c
i
rcu
it
s
t
o par
ti
cu
l
ar spec
i
f
i
ca
ti
ons and
t
hen measure
t
he vo
lt
ages and curren
t
s
i
n
t
hese c
i
rcu
it
s.
ob
j
ec
ti
ves are
t
o ga
i
n fur
t
her exper
i
ence
i
n us
i
ng
t
he vo
lt
me
t
ers and amme
t
er and
t
o
s
t
udy some
i
mpor
t
an
t
arrangemen
t
s of res
i
s
t
ors frequen
tl
y used
i
n e
l
ec
t
ron
i
c c
i
rcu
it
s.
R
es
i
s
t
ors are c
i
rcu
it
componen
t
s wh
i
ch are spec
i
f
i
ca
ll
y bu
ilt
t
o prov
i
de a g
i
ven amoun
t
of
res
i
s
t
ance. You w
ill
be us
i
ng
fi
xed
(va
l
ue) and var
i
ab
l
e res
i
s
t
ors
i
n
t
he exper
i
men
t
.
Fi
xed res
i
s
t
ors have
t
he
i
r res
i
s
t
ance and
t
o
l
erance pr
i
n
t
ed on
t
hen w
it
h a co
l
or code as
shown be
l
ow
:
TOLE
R
AN
C
E
± 5%
± 10%
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41
E
QUIPM
E
N
T
AND
S
UPP
L
I
E
S
TWO DMM
S
0-25V
P
OWE
R
S
U
PP
LY
A
SS
O
R
TMENT O
F
R
E
S
I
S
TO
R
S
LEAD
S
BR
EAD
B
OA
R
D
S
ALLEGATO
R
C
LI
PS
JUM
P
E
R
WI
R
E KIT
T
H
E
ORY
R
E
S
I
S
T
OR
S
IN
S
E
RI
E
S
-
T
H
E
VO
LT
AG
E
DIVID
E
R
St
udy
t
he comb
i
na
ti
ons of res
i
s
t
ors
i
n your
t
ex
t
.
The res
i
s
t
ance of n res
i
s
t
ors
i
n ser
i
es
i
s g
i
ven as
:
Therefore
t
he equ
i
va
l
en
t
res
i
s
t
ance of
t
wo res
i
s
t
ors
i
n ser
i
es
i
s
The correspond
i
ng c
i
rcu
it
i
s shown be
l
ow
:
A
+
b
_
V
a
Fi
gure 1
,
I
=
/
R
and der
i
ve
t
he vo
lt
age d
i
v
i
der equa
ti
on
Inc
l
ude
t
h
i
s der
i
va
ti
on
i
n
t
he
t
heory
por
ti
on of your repor
t
.
R
E
S
I
S
T
OR
S
IN PARA
LLEL
-
T
H
E
CURR
E
N
T
DIVID
E
R
R
es
i
s
t
ors
i
n para
ll
e
l
comb
i
ne accord
i
ng
t
o
t
he equa
ti
on
:
R
2
R
1
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42
The correspond
i
ng d
i
agram
i
s
:
I
A
Fi
gure 2
and
.
Inc
l
ude
t
hese der
i
va
ti
ons
i
n your repor
t
.
PROC
E
DUR
E
PAR
T
1: VO
LT
AG
E
DIVID
E
R
Des
i
g
n
a vo
lt
age d
i
v
i
der c
i
rcu
it
, such as
t
he one
i
n f
i
gure 1.
The power supp
l
y vo
lt
age
i
s
5.0 V,
t
he curren
t
i
s
t
o be 3.31 mA, and
t
he vo
lt
age
V
ab
shou
l
d be 1.69 V.
Draw a nea
t
schema
ti
c d
i
agram w
it
h
t
he proper res
i
s
t
or va
l
ues
l
abe
l
ed, have
it
approve
by your
i
ns
t
ruc
t
or.
If,
t
he va
l
ues ca
l
cu
l
a
t
e for
t
he res
i
s
t
ors are no
t
ava
il
ab
l
e, use
t
he c
l
oses
t
va
l
ue
res
i
s
t
or ava
il
ab
l
e, or comb
i
na
ti
ons of res
i
s
t
ors
i
n ser
i
es, and ca
l
cu
l
a
t
e new vo
lt
ages and
curren
t
s.
B
u
il
d
t
he c
i
rcu
it
, and ver
i
fy your des
i
gn by measur
i
ng
t
he pred
i
c
t
ed curren
t
and vo
lt
age. No
t
e
t
he
l
oca
ti
on of
t
he amme
t
er and vo
lt
me
t
er
i
n f
i
gure 1.
If you cou
l
d no
t
R
1
+
_
+
_
+
R
2
_
I
1
I
2
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43
f
i
nd
t
he exac
t
va
l
ues, use va
l
ues c
l
ose
t
o wha
t
you need and
t
hen re-ca
l
cu
l
a
t
e
t
he
vo
lt
ages.
C
ompare
t
hese new vo
lt
ages w
it
h measured va
l
ues.
PAR
T
2: CURR
E
N
T
DIVID
E
R
Des
i
g
n
a curren
t
d
i
v
i
der c
i
rcu
it
where
t
he power supp
l
y vo
lt
age
i
s 10 V,
I
= 6.0 mA and
.
No
t
e how
t
he amme
t
er
i
s connec
t
ed
i
n ser
i
es
t
o measure curren
t
I
1
. You w
ill
need a s
i
m
il
ar connec
ti
on
t
o measure
I
,
I
1
,
and
I
2
.
If,
t
he va
l
ues ca
l
cu
l
a
t
ed for
t
he
res
i
s
t
ors are no
t
ava
il
ab
l
e, use
t
he c
l
oses
t
va
l
ue res
i
s
t
or ava
il
ab
l
e, or comb
i
na
ti
ons of
res
i
s
t
ors
i
n ser
i
es, and ca
l
cu
l
a
t
e new curren
t
s.
B
u
il
d
t
he c
i
rcu
it
, and ver
i
fy your des
i
gn
by measur
i
ng
t
he pred
i
c
t
ed curren
t
and vo
lt
age. No
t
e
t
he
l
oca
ti
on of
t
he amme
t
er and
vo
lt
me
t
er
i
n f
i
gure 2.
T
H
E
R
E
POR
T
(see wr
i
t
in
g a re
p
ort) (
E
V
E
RY
T
HING MU
S
T
BE
T
YP
E
D-U
S
E
WORD AND
E
QUA
T
ION
E
DI
T
OR OR
E
QUIVA
LE
N
T
)
U
nl
ess a forma
l
re
p
ort
i
s re
qui
re
d
b
y yo
u
r
p
rofessor, yo
u
r re
p
ort s
h
a
ll
co
n
s
i
st of:
T
h
eory:
Der
i
ve
t
he equa
ti
ons for par
t
s 1 and 2
A
n
a
l
ys
i
s a
nd
di
sc
u
ss
i
o
n
of res
ul
ts
:
Draw your own schema
ti
c for each par
t
us
i
ng
t
he
used. Do no
t
pho
t
oc
-wr
it
e
t
he
equa
ti
ons der
i
ved
i
n
t
he
t
heory and show ca
l
cu
l
a
ti
ons for par
t
s one and
t
wo.
C
ompare
t
he vo
lt
ages and curren
t
s, for wh
i
ch
t
he c
i
rcu
it
was des
i
gned, w
it
h
t
he measures va
l
ues.
Use error propaga
ti
on
t
o pred
i
c
t
t
he error of
t
he ca
l
cu
l
a
t
ed vo
lt
ages and curren
t
s.
Assume neg
li
g
i
b
l
e error
i
n
t
he power supp
l
y vo
lt
age. Assume 5%
t
o
l
erance
i
n
t
he
res
i
s
t
ors.
Co
n
c
lu
s
i
o
n
A
pp
e
ndi
x
w
it
h or
i
g
i
na
l
da
t
a shee
t
and or
i
g
i
na
l
ca
l
cu
l
a
ti
ons
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44
T
H
E
O
S
C
I
LL
O
S
C
O
P
E
IN
T
RODUC
T
ION
The osc
ill
oscope
i
s one of
t
he mos
t
versa
til
e
t
es
t
i
ns
t
rumen
t
s used
i
n sc
i
ence and
eng
i
neer
i
ng.
Your
i
ns
t
ruc
t
or w
ill
l
ec
t
ure on
it
s bas
i
c usage.
A func
ti
on genera
t
or w
ill
be
connec
t
ed
t
o
t
he osc
ill
oscope and each s
t
uden
t
w
ill
prac
ti
ce
t
he
i
n
iti
a
l
se
t
up of
t
he scope
and prac
ti
ce measur
i
ng vo
lt
age and per
i
od of a s
i
nuso
i
da
l
vo
lt
age. The frequency w
ill
be
ca
l
cu
l
a
t
ed from
t
he per
i
od and compared w
it
h
t
he frequency
i
nd
i
ca
t
ed on
t
he genera
t
or.
An ora
l
t
es
t
w
ill
be adm
i
n
i
s
t
ered
t
o each s
t
uden
t
t
o check
t
he
i
r prof
i
c
i
ency w
it
h
t
he
scope.
A wr
itt
en mu
lti
p
l
e cho
i
ce qu
i
z w
ill
a
l
so be g
i
ven a
t
t
he end of
t
he c
l
ass per
i
od.
The f
i
gure be
l
ow shows
t
he
C
on
t
ro
l
P
ane
l
you w
ill
f
i
nd on our
l
ab osc
ill
oscopes (as we
ll
as free-s
t
and
i
ng H
it
ach
i
osc
ill
oscopes).
The scope D
i
sp
l
ay
CR
T (no
t
shown)
i
s
t
o
t
he
l
ef
t
of
t
he con
t
ro
l
pane
l
.
The numbered
l
abe
l
s are
i
ndexed
t
o
t
he
S
e
t
-up
P
rocedures (Tab
l
e 1)
prov
i
ded on
t
he nex
t
page.
The number
i
ng
i
s a
l
so cons
i
s
t
en
t
w
it
h
t
he osc
ill
oscope
H
it
ach
i
Opera
ti
on Manua
l
(ava
il
ab
l
e
i
n
l
ab off
i
ce),
i
f add
iti
ona
l
t
echn
i
ca
l
i
nforma
ti
on
i
s
sough
t
, such as
t
he mean
i
ng of
l
abe
l
s no
t
addressed
i
n Tab
l
e 1.
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45
Fi
gure 1
H
it
ach
i
Mode
l
V 422 Osc
ill
oscope
C
on
t
ro
l
P
ane
l
PROC
E
DUR
E
S
COP
E
S
ET
UP
C
onnec
t
t
he fema
l
e
B
N
C
t
o fema
l
e
B
N
C
cab
l
e
t
o
t
he func
ti
on genera
t
or and
t
hen
t
o
t
he
osc
ill
oscope.
S
e
t
t
he func
ti
on genera
t
or frequency
t
o 1 k
il
oher
t
z (kHz) and sw
it
ch
it
t
o
t
he s
i
ne func
ti
on.
S
e
t
t
he amp
lit
ude
t
o abou
t
t
he m
i
dd
l
e pos
iti
on.
Turn on power
t
o
t
he
scope (bu
tt
on 1) and
t
he func
ti
on genera
t
or.
F
o
ll
ow
t
he bas
i
c osc
ill
oscope se
t
up
procedure prov
i
ded
i
n Tab
l
e 1 be
l
ow.
E
QUIPM
E
N
T
L
I
S
T
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46
H
it
ach
i
V 422
osc
ill
oscope
F
unc
ti
on genera
t
or
B
N
C
sp
litt
er
t
ee-ma
l
e
t
o fema
l
e
2 fema
l
e
B
N
C
t
o fema
l
e
B
N
C
cab
l
e
F
ema
l
e
B
N
C
t
o banana
j
ack adap
t
er
DMM
Osc
ill
oscope qu
i
z
Tab
l
e 1
S
e
t
up
P
rocedures for H
it
ach
i
Mode
l
V 422 Osc
ill
oscope
S
TE
P
CON
T
RO
L
#
S
ee F
i
g
u
re 1
CON
T
RO
L
NAM
E
S
ET
CON
T
RO
L
T
O:
1
1
P
OWE
R
ON
2
4
ILLUM
MID
P
O
S
ITION
3
26
TIME
/
DIV
0.1m
illi
second (ms)
4
27
S
W
P
VA
R
F
ULLY
C
LO
C
KWI
S
E
(un
til
it
c
li
cks off)
5
29
P
O
S
ITION
(
P
ULL X 10 MAG)
MID
P
O
S
ITION
P
U
S
H IN
6
30
C
H1 ALT
/
MAG
OUT
7
35
MODE
AUTO
8
34
LEVEL
[
P
ULL (-)
S
LO
P
E]
MID
P
O
S
ITION
P
U
S
H IN
9
31
S
OU
RC
E
INT
10
21
MODE
C
HO
P
11
32
INT T
R
IG
C
H1
CHANN
EL
1 OR X-
S
E
C
T
ION
12
13
VOLT
S/
DIV
1 V
13
15
VA
R
(
P
ULL X5 GAIN)
F
ULLY
C
LO
C
KWI
S
E
P
U
S
H IN
14
19
P
O
S
ITION
(
P
ULL D
C
O
FFS
ET)
MID
P
O
S
ITION
P
U
S
H IN
15
11
A
C
/
GND
/
D
C
D
C
CHANN
EL
2 OR Y-
S
E
C
T
ION
16
12, 14, 16, 20,
S
ET
A
LL
CON
T
RO
L
S
T
H
E
S
AM
E
A
S
FOR CHANN
EL
1
17
6
INTEN
S
ITY
S
ET
F
O
R
VI
S
I
B
LE
NOT TOO
BR
IGHT
18
3
F
O
C
U
S
S
ET
F
O
R
S
HA
R
P
E
S
T
Ad
j
us
t
con
t
ro
l
knob 13 (VOLT
S/
DIV) so
t
he s
i
ne wave f
it
s on
t
he screen.
You shou
l
d
now have a fu
ll
wave d
i
sp
l
ayed on
t
he screen.
AC M
E
A
S
UR
E
M
E
N
T
C
oun
t
t
he number of hor
i
zon
t
a
l
d
i
v
i
s
i
ons and de
t
erm
i
ne
t
he per
i
od of
t
he wave d
i
sp
l
ayed
on
t
he screen.
F
rom
t
he per
i
od, de
t
erm
i
ne
t
he frequency and compare
it
w
it
h 1 kHz.
C
oun
t
t
he number of ver
ti
ca
l
d
i
v
i
s
i
ons from
t
he bo
tt
om of
t
he s
i
ne wave
t
o
t
he peak of
t
he s
i
ne wave. Us
i
ng
t
he VO
(
V
P-P
).
D
i
v
i
de
t
h
i
s vo
lt
age by 2
t
o de
t
erm
i
ne
t
he amp
lit
ude of
t
he s
i
ne wave.
Ma
k
e
s
u
re a
ll
co
n
tro
l
s are
in
t
h
e ca
lib
rate
d
mo
d
e.
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47
RM
S
M
E
A
S
UR
E
M
E
N
T
C
onnec
t
a
B
N
C
t
ee sp
litt
er
t
o
t
he genera
t
or.
C
onnec
t
t
he fema
l
e
B
N
C
t
o fema
l
e
B
N
C
cab
l
e
t
o
t
he
B
N
C
t
ee on
t
he func
ti
on genera
t
or and
t
hen
t
o
t
he osc
ill
oscope.
C
onnec
t
t
he
fema
l
e
t
o banana
j
ack adap
t
er
t
o
t
he end of
t
he
B
N
C
t
ee and
t
hen connec
t
t
o
t
he DMM.
S
e
t
t
he DMM
t
o read A
C
and ad
j
us
t
t
he ou
t
pu
t
of
t
he A
C
genera
t
or
t
o read 5 V.
Th
i
s 5 V
read
i
ng
i
s
t
he
rms
, or
effect
i
ve vo
l
tage
. The peak vo
lt
age of
t
he s
i
nuso
i
da
ll
y vary
i
ng
vo
lt
age
i
s 1.41
ti
mes
t
he
rms
vo
lt
age. The peak vo
lt
age refers
t
o
t
he amp
lit
ude of
t
he
s
i
ne-wave. D
i
sconnec
t
t
he banana
j
ack adap
t
er and connec
t
t
he
B
N
C
cab
l
e from
t
he
genera
t
or
t
o
t
he scope.
Measure
V
P-P
and from
it
de
t
erm
i
ne
t
he peak vo
lt
age.
C
ompare
t
he peak vo
lt
age w
it
h 1.41
ti
mes
t
he
rms
vo
lt
age.
R
epea
t
t
hese measuremen
t
s and
ca
l
cu
l
a
ti
ons for severa
l
o
t
her vo
lt
ages.
Take
t
urns w
it
h your par
t
ner
;
prac
ti
ce se
tti
ng up
t
he scope and measur
i
ng d
i
fferen
t
vo
lt
ages and de
t
erm
i
n
i
ng d
i
fferen
t
frequenc
i
es by measur
i
ng
t
he per
i
od.
C
ompare each
of
t
he ca
l
cu
l
a
t
ed frequenc
i
es w
it
h
t
he frequency se
t
on
t
he genera
t
or.
When you fee
l
conf
i
den
t
us
i
ng
t
he osc
ill
oscope, have your
i
ns
t
ruc
t
or g
i
ve you an ora
l
qu
i
z on us
i
ng
t
he
osc
ill
oscope.
O
S
CI
LL
O
S
COP
E
QUI
Z
When comp
l
e
t
ed w
it
h
t
he
l
ab exerc
i
ses above, your
i
ns
t
ruc
t
or w
ill
g
i
ve you a 15 ques
ti
on
mu
lti
p
l
e cho
i
ce qu
i
z.
Make sure you are fam
ili
ar w
it
h
t
he func
ti
on of
t
he con
t
ro
l
s,
espec
i
a
ll
y
t
he TIME
/
DIV and VOLT
/
DIV con
t
ro
l
s and wha
t
effec
t
chang
i
ng
t
hem has on
t
he screen d
i
sp
l
ay.
R
E
POR
T
No repor
t
i
s requ
i
red for
t
h
i
s
l
ab, your grade w
ill
be de
t
erm
i
ned from
t
he ora
l
qu
i
z and
t
he wr
itt
en qu
i
z, 50% each.
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48
D
IGI
T
A
L
O
S
C
I
LL
O
S
C
O
P
E
E
X
E
R
I
M
E
N
T
TE
K
T
R
O
N
I
X D
IGI
T
A
L
O
S
C
I
LL
O
S
C
O
P
E
AND FUNC
T
IO
N
G
E
N
E
RA
T
IO
R
O
P
E
RA
T
IO
N
IN
T
IA
L
S
ET
UP
Af
t
er connec
ti
ng
t
he s
i
gna
l
t
o be d
i
sp
l
ayed press
t
he
R
un/S
to
p
bu
tt
on so
i
s g
l
ows green.
Nex
t
press
t
he
A
u
toset
bu
tt
on. On
t
he
A
u
toset
menu
t
o
t
he r
i
gh
t
of
t
he screen, se
l
ec
t
t
o
d
i
sp
l
ay one waveform or mu
lti
p
l
e waveforms.
P
ress
t
he
Defa
ul
t
S
et
up
.
P
ress
t
he ver
ti
ca
l
Me
nu
bu
tt
ons
for each channe
l
and se
t
t
he vo
lt
age a
tt
enua
ti
on a
t
1X.
B
A
S
IC DI
S
P
L
AY AND CON
T
RO
L
S
1.
The acqu
i
s
iti
on readou
t
shows when an acqu
i
s
iti
on
i
s runn
i
ng or s
t
opped.
Icons are
:
R
un
:
Acqu
i
s
iti
on enab
l
ed
St
op
:
Acqu
i
s
iti
ons no
t
enab
l
ed.
2.
The
t
r
i
gger pos
iti
on
i
con shows
t
he
t
r
i
gger pos
iti
on
i
n
t
he acqu
i
s
iti
on. Turn
t
he
Hor
i
zo
n
ta
l
Pos
i
t
i
o
n
knob
t
o ad
j
us
t
t
he pos
iti
on of
t
he marker.
3.
The
t
r
i
gger s
t
a
t
us readou
t
shows
:
Armed
:
The osc
ill
oscope
i
s acqu
i
r
i
ng pre
t
r
i
gger da
t
a. A
ll
t
r
i
ggers are
i
gnored
i
n
t
h
i
s s
t
a
t
e.
R
eady
:
A
ll
pre
t
r
i
gger da
t
a has been acqu
i
red and
t
he osc
ill
oscope
i
s ready
t
o
accep
t
a
t
r
i
gger.
osc
ill
oscope has seen a
t
r
i
gger and
i
s acqu
i
r
i
ng
t
he pos
tt
r
i
gger
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49
da
t
a.
St
op
:
The osc
ill
oscope has s
t
opped acqu
i
r
i
ng waveform da
t
a.
4.
The cen
t
er gra
ti
cu
l
e readou
t
shows
t
he
ti
me a
t
t
he cen
t
er gra
ti
cu
l
e. The
t
r
i
gger
ti
me
i
s zero.
5.
The
t
r
i
gger
l
eve
l
i
con shows
t
he Edge or
P
u
l
se W
i
d
t
h
t
r
i
gger
l
eve
l
on
t
he
waveform. The
i
con co
l
or corresponds
t
o
t
he
t
r
i
gger source co
l
or.
6.
The
t
r
i
gger readou
t
shows
t
he
t
r
i
gger source,
l
eve
l
, and frequency. Tr
i
gger
readou
t
s for o
t
her
t
r
i
gger
t
ypes show o
t
her parame
t
ers.
7.
The hor
i
zon
t
a
l
pos
iti
on
/
sca
l
e readou
t
shows
t
he ma
i
n
ti
me base se
tti
ng
(ad
j
us
t
w
it
h
t
he
Hor
i
zo
n
ta
l
S
ca
l
e
knob).
8.
The channe
l
readou
t
shows
t
he ver
ti
ca
l
sca
l
e fac
t
or (per d
i
v
i
s
i
on) for each
channe
l
. Ad
j
us
t
w
it
h
t
he
Vert
i
ca
l
S
ca
l
e
knob for each channe
l
.
9.
The waveform base
li
ne
i
nd
i
ca
t
or shows
t
he ground reference po
i
n
t
s (
t
he
zero-vo
lt
l
eve
l
) of a waveform (
i
gnor
i
ng
t
he effec
t
of offse
t
). The
i
con co
l
ors
correspond
t
o
t
he waveform co
l
ors. If
t
here
i
s no marker,
t
he channe
l
i
s no
t
d
i
sp
l
ayed.
V
E
R
T
I
CA
L
C
O
N
T
R
O
L
S
Pos
i
t
i
o
n
(1 a
nd
2).
P
os
iti
ons a waveform ver
ti
ca
ll
y.
1 &am
p
; 2 Me
nu
.
D
i
sp
l
ays
t
he Ver
ti
ca
l
menu se
l
ec
ti
ons and
t
ogg
l
es
t
he d
i
sp
l
ay
of
t
he channe
l
waveform on and off.
S
ca
l
e (1 &am
p
; 2).
S
e
l
ec
t
s ver
ti
ca
l
sca
l
e fac
t
ors.
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50
HO
R
IZONTAL
C
ONT
R
OL
S
Pos
i
t
i
o
n
.
Ad
j
us
t
s
t
he hor
i
zon
t
a
l
pos
iti
on of a
ll
channe
l
and ma
t
h waveforms. The
reso
l
u
ti
on of
t
h
i
s con
t
ro
l
var
i
es w
it
h
t
he
ti
me base se
tti
ng.
NOT
E
.
T
o make a
l
arge ad
j
us
t
men
t
t
o
t
he hor
i
zon
t
a
l
pos
iti
on,
t
urn
t
he
Hor
i
zo
nt
a
l
S
ca
l
e
knob
t
o a
l
arger va
l
ue, change
t
he hor
i
zon
t
a
l
pos
iti
on, and
t
hen
t
urn
t
he
Hor
i
zo
nt
a
l
S
ca
l
e
knob back
t
o
t
he prev
i
ous va
l
ue.
NOT
E
.
T
o se
t
t
he hor
i
zon
t
a
l
pos
iti
on
t
o zero, push
t
he hor
i
zon
t
a
l
pos
iti
on knob.
Ac
qui
re.
D
i
sp
l
ays
t
he acqu
i
s
iti
on modes
S
amp
l
e,
P
eak De
t
ec
t
, and Average.
S
ca
l
e.
S
e
l
ec
t
s
t
he hor
i
zon
t
a
l
ti
me
/
d
i
v
i
s
i
on (sca
l
e fac
t
or).
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51
Us
in
g t
h
e me
nu
system
When you push a fron
t
-pane
l
bu
tt
on,
t
he osc
ill
oscope d
i
sp
l
ays
t
he correspond
i
ng
menu on
t
he r
i
gh
t
s
i
de of
t
he screen.
T
h
e me
nu
s
h
ows t
h
e o
p
t
i
o
n
s t
h
at are
ava
il
a
bl
e w
h
e
n
yo
u
pu
s
h
t
h
e
unl
a
b
e
l
e
d
o
p
t
i
o
n
bu
tto
n
s
di
rect
l
y to t
h
e r
i
g
h
t of t
h
e
scree
n
. Rotate t
h
e m
ul
t
ipu
r
p
ose
kn
o
b
to t
h
e
d
es
i
re
d
se
l
ect
i
o
n
o
n
pu
s
h
t
h
e
kn
o
b
to
e
n
ter t
h
e se
l
ect
i
o
n
.
U
S
ING
T
H
E
CUR
S
OR
P
ress
t
he
C
u
rsor
bu
tt
on and se
l
ec
t
T
i
me
or
Am
pli
t
ud
e,
se
l
ec
t
C
u
rsor 1
or
C
u
rsor 2.
On
t
he d
i
sp
l
ay
t
o
t
he r
i
gh
t
of
t
he screen, read
t
he
or
t
he
.
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52
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53
TE
K
T
R
O
N
I
X FUNC
T
IO
N
G
E
N
E
RA
T
O
R
O
P
E
RA
T
IO
N
Item Descr
ip
t
i
o
n
1
B
eze
l
bu
tt
ons
2 Numer
i
c keypad,
i
nc
l
ud
i
ng numer
i
c, po
i
n
t
, p
l
us
/
m
i
nus s
i
gn
3 Genera
l
purpose knob
4
C
hanne
l
copy bu
tt
on
5 U
tilit
y bu
tt
on
6 He
l
p bu
tt
on
7 Arrow bu
tt
ons a
ll
ow you
t
o se
l
ec
t
a spec
i
f
i
c number on
t
he d
i
sp
l
ay screen when
chang
i
ng amp
lit
ude, phase, frequency, or o
t
her such va
l
ues
8
C
hanne
l
2 On
/
Off bu
tt
on
9
C
hanne
l
2 ou
t
pu
t
connec
t
or
10
C
hanne
l
1 On
/
Off bu
tt
on
11
C
hanne
l
1 ou
t
pu
t
connec
t
or
12
C
h1
/
2
:
S
w
it
ch channe
l
on
t
he screen
B
o
t
h
:
S
how
t
he parame
t
ers of
t
he
t
wo channe
l
s a
t
t
he same
ti
me
Mod
:
R
un modes,
i
nc
l
ud
i
ng con
ti
nuous, modu
l
a
ti
on, sweep and burs
t
13 U
S
B
connec
t
or
14
F
unc
ti
on bu
tt
ons
15
P
ower bu
tt
on
16
S
creen
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54
INI
T
IA
L
S
ET
UP
1. Turn on
t
he power (bu
tt
on 15) and
t
urn
O
n
channe
l
1
(bu
tt
on 10)
(bu
tt
on 8)
i
f
channe
l
2
i
s
t
o be used a
l
so.
2. Use bu
tt
ons 14
t
o se
l
ec
t
t
he des
i
red waveform-for examp
l
e
t
he
Sin
e
func
ti
on
i
s shown
3.
P
ress
t
he Mod bu
tt
on
t
he se
l
ec
t
C
on
ti
nuous on
t
he
B
eze
l
bu
tt
ons (bu
tt
ons 13).
The d
i
sp
l
ay be
l
ow shou
l
d now be d
i
sp
l
ayed.
4. To en
t
er a frequency, press
Fre
q/
Per
i
o
d
.
P
ress
it
aga
i
n
t
o choose
Per
i
o
d
. The se
l
ec
t
ed
parame
t
er w
ill
be h
i
gh
li
gh
t
ed w
it
h awh
it
e background. Use
t
he genera
l
purpose knob
t
o
se
t
frequency va
l
ue d
i
rec
tl
y, and use
t
he
. Or
push
t
he numer
i
c pane
l
bu
tt
on, and an
i
npu
t
box w
ill
pop up. En
t
er
t
he frequency va
l
ue
and choose
t
he
5. To en
t
er and amp
lit
ude (vo
lt
age), press
Am
p
.
Use
t
he
ge
n
era
l
pu
r
p
ose
kn
o
b
t
o se
t
Vo
lt
age (
V
pp
)
va
l
ue d
i
rec
tl
y. Use
t
he genera
l
purpose knob
t
o se
t
frequency va
l
ue
d
i
rec
tl
y. Or push
t
he numer
i
c pane
l
bu
tt
on, and an
i
npu
t
box w
ill
pop up. En
t
er
t
he
vo
lt
age va
l
ue and choose
t
he
proper un
it
(ususa
ll
y
V
pp
).
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55
6. Offse
t
. The offse
t
i
s usua
ll
y se
t
t
o zero.
Th
i
s w
ill
make
t
he waveform amp
lit
ude
symme
t
r
i
c abou
t
t
he x-ax
i
s.
P
ress
Offset
and use
t
he
ge
n
era
l
pu
r
p
ose
kn
o
b
t
o se
t
t
he
offse
t
t
o
zero
.
7. To se
l
ec
t
t
he
O
u
t
pu
t
i
mpedance
:
P
ress
Ut
ili
ty
,
O
u
t
pu
t
S
et
up
,
t
hen
CH
L
oa
d
T
H
E
E
XP
E
RIM
E
N
T
E
QUIP
E
M
E
N
T
:
TEKT
R
ONIX DIGITAL O
S
C
ILLO
S
C
O
P
E
TEKT
R
ONIX A
F
G1000
S
E
R
IE
S
F
UN
C
TION GENE
R
ATO
R
MULTIMETE
R
L
i
s
t
en
t
o
t
he
l
ec
t
ure and
t
ake no
t
es.
1.
S
ett
in
g
up
of t
h
e osc
ill
osco
p
e (O
S
C).
a.
Turn on
t
he power
t
o
t
he O
S
C
, press
t
he Au
t
ose
t/
Au
t
orange.
b.
C
onnec
t
a
t
es
t
-
l
ead
t
o
C
h1.
R
emember
t
ha
t
t
he b
l
ack c
li
p-
l
ead mus
t
be
connec
t
ed
t
o ground.
The O
S
C
measures vo
lt
age w
it
h respec
t
t
o ground.
Observe po
l
ar
it
y!
c.
F
o
ll
ow
t
he
l
ec
t
ure
/
demons
t
ra
ti
on and
t
ry a
ll
t
he con
t
ro
l
s. You w
ill
no
t
2.
Meas
u
r
in
g co
n
sta
n
t DC vo
l
tage.
a.
C
onnec
t
a D
C
vo
lt
me
t
er and
t
he O
S
C
t
o
t
he D
C
power supp
l
y. Observe
po
l
ar
it
y.
b.
Ad
j
us
t
t
he D
C
power supp
l
y so
t
ha
t
t
he vo
lt
me
t
er reads 2.50 V. Ad
j
us
t
t
he
O
S
C
ver
ti
ca
l
con
t
ro
l
s (pos
iti
on and sca
l
e)
t
o ge
t
t
he mos
t
prec
i
se read
i
ng poss
i
b
l
e.
R
ecord your read
i
ngs.
c.
R
epea
t
s
t
ep (b) w
it
h 5.30 V and 13.70 V.
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56
3.
Meas
u
r
in
g t
i
me-vary
in
g DC vo
l
tage.
a.
C
onnec
t
t
he D
C
vo
lt
me
t
er and
t
he O
S
C
t
o
t
he O
S
C
ca
li
bra
ti
on s
i
gna
l
t
erm
i
na
l
s. Observe po
l
ar
it
y.
b.
Ob
t
a
i
n a p
i
c
t
ure s
i
m
il
ar
t
o
t
he one shown be
l
ow.
R
ead and record
t
he
vo
lt
age amp
lit
ude and
(
ti
me) per
i
od for one cyc
l
e. Does
t
h
i
s agree w
it
h wha
t
t
he manufac
t
urer
spec
i
f
i
es?
c.
The D
C
vo
lt
me
t
er reads
t
he
average
vo
lt
age.
R
ecord
t
he average vo
lt
age.
d.
C
a
l
cu
l
a
t
e
t
he average vo
lt
age.
(In
t
egra
ti
on over one per
i
od.) (1)
e.
Does
t
he ca
l
cu
l
a
t
ed average agree w
it
h
t
he D
C
vo
lt
me
t
er read
i
ng?
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57
4.
a.
S
e
t
t
he
f
unc
ti
on genera
t
or
t
age,
so
t
ha
t
it
has a 4-V
peak-
t
o-peak vo
lt
age ou
t
pu
t
(4 Vpp), as
i
nd
i
ca
t
ed
by
t
he osc
ill
oscope.
S
e
t
t
he frequency
a
t
100 Hz,
l
oad
b.
Measure
t
h
i
s vo
lt
age w
it
h
t
he D
C
vo
lt
me
t
er. Does
t
he D
C
vo
lt
me
t
er read
zero? Exp
l
a
i
n why.
c.
Measure
t
h
i
s vo
lt
age w
it
h
t
he A
C
vo
lt
me
t
er.
R
ecord
t
h
i
s va
l
ue.
The A
C
vo
lt
me
t
er reads
t
he roo
t
-mean-square, or rms vo
lt
age def
i
ned as
t
he square-roo
t
of
t
he average of
t
he vo
lt
age squared
:
(In
t
egra
ti
on over one per
i
od.)
(2)
d.
Keep
i
ng
t
he
amp
lit
ude
cons
t
an
t
, change
t
he frequency of
t
he wave-form
t
o
500 Hz and
t
hen
t
o
1 kHz and measure
t
he vo
lt
age w
it
h
t
he A
C
vo
lt
me
t
er. Wha
t
d
i
d you f
i
nd?
A
t
home
:
Use equa
ti
on (2)
t
o ca
l
cu
l
a
t
e
t
he rms vo
lt
age.
S
how each s
t
ep
i
n de
t
a
il:
a.
Wr
it
e an equa
ti
on express
i
ng
t
he vo
lt
age as a func
ti
on of
ti
me.
b.
S
quare
t
he func
ti
on and f
i
nd
t
he average of
t
he square over ¼ cyc
l
e.
c.
Wha
t
i
s
t
he average over
t
he en
ti
re cyc
l
e?
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58
d.
C
a
l
cu
l
a
t
e
t
he rms va
l
ue. Does
t
h
i
s resu
lt
depend on
t
he frequency?
e.
Does
t
h
i
s ca
l
cu
l
a
t
ed va
l
ue agree w
it
h
t
he measured va
l
ue
i
n s
t
ep 5c?
5.
O
b
serv
in
g s
inu
so
id
a
l
AC vo
l
tage.
R
epea
t
4a, 4b, and 4c for a s
i
nuso
i
da
l
vo
lt
age. Your d
i
sp
l
ay shou
l
d be s
i
m
il
ar
t
o
t
he p
i
c
t
ure be
l
ow.
Th
i
s vo
lt
age
i
s descr
i
bed by
t
he equa
ti
on
.
Si
nce
t
he average of
t
he s
i
ne squared func
ti
on
i
s ½, one can see
t
ha
t
or
(3)
d.
Use equa
ti
on (3) and
t
he A
C
vo
lt
me
t
er read
i
ng
t
o ca
l
cu
l
a
t
e
t
he peak
vo
lt
age.
e.
Does your resu
lt
agree w
it
h
t
he O
S
C
d
i
sp
l
ay?
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59
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60
WAVE
F
O
R
M
ANALY
S
I
S
AND
R
E
C
TI
F
IE
R
S
IN
T
RODUC
T
ION
PAR
T
1
The charg
i
ng and d
i
scharg
i
ng
curves for a capac
it
or w
ill
be d
i
sp
l
ayed on
t
he
osc
ill
oscope.
The d
i
sp
l
ay w
ill
be graphed and from
t
he graph,
t
he
RC
ti
me cons
t
an
t
w
ill
be de
t
erm
i
ned.
PAR
T
2
A ha
l
f-wave and a fu
ll
-wave rec
ti
f
i
er c
i
rcu
it
w
ill
be cons
t
ruc
t
ed and
t
he waveforms
d
i
sp
l
ayed on
t
he osc
ill
oscope.
Measuremen
t
s of per
i
od and peak vo
lt
age w
ill
be
t
aken.
The d
i
sp
l
ays w
ill
a
l
so be graphed.
PAR
T
3
A smoo
t
h
i
ng capac
it
or w
ill
be w
i
red
i
n para
ll
e
l
w
it
h
t
he
l
oad res
i
s
t
or and
t
he
waveform d
i
sp
l
ayed on
t
he osc
ill
oscope.
S
UPP
L
I
E
S
AND
E
QUIPM
E
N
T
O
S
CI
LL
O
S
COP
E
FUNC
T
ION G
E
N
E
RA
T
OR
C
E
N
TE
R
T
AP ADJU
S
T
A
BLE
T
RAN
S
FORM
E
R
DIOD
E
S
1
µ
F CAPACI
T
OR a
nd
450
µ
F CAPACI
T
OR
D
E
CAD
E
R
E
S
I
S
T
OR
B
R
E
AD
B
OARD
S
B
NC
T
O
B
ANANA JACK
ADAP
TE
R
O
S
CI
LL
O
S
COP
E
GRAPH PAP
E
R
B
NC
TEE
-
S
P
L
I
TTE
R
T
H
E
ORY:
PAR
T
1
The d
i
scharge equa
ti
on
t
or a capac
it
or
i
s g
i
ven by
and
t
he charg
i
ng equa
ti
on
i
s g
i
ven by
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61
C
ons
i
der
t
he fo
ll
ow
i
ng c
i
rcu
it:
No
t
e
t
ha
t
channe
l
1 d
i
sp
l
ays
t
he vo
lt
age across
t
he capac
it
or.
Th
i
s waveform
i
s shown
above as
t
he
V
c
graph.
PAR
T
2
A d
i
ode
i
s ana
l
ogous
t
o a va
l
ve
t
ha
t
on
l
y
l
e
t
s curren
t
f
l
ow
i
ng
i
n one d
i
rec
ti
on.
The
symbo
l
for a d
i
ode
i
s
To
C
H 2 ver
ti
ca
l
i
npu
t
To
C
H 1 ver
ti
ca
l
i
npu
t
To osc
ill
oscope ground
S
quare
wave
genera
t
or
decade res
i
s
t
or
box
+
-
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62
When
t
he po
l
ar
it
y
i
s as shown,
t
he d
i
ode
i
s sa
i
d
t
o be
forwar
d
bi
ase
d
and conven
ti
ona
l
curren
t
f
l
ows
i
n
t
he d
i
rec
ti
on of
t
he arrow w
it
h a
l
mos
t
no res
i
s
t
ance.
The forward b
i
as
vo
lt
age across
t
he d
i
ode as abou
t
0.5 vo
lt
s.
Si
nce
t
he d
i
ode has a
l
mos
t
no res
i
s
t
ance
when forward b
i
ased, a curren
t
li
m
iti
ng res
i
s
t
or
i
s used
i
n ser
i
es w
it
h
t
he d
i
ode.
When
t
he d
i
ode
i
s
reverse
bi
ase
d
,
very
littl
e curren
t
i
s a
ll
owed
t
o pass
t
hru
t
he d
i
ode and
it
has a very
l
arge res
i
s
t
ance and
it
i
s a
l
mos
t
li
ke an open c
i
rcu
it
.
-
+
PROC
E
DUR
E
PAR
T
1
W
i
re
t
he c
i
rcu
it
show.
C
H2 of
t
he osc
ill
oscope d
i
sp
l
ays
t
he square wave ou
t
pu
t
of
t
he
genera
t
or.
Th
i
s shou
l
d be a n
i
ce square wave.
S
e
t
t
he frequency of
t
he genera
t
or a
t
on
t
he channe
l
s so one charg
i
ng phase as seen by
t
he vo
lt
age across
t
he res
i
s
t
or
i
s d
i
sp
l
ayed
fu
ll
y on
t
he screen.
R
emember,
t
h
i
s shows
t
he curren
t
decay
i
ng exponen
ti
a
ll
y.
Draw a
PAR
T
2
The ha
l
f wave rec
ti
f
i
er.
W
i
re
t
he c
i
rcu
it
as shown.
Ad
j
us
t
t
he ver
ti
ca
l
and hor
i
zon
t
a
l
osc
ill
oscope d
i
sp
l
ay so one comp
l
e
t
e waveform
i
s
shown.
Draw
t
he waveform on
t
he osc
ill
oscope d
i
sp
l
ay paper prov
i
ded by your
i
ns
t
ruc
t
or.
S
how bo
t
h
t
he peak vo
lt
age and
t
he per
i
od.
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63
PAR
T
3
F
u
ll
wave rec
ti
f
i
er
W
i
re
t
he above c
i
rcu
it
us
i
ng
t
he A
C
t
ransformer ou
t
pu
t
a
t
t
he
t
op cen
t
er of your s
t
a
ti
on.
Use
R
L
Ad
j
us
t
t
he ver
ti
ca
l
and
hor
i
zon
t
a
l
osc
ill
oscope d
i
sp
l
ay so
t
wo comp
l
e
t
e waves are
shown.
Draw
t
he waveform on
t
he osc
ill
oscope d
i
sp
l
ay paper prov
i
ded by your
i
ns
t
ruc
t
or.
S
how bo
t
h
t
he peak vo
lt
age and
t
he per
i
od.
To
C
H 1 ver
ti
ca
l
i
npu
t
To osc
ill
oscope ground
s
i
ne wave
genera
t
or
To
C
H2 ver
ti
ca
l
i
npu
t
To
C
H1 ver
ti
ca
l
i
npu
t
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64
Us
i
ng a DMM se
t
on
t
he D
C
sca
l
e, measure
t
he ou
t
pu
t
vo
lt
age of
t
he fu
ll
wave rec
ti
f
i
er.
PAR
T
4
W
i
re a 100
µ
F
capac
it
or
i
n para
ll
e
l
w
it
h
t
he
l
oad res
i
s
t
or and d
i
sp
l
ay
t
wo fu
ll
waves on
t
he osc
ill
oscope. Keep
t
he same vo
lt
age sca
l
e as for
t
he fu
ll
wave d
i
sp
l
ay.
Draw a graph of
t
h
i
s d
i
sp
l
ay super
i
mposed on
t
he fu
ll
wave d
i
sp
l
ay.
ANALY
S
I
S
P
A
R
T 1
Draw
i
ng ver
ti
ca
l
and hor
i
zon
t
a
l
li
nes on
t
he d
i
scharge graph w
it
h f=100Hz and
t
he
i
s
t
akes
t
he curren
t
t
o decrease
t
o 37 % of
it
s
max
i
mum va
l
ue.
Th
i
s
ti
me
i
n
t
erva
l
shou
l
d be equa
l
t
o
.
Assume 10% error
i
n
C
and
5%
i
n
R
and propaga
t
e
t
he error
i
n
=
RC
.
P
A
R
T 2
The average vo
lt
age for
t
he fu
ll
wave rec
ti
f
i
er
i
s
:
To
C
H1 ver
ti
ca
l
i
npu
t
C
=100
µ
F
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65
Where
V
p
i
s
t
he peak
vo
lt
age and
T
i
s
t
he per
i
od for one ha
l
f of
t
he norma
l
s
i
n func
ti
on
per
i
od. Eva
l
ua
t
e
t
h
i
s
i
n
t
egra
l
and use
V
p
from your graph.
C
ompare
t
h
i
s ca
l
cu
l
a
t
ed va
l
ue
of V
avg
w
it
h
t
he va
l
ue as measured us
i
ng
t
he
DMM.
THE
R
E
P
O
R
T
:
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your repor
t
sha
ll
cons
i
s
t
of
:
Ana
l
ys
i
s and d
i
scuss
i
on of resu
lt
s
C
onc
l
us
i
on
Append
i
x w
it
h or
i
g
i
na
l
da
t
a shee
t
and
osc
ill
osco
p
e gra
ph
s
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66
D
ETE
R
M
I
N
I
N
G
µ
0
U
SI
N
G
A
CURR
E
N
T B
A
L
ANC
E
IN
T
RODUC
T
ION
:
A curren
t
ba
l
ance w
ill
be used
t
o measure
t
he force be
t
ween
t
wo
para
ll
e
l
conduc
t
ors as
t
he curren
t
t
hru
t
he conduc
t
ors
i
s var
i
ed.
The da
t
a w
ill
be graphed
and from
t
he s
l
ope of
t
he graph,
µ
0
w
ill
be de
t
erm
i
ned.
T
H
E
ORY
:
We have
l
earned
t
ha
t
para
ll
e
l
curren
t
s a
tt
rac
t
, wh
il
e an
ti
-para
ll
e
l
curren
t
s
repe
l
each o
t
her. The magn
it
ude of
t
he a
tt
rac
ti
ve or repu
l
s
i
ve force,
F
B
, depends upon
t
he
magn
it
ude of
t
he
t
wo curren
t
s,
I
1
and
I
2
and
t
he
i
r separa
ti
on d
i
s
t
ance
r
. The govern
i
ng
equa
ti
on for
t
he magne
ti
c force be
t
ween
t
he
t
wo w
i
res
i
s
equa
ti
on (1)
where
L
i
s
t
he
l
eng
t
h of
t
he w
i
res. If
t
he same curren
t
passes
t
hrough each w
i
re, equa
ti
on
(1) reduces
t
o
equa
ti
on (2)
In
t
h
i
s exper
i
men
t
, one w
i
re w
ill
be he
l
d
i
n a f
i
xed pos
iti
on wh
il
e
t
he o
t
her
i
s a
ll
owed
t
o
Move free
l
y on a kn
i
fe-edge fu
l
crum ba
l
anced by coun
t
erwe
i
gh
t
s. The w
i
res w
ill
be
arranged hor
i
zon
t
a
ll
y such
t
ha
t
t
he upper w
i
re
i
s
t
he free mov
i
ng w
i
re. Th
i
s w
i
re con
t
a
i
ns
a sma
ll
pan
i
n wh
i
ch we
i
gh
t
s may be p
l
aced.
The
t
wo w
i
res here carry curren
t
i
n oppos
it
e d
i
rec
ti
ons. Th
i
s w
ill
push
t
he free w
i
re
upwards from
it
s equ
ili
br
i
um pos
iti
on. However, p
l
ac
i
ng
t
he appropr
i
a
t
e we
i
gh
t
s
i
n
t
he
pan a
tt
ached
t
o
t
h
i
s w
i
re w
ill
push
t
he w
i
re back down. When
t
he grav
it
a
ti
ona
l
force
ac
ti
ng on
t
he we
i
gh
t
s exac
tl
y equa
l
s
t
he magne
ti
c force ac
ti
ng on
t
he w
i
re,
it
w
ill
rema
i
n
i
n
it
s equ
ili
br
i
um pos
iti
on.
S
how
t
ha
t
t
he mass requ
i
red
i
s g
i
ven by
equa
ti
on (3)
The va
l
ue of
r
w
ill
be measured and from
t
he s
l
ope of a graph of m vs.
I
2
,
t
he va
l
ue of
µ
0
can be de
t
erm
i
ned.
E
QUIPM
E
N
T
L
I
S
T
01
:
C
urren
t
B
a
l
ance Appara
t
us
10
:
Fi
ne
St
ee
l
Woo
l
02
:
Mod
i
f
i
ed Epsco
P
ower
S
upp
l
y
11
:
Tape Measure
03
:
Large Var
i
ac
12
:
Vern
i
er
C
a
li
per
04
:
S
hun
t
R
es
i
s
t
or
13
:
Tes
t
l
eads,
B
anana
05
:
Laser
14
:
A
lli
ga
t
or
C
li
ps
06
:
S
ma
ll
R
i
ng
St
and W
it
h 60cm Me
t
a
l
R
od
15
:
R
u
l
er
07
:
Me
t
er
Sti
ck
C
l
amp
16
:
D
i
g
it
a
l
Mu
lti
me
t
er
08
:
Me
t
er
Sti
ck
18
:
B
ubb
l
e Leve
l
09
:
M
i
cro We
i
gh
t
S
e
t
19
:
M
i
crome
t
ers
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67
T
H
E
APPARA
T
U
S
F
IGU
R
E 1
LA
S
E
R
MI
RR
O
R
METE
R
S
TI
C
K
L
a
m
i
rror
D
b
d
LA
S
E
R
METE
R
S
TI
C
K
d
r
R
R
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68
S
HUNT
R
E
S
I
S
TO
R
MODI
F
IED E
PS
C
O
P
OWE
R
S
U
PP
LY
DMM
F
IGU
R
E 2
LA
R
GE
VA
R
IA
C
KNI
F
E
EDGE
P
IVOT
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69
APPARA
T
U
S
S
ET
UP
A
L
IGNM
E
N
T
The appara
t
us shou
l
d be a
li
gned and ready
t
o go.
If no
t
, you w
ill
need
t
o do
t
he
fo
ll
ow
i
ng
:
Hand
l
e
t
he equ
i
pmen
t
ge
n
t
l
y.
Fi
rs
t
, remove
t
he frame from
t
he ba
l
ance and
c
l
ean
t
he kn
i
fe edges and suppor
t
s w
it
h s
t
ee
l
woo
l
so
t
hey make good e
l
ec
t
r
i
ca
l
con
t
ac
t
.
If
t
here are any burrs on
t
he kn
i
fe edges, con
t
ac
t
your
i
ns
t
ruc
t
or.
Pl
ace
t
he ba
l
ance on
t
he
t
ab
l
e and
l
eve
l
it
us
i
ng
t
he ad
j
us
t
men
t
screws on
t
he base.
Make sure
t
he ba
l
ance
i
s
f
i
rm
l
y s
it
ua
t
ed on
t
he
t
ab
l
e.
To a
li
gn
t
he
t
wo fron
t
bars, exam
i
ne
t
hem for s
t
ra
i
gh
t
ness.
If
t
hey appear
t
o be ben
t
,
con
t
ac
t
your
i
ns
t
ruc
t
or.
To check
t
he a
li
gnmen
t
,
li
f
t
t
he frame up by ro
t
a
ti
ng
t
he
a
li
gnmen
t
p
i
ns
i
n
t
o
t
he con
i
ca
l
ho
l
es
l
oca
t
ed under
t
he back of
t
he frame by
t
he kn
i
fe
edges. Le
t
t
he frame down s
l
ow
l
y and check for a
li
gnmen
t
by p
l
ac
i
ng a co
i
n on
t
he
we
i
gh
t
pan
t
o force
t
he bars
t
oge
t
her w
it
hou
t
d
i
s
t
or
ti
ng
t
hem.
If
t
he bars are no
t
para
ll
e
l
and one d
i
rec
tl
y above
t
he o
t
her, use
t
he ad
j
us
ti
ng screws
t
o make
t
he bars
t
ouch each
o
t
her un
i
form
l
y across
t
he
i
r en
ti
re
l
eng
t
h.
Pl
ace a wh
it
e paper beh
i
nd
t
he bars
t
o he
l
p
ascer
t
a
i
n
t
ha
t
t
here are no gaps. I
t
i
s a
l
mos
t
i
mposs
i
b
l
e
t
o ach
i
eve perfec
t
con
t
ac
t
bu
t
good resu
lt
s can s
till
be ob
t
a
i
ned.
C
heck a
li
gnmen
t
aga
i
n as
i
ns
t
ruc
t
ed above.
S
ET
-UP
The upper frame ro
t
a
t
es abou
t
t
he kn
i
fe edges,
t
he m
i
rror ro
t
a
t
es w
it
h
it
.
A
d
j
u
st t
h
e
co
un
ter
b
a
l
a
n
ce (co
un
ter
p
o
i
se),
l
ocate
d
b
e
hind
t
h
e m
i
rror, so t
h
e two fro
n
t
b
ars are
se
p
arate
d
b
y a co
upl
e of m
illi
meters w
h
e
n
at e
quilib
r
iu
m
. There
i
s ano
t
her
coun
t
erpo
i
se
l
oca
t
ed under
t
he frame wh
i
ch can be ad
j
us
t
ed
t
o de
t
erm
i
ne
t
he per
i
od of
osc
ill
a
ti
ons for
t
he frame.
Ad
j
us
t
t
h
i
s coun
t
erpo
i
se un
til
t
he per
i
od of osc
ill
a
ti
on
i
s one
t
o
t
wo seconds.
There
i
s an a
l
um
i
num b
l
ade wh
i
ch osc
ill
a
t
es be
t
ween
t
wo damp
i
ng
magne
t
s.
The osc
ill
a
ti
ons shou
l
d d
i
e ou
t
w
it
h
i
n 10
t
o 15 seconds when
t
he damp
i
ng
magne
t
s are abou
t
2 mm apar
t
.
B
e sure
t
ha
t
t
he a
l
um
i
num b
l
ade does no
t
rub aga
i
ns
t
t
he
po
l
e faces of
t
he magne
t
s.
S
e
t
up
t
he
l
aser and me
t
er s
ti
ck as shown
it
t
he above d
i
agrams.
The
l
aser shou
l
d be a
t
l
eas
t
t
wo me
t
ers from
t
he m
i
rror.
M
E
A
S
URING
T
H
E
CURR
E
N
T
The
de
t
erm
i
ned by read
i
ng
t
he vo
lt
age across
t
he
s
hun
t
The va
l
ue of
t
he shun
t
res
i
s
t
or
i
s wr
itt
en on
t
he shun
t
res
i
s
t
or wooden b
l
oc
k.
Recor
d
t
h
e
va
lu
e of t
h
e s
hun
t res
i
stor.
PROC
E
DUR
E
Turn on
t
he
l
aser bu
t
l
eave
t
he shu
tt
er c
l
osed for
t
he
ti
me be
i
ng.
Measure
t
he
l
eng
t
h
L
of
t
he
t
op bar and es
ti
ma
t
e
it
uncer
t
a
i
n
t
y.
To de
t
erm
i
ne
t
he cen
t
er
t
o cen
t
er d
i
s
t
ance,
r
,
be
t
ween
t
he para
ll
e
l
bars,
d
needs
t
o be
measured and
t
w
i
ce
t
he rad
i
us of
t
he bar (or
t
he d
i
ame
t
er of one bar)
i
s added
t
o
d
.
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70
Us
i
ng m
i
crome
t
ers, measure
t
he d
i
ame
t
er,
2R
,
of one of
t
he bars. Es
ti
ma
t
e
t
he
uncer
t
a
i
n
t
y
i
n
2R
.
To de
t
erm
i
ne
d
, p
l
ace a co
i
n
i
n
t
he
t
ray
t
o br
i
ng
t
he bars
t
oge
t
her.
Open
t
he shu
tt
er on
t
he
l
aser and a
li
gn
t
he
l
aser so
t
he beam ref
l
ec
t
s off of
t
he m
i
rror and
on
t
o
t
he me
t
er s
ti
ck.
Ca
u
t
i
o
n
,
d
o
n
ot
l
oo
k
in
to t
h
e
b
eam or at t
h
e
ref
l
ecte
d
b
eam.
Do
n
ot a
ll
ow t
h
e
b
eam to
s
tray
b
eyo
nd
t
h
e
s
tat
i
o
n
a
nd
u
s
e t
h
e
s
hu
tter (
b
eam
bl
oc
k
) w
h
e
n
n
ot
in
u
s
e.
R
ecord
t
he me
t
er s
ti
ck read
i
ng a
t
t
he cen
t
er of
t
he spo
t;
t
h
i
s w
ill
be
Y
1
.
R
emove
t
he co
i
n and
l
e
t
t
he bar come
t
o equ
ili
br
i
um.
Aga
i
n record
t
he me
t
er s
ti
ck read
i
ng for
t
he cen
t
er of
t
he
spo
t:
t
h
i
s w
ill
be
Y
2
. The va
l
ue
D
i
n f
i
gure 1
i
s found form
D
=
Y
2
Y
1
.
Us
i
ng
t
he
l
aw of
ref
l
ec
ti
on and s
i
m
il
ar
t
r
i
ang
l
es, prove,
i
n
t
he ana
l
ys
i
s sec
ti
on,
t
ha
t
equa
ti
on (4
)
d
shou
l
d be abou
t
2 or 3 mm
.
Note,
r
=
2R
+
d
.
The va
l
ue of
Y
2
i
s
t
he equ
ili
br
i
um pos
iti
on for
t
he upper bar.
Pl
ace a 50 mg we
i
gh
t
on
t
he we
i
gh
t
pan and, us
i
ng
t
he var
i
ac, ad
j
us
t
t
he curren
t
t
hrough
t
he bars un
til
t
he
l
aser spo
t
re
t
urns
t
o
t
he equ
ili
br
i
um pos
iti
on,
Y
2
. Recor
d
t
h
e vo
l
tage
across t
h
e s
hun
t res
i
stor
.
Increase
t
he we
i
gh
t
s by 50 mg and aga
i
n
i
ncrease
t
he curren
t
t
o br
i
ng
t
he bar back
t
o
t
he equ
ili
br
i
um as
i
nd
i
ca
t
ed by
t
he spo
t
re
t
un
i
ng
t
o
Y
2
on
t
he
me
t
er s
ti
ck.
Aga
in
,
recor
d
t
h
e vo
l
tage across t
h
e s
hun
t res
i
stor
R
epea
t
for 50 mg
we
i
gh
t
i
ncreases up
t
o 300 mg.
ANA
L
Y
S
I
S
Der
i
ve equa
ti
on (4) and use
it
t
o f
i
nd
r
.
Us
i
ng
t
he vo
lt
age read
i
ngs and
t
he va
l
ue of
t
he shun
t
res
i
s
t
or, ca
l
cu
l
a
t
e
t
he curren
t
s
for each we
i
gh
t
.
Graph m verses
I
2
.
Us
i
ng
t
he s
l
ope of
t
h
i
s
li
ne a
l
ong w
it
h equa
ti
on (3),
,
de
t
erm
i
ne
µ
0.
No
t
e
:
s
l
ope =
.
Assume a 2% error
i
n
t
he s
l
ope of
t
he
li
ne, and a 2% error
i
n
r
. Use your es
ti
ma
t
ed error
i
n
L
t
o ca
l
cu
l
a
t
e a % error
i
n
L
.
P
ropaga
t
e
t
he error
i
n
µ
0
.
C
a
l
cu
l
a
t
e
t
he percen
t
d
i
screpancy
i
n
µ
0
-7
T
m
/
A
R
E
POR
T
T
H
E
R
E
POR
T
(see wr
i
t
in
g a re
p
ort)
Un
l
ess a forma
l
repor
t
i
s requ
i
red by your professor, your repor
t
sha
ll
cons
i
s
t
of
:
Theory,
i
nc
l
ud
i
ng any der
i
va
ti
ons
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71
Ana
l
ys
i
s and d
i
scuss
i
on of resu
lt
s
C
onc
l
us
i
on
Append
i
x w
it
h or
i
g
i
na
l
da
t
a shee
t
and answers
t
o any ques
ti
ons
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72
e
/
m
E
XP
E
R
I
M
E
N
T
Th
e
o
r
y
2
2
3
)
(
)
4
5
(
2
I
r
N
a
V
m
e
o
B
v
q
F
m
m
F
v
B
2
2
1
mv
eV
r
mv
F
c
2
a
I
N
B
o
2
3
)
4
5
(
]
[
A
m
T
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73
Op
er
a
t
ion
M
eas
ur
i
ng
e/
m
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74
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75
E
rror
i
n
V
:
E
rror
i
n
r:
E
rror
i
n
I
:
A
ccele
r
a
t
i
ng
V
o
l
t
a
g
e
V
r
le
ft
r
r
i
ght
H
el
mho
l
tz
Curr
e
nt
200
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
200
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
200
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
250
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
250
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
250
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
300
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
300
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
300
V
r
i
n
si
d
e
=
r
i
n
si
d
e
=
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76
ANAL
YS
I
S
a
nd
D
I
S
CU
SS
I
ON:
C
op
y
a
ll
of
y
ou
r
data
i
nto and
EX
C
E
L
s
p
r
ead
s
heet and p
r
og
r
a
m
a
c
o
l
u
m
n to
c
a
lc
u
l
ate the
v
a
l
ue of
r
w
h
ic
h
will
be the a
v
e
r
age of
r
le
ft
and
r
r
i
ght
fo
r
both
r
i
n
si
d
e a
nd
r
out
si
d
e
fo
r
a f
ix
ed a
cc
e
l
e
r
at
i
ng
v
o
l
tage and he
lm
ho
l
t
s
c
u
rr
ent.
P
r
og
r
a
m
the e/
m
equat
i
on
i
n the
l
a
s
t
c
o
l
u
m
n
(y
ou
s
hou
l
d ha
v
e 18
r
o
ws
of data
i
n
y
ou
r
s
p
r
ead
s
heet
)
.
P
ri
nt the p
r
og
r
a
m
i
n the
ana
lysis
s
e
c
t
i
on of
y
ou
r
r
epo
r
t.
Us
e
EX
C
E
L fun
c
t
i
on
s
(
AVE
R
A
G
E
;
S
TD
EV
)
to
c
a
lc
u
l
ate and
a
v
e
r
age and
s
tanda
r
d de
vi
at
i
on.
D
ete
rmi
ne the pe
rc
ent d
iscr
epan
cy
of e/
m
.
Us
e
c
ha
r
ge e = 1.60217646 × 10
-
19
c
ou
l
o
m
b
s
and
e
l
e
c
t
r
on
m
a
ss
= 9.10938188 × 10
-
31
kil
og
r
a
ms
.
N
ote: pe
rc
ent d
iscr
epan
cy
=
c
on
v
e
r
ted to
%
.
O
ne
w
a
y
to get a p
r
ed
ic
ted
%
e
rr
o
r
is
c
on
v
e
r
ted to
%
.
A
nothe
r
w
a
y
to get a p
r
ed
ic
ted e
rr
o
r
is
to u
s
e d
i
ffe
r
ent
i
a
l
e
rr
o
r
p
r
opagat
i
on.
S
ee the handout on
e
rr
o
r
p
r
opagat
i
on. If th
is
m
ethod
is
r
eque
s
ted b
y
y
ou
r
i
n
s
t
r
u
c
to
r
,
s
ho
w
a
ll
of the deta
ils
of
y
ou
r
e
rr
o
r
p
r
opagat
i
on
i
n the ana
lysis
s
e
c
t
i
on and u
s
e equat
i
on ed
i
to
r
fo
r
the a
l
geb
r
a.
N
ote
i
f the pe
rc
ent d
iscr
epan
cy
is
l
e
ss
than the p
r
ed
ic
ted e
rr
o
r
.
(i
.e. a
r
e
y
ou
r
r
e
s
u
l
t
s
wi
th
i
n the
m
a
r
g
i
n of e
rr
o
r
?
)
R
e
port:
Wri
te a fo
rm
a
l
r
epo
r
t fo
r
th
is
l
ab un
l
e
ss
to
l
d othe
rwis
e b
y
y
ou
r
i
n
s
t
r
u
c
to
r
.
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77
S
I
MP
LE
A
C C
I
RC
U
I
T
S
IN
T
RODUC
T
ION:
In par
t
1 of
t
h
i
s exper
i
men
t
, ca
l
cu
l
a
t
ed vo
lt
ages for
R
, L, and
C
i
n a
ser
i
es
c
i
rcu
it
w
ill
be compared w
it
h
t
he measured va
l
ues.
In par
t
2,
t
he phase
re
l
a
ti
onsh
i
p be
t
ween vo
lt
ages and curren
t
for an
i
nduc
t
or, capac
it
or and res
i
s
t
or
i
n a
ser
i
es
R
, L,
C
, c
i
rcu
it
w
ill
be measured and compared
t
o
t
he ca
l
cu
l
a
t
ed va
l
ue of
t
he phase
d
i
fference.
In par
t
3 of
t
h
i
s exper
i
men
t
,
t
he frequency response w
ill
be de
t
erm
i
ned by
vary
i
ng
t
he frequency of
t
he genera
t
or and measur
i
ng
t
he vo
lt
age across
t
he res
i
s
t
or.
P
ar
t
s 1 and 2 w
ill
be performed
t
he f
i
rs
t
week and par
t
3
t
he second week.
Th
i
s
l
ab
i
s
wor
t
h
t
w
i
ce wha
t
t
he o
t
her
l
abs are wor
t
h.
T
H
E
ORY
Part 1:
The vo
lt
ages
i
n a ser
i
es
R
L
C
c
i
rcu
it
add as vec
t
ors
;
hence,
,
t
he
i
mpedance
where
, and
and
t
he curren
t
.
,
.
,
, and
Part 2:
v(
t
)=V
max
-
The curren
t
i
s
t
hen
i
(
t
)= I
max
s
i
n
where
i
s
t
he phase d
i
fference be
t
ween
t
he curren
t
and vo
lt
age.
The vo
lt
age across
R
i
s
V
R
= I
max
Rs
i
n
wh
i
ch as we see
i
s
i
n phase w
it
h
t
he curren
t
s
i
nce
=0
for bo
t
h.
The vo
lt
age across
t
he capac
it
or
i
s g
i
ven by
V
C
= I
max
X
c
s
i
n(
-90° )
where
.
The vo
lt
age across
t
he
i
nduc
t
or
i
s g
i
ven by
V
L
= I
max
X
L
s
i
n(
+90° )
where
.
where
.
As shown
i
n
t
he d
i
agram be
l
ow
:
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78
FIGUR
E
1
The phase d
i
fference can b
e
measured us
i
ng
t
he osc
ill
oscope us
i
ng
t
he d
i
agram be
l
ow
:
FIGUR
E
2
Si
nce
t
he measuremen
t
s are
i
n seconds, we can conver
t
t
he
ti
me measuremen
t
t
o degrees
us
i
ng
t
he propor
ti
ona
lit
y
:
-over po
i
n
t
s, as shown
i
n
t
he
Part 3:
D
i
g
it
a
l
mu
lti
-me
t
ers measure rms curren
t
s and vo
lt
ages.
.
S
ubs
tit
u
ti
ng
and
i
n
t
o
t
he above equa
ti
on, we have
;
V
T
T
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79
No
t
e
t
ha
t
t
he curren
t
i
s a max
i
mum when
= 0
or when
. Th
i
s
i
s ca
ll
ed
t
he resonance frequency.
FIGUR
E
3
E
QUIPM
E
N
T
:
Ac genera
t
or
Osc
ill
oscope
DMM
R
, L, and
C
decade boxes
F
requency coun
t
er
Osc
ill
oscope graph paper
PROC
E
DUR
E
AND ANA
L
Y
S
I
S
Part 1:
Vo
l
tage a
nd
C
u
rre
n
t Re
l
at
i
o
n
s
hip
s
A p
l
o
t
of
t
he rms curren
t
versus
t
he frequency
i
s
shown for
t
hree res
i
s
t
ance va
l
ues.
In each case,
t
he
max
i
mum curren
t
i
s a
t
t
he resonance frequency.
No
ti
ce
t
ha
t
t
he peak becomes h
i
gher and narrower as
R
becomes sma
ll
er and
t
he more narrow
t
he band
w
i
d
t
h of frequency passed. Th
i
s c
i
rcu
it
i
s ca
ll
ed a
band pass f
ilt
er.
Si
nce
t
he power de
li
vered
t
o
t
he
l
oad res
i
s
t
or
i
s propor
ti
ona
l
t
o
t
he ha
l
f power
po
i
n
t
s occur a
t
a frequency above and be
l
ow
t
he
resonance frequency where
t
he curren
t
i
s
.
These
frequenc
i
es are
t
he cu
t
-off frequenc
i
es
, and
.
i
s ca
ll
ed
t
he bandw
i
d
t
h.
0
t
he
h
i
gher
t
he qua
lit
y fac
t
or Q.
it
can be shown
t
ha
t
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80
P
r
i
or
t
o c
l
ass, g
i
ven
t
he
R
L
C
c
i
rcu
it
shown above, ca
l
cu
l
a
t
e
t
he va
l
ues of
I
S
, V
R,
V
L
,
and
V
C
g
i
ven
V
S
=
5V
rms
,
R
=
10
L
=
1H, C
=
0.022
µ
F,
for
t
he
t
hree frequenc
i
es 800Hz,
1074Hz and 1.4 kHz. Do
t
hese ca
l
cu
l
a
ti
ons nea
tl
y and a
tt
ach
t
hem
t
o
t
h
i
s handou
t
as par
t
of your repor
t
.
W
i
re
t
he c
i
rcu
it
w
it
h
t
he va
l
ues g
i
ven for
R
, L,
and
C
.
A
tt
ach
t
he frequency coun
t
er
across
t
he power supp
l
y.
S
e
t
t
he supp
l
y vo
lt
age for
V
S
=
5V
rms
and
f
=
800Hz.
Recor
d
t
h
e c
u
rre
n
t
I
S
and use
t
he DMM
t
o measure
V
R
,
V
L
, and
V
C
.
R
epea
t
t
hese
measuremen
t
s for
f
=
1074Hz
and
f
=
1400Hz.
R
ecord
t
hese
measuremen
t
s
i
n
t
he
t
ab
l
e
be
l
ow and compare
t
hem
t
o
t
he ca
l
cu
l
a
t
ed va
l
ues.
You w
ill
need
t
o keep V
s
se
t
a
t
5V
rms
when chang
i
ng frequenc
i
es.
Meas
C
a
l
c
Meas
C
a
l
c
Meas
C
a
l
c
Meas
C
a
l
c
f(Hz)
V
R
V
R
%d
i
ff
V
L
V
L
%d
i
ff
V
C
V
C
%d
i
ff
I
S
I
S
%d
i
ff
800
1074
1400
C
a
l
cu
l
a
t
e V
T
us
i
ng
t
he equa
ti
on
, and
t
he measuremen
t
s for
V
R,
V
L
,
and
V
C
.
C
ompare
t
hese
va
l
ues
t
o
t
he
5V
rms
of
t
he supp
l
y vo
lt
age.
Fre
qu
e
n
cy (Hz)
%
di
ffere
n
ce from 5V
rms
800
1074
1400
=
V
T
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81
Part 2:
P
h
ase re
l
at
i
o
n
s
hip
b
etwee
n
I a
nd
V
T
Us
i
ng
t
he ser
i
es
R
L
C
c
i
rcu
it
, se
t
t
he s
i
gna
l
genera
t
or
t
o 2 kHz.
S
e
t
t
he
i
nduc
t
or
t
o 1H,
connec
t
ed
t
o ground.
1.
C
onnec
t
channe
l
1
i
npu
t
across
t
he res
i
s
t
or
t
o d
i
sp
l
ay
t
he vo
lt
age across
R
.
2.
C
onnec
t
channe
l
2
i
npu
t
t
o
t
he genera
t
or ou
t
pu
t
and connec
t
t
he osc
ill
oscope ground
t
o
t
he genera
t
or ground.
3.
S
e
t
t
he osc
ill
oscope
t
o
t
r
i
gger on
t
he channe
l
1 s
i
gna
l
.
4.
Ad
j
us
t
t
he con
t
ro
l
s so one comp
l
e
t
e wave
i
s d
i
sp
l
ayed for
t
he channe
l
1 s
i
gna
l
.
Th
i
s
i
s
t
he reference waveform.
5.
S
uper
i
mpose
t
he channe
l
2 waveform (genera
t
or
i
npu
t
) on
t
o
t
he channe
l
1 waveform.
6.
Ad
j
us
t
t
he ver
ti
ca
l
d
i
sp
l
ay so bo
t
h waveforms have abou
t
t
he same amp
lit
ude. The
d
i
sp
l
ay shou
l
d now
l
ook s
i
m
il
ar
t
o f
i
gure 2.
osc
ill
oscope graph paper.
B
e sure
t
o no
t
e
t
he
ti
me
/
d
i
v
i
s
i
on sca
l
e.
7.
C
ompu
t
e
t
he phase d
i
fference
i
n degrees us
i
ng
8.
C
ompare
t
h
i
s
t
o
t
he phase d
i
fference us
i
ng
.
% d
i
screpancy
Part 3:
S
er
i
es Reso
n
a
n
ce
TO
C
HANNEL
1 ON
CR
O
TO
C
HANNEL
2 ON
CR
O
=
V
T
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82
Us
i
ng
t
he
R
L
C
ser
i
es c
i
rcu
it
,
l
e
t
L
= 30mH,
C
= 0.01
µ
F
, and
R
R
shou
l
d be connec
t
ed
t
o
t
he ground
t
erm
i
na
l
of
t
he genera
t
or.
1.
C
a
l
cu
l
a
t
e
t
he resonance frequency of your c
i
rcu
it
2
C
onnec
t
t
he osc
ill
oscope
C
H1
i
npu
t
across
t
he res
i
s
t
or.
Make sure
t
he osc
ill
oscope
ground
i
s connec
t
ed
t
o
t
he genera
t
or ground.
3.
S
e
t
t
he genera
t
or ou
t
pu
t
t
o 10kHz and 2V
rms
4.
S
e
t
t
he
t
r
i
gger mode
t
o channe
l
1 and ob
t
a
i
n a s
t
eady d
i
sp
l
ay.
5.
C
onnec
t
a frequency coun
t
er across
t
he genera
t
or ou
t
pu
t
.
6.
S
weep
t
he genera
t
or over
t
he resonan
t
frequency , back and for
t
h above and be
l
ow
t
he resonan
t
frequency.
Look a
t
t
he osc
ill
oscope d
i
sp
l
ay and no
t
e
t
ha
t
max
i
mum
amp
lit
ude of
t
he res
i
s
t
or vo
lt
age occurs a
t
resonance.
(Why?)
7.
R
ead
t
he resonan
t
frequency on
t
he frequency coun
t
er and record
it
be
l
ow.
8.
C
omp
l
e
t
e
t
he
t
ab
l
e be
l
ow.
Impor
t
an
t
!
The genera
t
or ou
t
pu
t
vo
lt
age (V
S
) mus
t
be kep
t
cons
t
an
t
t
hroughou
t
t
he exper
i
men
t
.
Th
i
s means
t
ha
t
you mus
t
ad
j
us
t
t
he ou
t
pu
t
vo
lt
age on
t
he power supp
l
y every
ti
me you change
t
he frequency.
f(resonan
t
)=
f
3k
4k
5k
6k
7k
8k
8.5k
9.2k
9.5k
10k
11k
12k
13k
14k
15k
V
R
Us
i
ng
EX
C
EL graph V
R
vs. f and from
t
he graph, de
t
erm
i
ne
t
he bandw
i
d
t
h
.
Us
i
ng
ca
l
cu
l
a
t
e
t
he
qua
lit
y fac
t
or and compare
it
w
it
h
.
S
how your ca
l
cu
l
a
ti
ons be
l
ow.
R
E
POR
T
A
t
t
he end of
t
he second c
l
ass per
i
od, hand
i
n
t
h
i
s
l
ab handou
t
w
it
h a
ll
of
t
he
t
ab
l
es f
ill
ed
i
n.
A
tt
ach
t
he graphs and your ca
l
cu
l
a
ti
ons.
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83
B
e co
n
c
i
se.
Wr
i
te
in
t
h
e t
hi
r
d
p
erso
n
.
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84
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