www.physics.ubc.ca/~enph259 for protected documents: user: us pwd: Gr8stuff Course Learning goals • Proper laboratory notebook record keeping • Data analysis (curve fiBng, etc.) • Uncertainty and error analysis • MinimizaIon of measurement errors • WriIng up formal lab reports (with APSC 202) • Concise verbal communicaIon of technical results (with APSC 202) • Basic analog electronics: operaIonal amplifiers, transient AC analysis, analog to digital convertors (with EECE 251) • Basic digital electronics: truth tables, Boolean logic gates (with EECE 251) ENPH 259 Group AcIviIes for Sept 6 2012 Please complete these exercises on your OWN piece of paper. If you have quesIons talk with your group mates or raise your hand and Evan or David will come to help When measuring a physical quanIty one MUST quote an uncertainty in the measurement (as well as the measurement) to be meaningful. Determine both the “best” value and uncertainty of the following measurements. 1)  A single measurement from each of these two meters 2)  A measurement of the number people in line at the SUB’s Starbucks on five Thursdays at 4:05 pm yields this data: 14,10,6,20,14. What is the best measurement of the lineup and the uncertainty? ENPH 259 Group AcIviIes for Sept 6 2012 Please complete these exercises on your OWN piece of paper. If you have quesIons talk with your group mates or raise your hand and Evan or David will come to help When measuring a physical quanIty one MUST quote an uncertainty in the measurement (as well as the measurement) to be meaningful. Determine both the “best” value and uncertainty of the following measurements. 1)  A single measurement from each of these two meters -­‐83.00 +/-­‐ 0.25 This might be a bit
high of an uncertainty,
but I think most of us
can estimate better
than ½ of the lowest
gradation (which is
0.50)
36 dB +/-­‐ 1 dB
I would think anything lower
than +/-1 dB is too tight.
Again, it isn’t “wrong” to
specify a higher uncertainty
but you’d like to have the
lowest uncertainty that you
feel comfortable with
2)  A measurement of the number people in line at the SUB’s Starbucks on five Thursdays at 4:05 pm yields this data: 14,10,6,20,14. What is the best measurement the uncertainty of
of the lineup and the uncertainty? The mean was 12.8, rounded up to 13 as you can’t BTW,
each individual
have .8 of a person. +/-7 as that is the range from the
mean. One can do better (i.e. lower uncertainty) with
stat analysis and standard deviation. More on this
later. Next week.
13 +/-­‐ 7
measurement of people is
at least +/-1...it isn’t 0!
…there is a “beeer” (i.e. staIsIcally method to make a beeer esImate on the uncertainty with repeated measurements…more on error analysis and uncertainIes next n
v
u
1X
X
week. x̄ =
xi ⌘ u
t 1
(x
x̄)
n
n
i=1
n
1
i
i=1
2
ENPH 259 Group AcIviIes for Sept 6 2012 Please complete these exercises on your OWN piece of paper. If you have quesIons talk with your group mates or raise your hand and Evan or David will come to help Voltage (V)
When examining signals (voltages, currents, etc.) that are constant (i.e. DC), one can just use that value to characterize the voltage. The situaIon isn’t so clear when the signals are Ime varying (or AC) as different waveforms have different characterisIcs. 4) For the following periodic waveforms find at least two different parameters to characterize each wave ( V
average
, etc.) 4
0
-2
4
0
-4
4
0
-4
0
1
5) To find a disInguishing characterisIc, calculate the average power (over period T) dissipated when the sine and square waveappear across a resistor with resistance R. Are these two powers different? Should they be different? 2
3
time (ms)
4
FYI R 1
< P >=
T
5
Z
6
T
[P (t)] dt
0
Bonus: do the same for the triangle wave 6) Find the “effecIve” DC voltages that would give rise to the same average powers by comparing it to the average power of a DC voltage across the same R. Are they different in the two cases? ENPH 259 Group AcIviIes for Sept 6 2012 Please complete these exercises on your OWN piece of paper. If you have quesIons talk with your group mates or raise your hand and Evan or David will come to help Voltage (V)
When examining signals (voltages, currents, etc.) that are constant (i.e. DC), one can just use that value to characterize the voltage. The situaIon isn’t so clear when the signals are Ime varying (or AC) as different waveforms have different characterisIcs. 4) For the following periodic waveforms find at least two different parameters to characterize each wave ( V
average
, etc.) 4
0
1P)
-2
4
0
tu
t.
=
T
si'aut., [
:
"l'!ür*
a
(p)= +à ['vis^'r$)Jt
r1 i1,.. (l-y,,s{jj
z
)¡.
-4
= îk
4
0
-4
1
5) To find a disInguishing characterisIc, calculate the average power (over period T) dissipated when the sine and square waveappear across a resistor with resistance R. Are these two powers different? Should they be different? \z
T
I t- å''^*+)
= å+dur'Irl
3
4
5
' l+ à
0
\tl
0
2
u,'
l-ß\r Yr'l
y/
time (ms)
=
ç,t
Sluavrt
<{r>
=
îi¡z^r,,[IuJ
Å
( ,^:_)
They are different and should be different as the voltages are different
wc"v-(_
Çt {rì^^gle
6) Find the “effecIve” DC voltages that would give rise to the same average powers by .4lra
comparing it to the average power of a DC voltage across the same R. Are they different in <øtÇxffift
the two cases? Compare with P=V_dc^2/R For sinusoid: V_dc=Vp/sqrt(2) For Square: V_dc=Vmax
I
I
0
6
ENPH 259 Group AcIviIes for Sept 6 2012 Please complete these exercises on your OWN piece of paper. If you have quesIons talk with your group mates or raise your hand and Evan or David will come to help 4
0
Þ (t.l
-2
I =Q)n I (lrj
(
Voltage (V)
4
0
-4
4
0
-4
(+l^
=
(l
ç rt(+)ctrl
d
=
<d>
o
(r/"4 :
_l_-
+
ï
.u- lo r
*o
rl(Ð.ArJ
f
t
,
îf
rl(+).ArJ
r-.----,A-fl
t*o.N
r lGlrn
l"j
o
=
rsqrA (=-
0
1
2
3
time (ms)
4
5
6) This “effecIve” DC voltage is the known as the Root Mean Square (or RMS) of the Ime s
Z T
varying signal. Show that V
rms
is calculated via: Vrms =
1
T
2
[V (t)] dt
0
…this is the V rms
that is displayed on your Lab DMMs. And it is the quanIty that is used to disInguish AC signals 6