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Please see attached files, the data is provided as well. Also i’m attaching lab guidlines. If you have questions, please let me know.
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Title
Name 1:
Course number
LAI:
Date
Name 2:
Section:
Name 3:
Experiment: Measurement Example
Name 4:
Synthesis Question 1:
Purpose: The aim of this experiment was to confirm that the mass of the machine key
falls within the tolerance given by its manufacturer.
IV: NA
Guest User 5/23/2018 9:27 AM
Comment [1]: Always start the report with
a purpose that matches the Synthesis Question.
Avoid copying the Synthesis Question.
DV: NA
CV: NA
Guest User 5/23/2018 9:28 AM
Comment [2]: Identify independent
variable (IV), dependent variable (DV), and
Controlled variables (constants – CV) when it
applies.
Materials:
•
Machine key
•
Postal scale
•
Digital balance
Procedure: Several measurements of the key mass were made using two different devices
and compared it to the tolerance.
First, a postal scale with tick marks 6 grams apart was used to measure the mass of the
machine key.
Guest User 4/5/2018 2:14 PM
Comment [3]: The procedure should be
written in the way that anyone following your
steps should be able to produce the same thing
without confusion.
Do not include numbers in the procedure.
Next, a digital balance was used to measure the key’s mass. According to the manual of
the device, its uncertainty of the balance is ± 0.1 grams.
Data:
The measurements are organized in Table 1 below.
Table 1: Measurements and Given Tolerance of Machine Key Mass
Source
Measurement (g)
Postal Scale
93 ± 3
Digital Scale
95.1 ± 0.1
Manufacturer
93 ≤ x ≤ 96
Guest User 4/26/2018 12:24 PM
Comment [4]: Data should always be
organized in a data table. Include all trials and
the average value of the dependent variable.
The units should be entered only in the heading
of the table. If the uncertainty has a constant
value for all measurements (for example the
uncertainty given by the manifacture), include
it in the heading. If you calculate the standart
deviation, then create a separate column.
In some labs you do not measure quantities,
but observe what is happening. In these kind of
labs, the “Data” section is replaced by the
“Observation” section.
The third data (manifacturer) refers to the manufacturer statement that the mass should be
95 g, but could be as low as 93 g or as high as 96 grams.
1
Evaluation of Data (Analysis):
The measurements in the data table were also shown graphically in the Figure 1 below
for an easier comparison.
Guest User 4/5/2018 2:14 PM
Comment [5]: Evaluation of data (a.k.a.
Analysis) include calculations, graphs, analysis
of the graph, how the uncertainty has been
selected, etc.
Figure 1: Comparing Measurements and Tolerance
The uncertainty of the postal scale was chosen 3 grams as one half of the smallest
devision of the scale, which is 6 grams.
According to the graphical representation, the mass given by the postal scale is consistent
with the manufacturer’s claim because the green and red lines overlap. However, the
postal scale measurement, m = 93 ± 3 g, can not be used to conclude that the
manufacturer’s value is accurate because this measurement also includes masses outside
also answer questions
asked in lab manual.
the tolerance. The measurement from the digital balance, m = 95.1 ± 0.1 g, on the other
hand, confirms that the key’s mass is within the manufacturer tolerance, 93 ≤ x ≤ 96 g.
The possible masses given by that measurement fall within tolerance.
Conclusion:
The experimenter can conclude that the mass of the key measured with the digital
balance, m = 95.1 ± 0.1 g, does indeed fall within the range claimed by the manufacturer,
93 ≤ x ≤ 96 g.
2
Guest User 4/5/2018 2:14 PM
Comment [6]: The conclusion should
answer the question raised in the purpose.
Synthesis Question 2:
Purpose: The goal of this experiment is to measure the mass of a single sheet of paper
and evaluate the success of a clever measurement trick.
IV: NA
DV: NA
CV: NA
Materials:
•
Print papers
•
Postal scale
•
Digital scale
Procedure:
The total mass of 20 sheets of paper was measured using the mechanical postal
•
scale.
•
The mass of the 20 sheets was divided by 20 to find the mass of one sheet.
•
The mass of one sheet was measured using the digital scale.
Data:
The measurements are organized in Table 2 below.
Table 2: Measurements and Given Tolerance of Papers Mass
Measurement (g)
Measurement (g)
(for 20 sheets)
(for 1 sheets)
Postal Scale
96 ± 3
4.8 ± 0.2
Digital Scale
NA
4.5 ± 0.1
Source
3
Guest User 4/5/2018 2:13 PM
Comment [7]: The trick is successful if the
value obtained by using it is within the same
range as the value given by the digital scale.
This is a quick way of measuring the mass of
one page with small uncertainty when
measuring tools with high precision are not
present.
Evaluation of Data (Analysis):
The measurements in the data table were also shown graphically in the Figure 2 below.
Figure 2: Comparing Direct and Calculated Measurements of Paper Mass
As seen by the graphical representation of the measurements, the uncertainties do not
overlap. The discrepancy between the two measured values is 0.3 g. This discrepancy is
the same as the sum of the uncertainties. This means that the only possible value that
satisfies both measurements is a mass of exactly 4.60 grams, a claim that is not supported
by the measurements, therefore it can not be made without further data collections. Since
the digital scale has a smaller uncertainty, the direct measurement from it would be more
acceptable. However, the value of the mass given by the measurement trick is within the
range of the value given by the digital scale. Therefore, the trick is considered to be a
successful one.
The percentage difference between the two values of the mass of one sheet is calculated
below.
!! − !!
4.8 − 4.5
% !”##$%$&’$ = ! + ! × 100% =
× 100% = 6%
4.8 + 4.5
!
!
2
2
The value of the percentage difference of 6% would be another good reason to state that
the trick gave a useful approximation of the actual value of the mass of one page.
Conclusion:
The mass of one page found by using the clever measurement trick (measuring the mass
of 20 pages and dividing it by 20 to find the mass of one page) is 4.8 ± 0.2 gr. Since this
value is within the same range as the value from digital scale, 4.5 ± 0.1 gr, the trick is
considered to be successful.
Guest User 4/26/2018 12:34 PM
Comment [8]: The conclusion addresses
whether the trick is successful or not, stated
in the purpose.
4
DC Circuits – Kirchhoff’s Rules
Purpose
To study Kirchhoff’s rules as they apply to complex DC circuits.
Theory
Kirchhoff’s rules provide a general procedure for anayzing dc circuits no matter how
complex they might be. Kirchhoff’s rules may be stated as follows:
1. The sum of the currents entering any junction in a circuit must be equal to the sum of the
currents leaving that junction.
2. The sum of the potential differences across all elements around any closed circuit loop
must be zero.
As an example, let’s apply Kirchhoff’s rule in a circuit shown in Fig.1. Assuming the
directions of current in each of the resistors are as indicated by arrows. If we apply the junction rule
at the junction ‘e’ in the circuit, it gives
R2
a
b
I 3 I1 I 2
c
(1)
I2
Applying the loop rules in loop 1 (fabef) and
traversing clockwise as indicated, we get
1 I 3R3 I1R1 0
1
Similarly we can apply the loop rule in loop 2
(ebcde) and traversing clockwise as indicated,
we get
I 3R3 I 2 R2 2 0
I3
2
(2)
(3)
I1
f
e
d
Fig. 1. Circuit diagram for Kirchhoff’s rules
For known values of resistance and battery voltages (emfs) three unknown currents can be
determined by solving these three equations. In case of real direction of current is reverse to the
assumed direction, the solution of the current will be negative .
You are going to construct a circuit containing several resistors along with a battery and
verify these rules. Practically it is easy to measure potential difference using a voltmeter than
measuring current. For a resistor of know resistance once you measured the potential difference,
you can calculate the magnitude of current from Ohm’s law,
I V and the direction of the current can be determined
R
from the polarity of the voltmeter reading. As illustrated in
Fig. 2, if the voltage reading across the resistor, Vab, is
positive (with red terminal of the voltmeter is at ‘a’ and
black terminal is at ‘b’) then the potential at the terminal ‘a’
is higher than that at ‘b’ hence the current is flowing from
‘a’ to ‘b’. If Vab is negative the current is reverse.
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Fig. 2. V measurement across R.
1
Apparatus
Circuit board that contains resistors: R1 ~100 , R2 ~10 , R3 ~50 , R4 ~20 , decade resistance
box (variable R), switch, power supply, digital multimeter.
Description of apparatus
Figure 3 shows the apparatus you will use in this lab and circuit connections. You will be
Digital multimeter
Power supply
R1
Switch
R2
R3
R4
Resistors board
Decade resistance
box
Fig. 3. Experimental set up
using a power supply instead of the battery in the circuit. A digital multimeter is a used to measure
the resistance and voltage. A digital multimeter is a test tool used to measure multiple
measurements such as voltage (volts), current (amps) and resistance (ohms). They can be used for
AC and DC electrical measurments. It is a standard diagnostic tool for technicians in the
electrical/electronic industries. Some meters can also test continuty of circuit and measure
temperature.
Decade resistance box is a easy to use variable resistance box. The knobs can be rotated to
quickly adjust the resistance value at different decimal places some even at the fraction of unit.
Procedure
You are going to construct the circuits as shown in Fig. 4 to test both the junction and loop
rules in two situations (I) with the switch S closed, and (II) with the switch S open,
1. Make sure the power supply is off before begin. Before connecting the resistors in the circuit,
measure each of the resistors, R1, R2, R3, and R4. Use the digital multieter set for the most
sensitive ohms range. Make sure the resistor is isolated from any other connection
while measuring the resistance of individual component. Each of the resistances should
be recorded to at least 3 significant figures. Note down the values in table 1 and 2.
2. Wire the circuit as shown in figure 4 with the switch S closed. Ask your instructor to check
the wiring before you begin to make measurement.
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2
Part I. Switch S closed
3. Set the digital multimeter
to measure voltages with
the red probe inserted into
the plog marked V and
black probe into COM on
the multimeter. Set the
range to 20 V. Set the
voltage control on the
power supply to zero
(turning the knob all the
way down
countercockwise). Now,
turn on the power supply
and adjust the voltage
control slowly and set to 5
volts. Measure the output
voltage of the power
supply (battery eliminator).
It should be approximately
5 volts.
R1 = 100
R2 = 10
d
R3 = 50
b
c
Decade
resistance box
R4 = 22
Switch (S)
e
a
Power supply
Fig. 4. Circuit diagram (a) switch closed
for part I and (b) switch open for part II.
4. Measure the voltage across R1, adjusting the decade box so that the voltage across R1 is as
close to 2 volts as possible. Record this voltage in table 1, keeping all significant figures.
5. Measure the magnitudes and directions (+ or -) of the voltage drops across each of the
resistors, including the decade resistance box. Make sure you have recorded the voltage by
connecting the probes properly. For example, when you are measuring the voltage Vde, i.e.,
the voltage across R4, the red terminal of the multimiter should be connected at point ‘d’ and
black terminal at ‘e’. Record these measurements keeping all fignificant figures, in the data
table 1.
6. Disconnect the decade resitance box from the circuit (one side is sufficient) and measure its
resistance as precisely as possible and record in table 1.
Part II. Switch S open
7. Reconnect the decade resistance box the circuit (that you just disconnected). Do not change
the value of the decade resistance box.
8. Now, open the switch S. Measure all voltages across the resistors as above. Make sure you
have recorded the voltage by connecting the probes in the same way as in part I for each
resistor.
9. Record these results in the table 2 for further calculation and analysis.
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3
Computation
1. Fill in the tables by calculating the current (to 3 significant figures) through each of the
resistors for each of the voltage measurements made above.
2. Carefully draw the circuit for part I corresponding to the case when the switch S is closed.
Show the direction of the current through each of the resistors. Identify and label all of the junction
in this circuit. Identify each of the closed loops associated with this circuit.
3. Based on your measurements, calculate the sum of the currents at each junction and the
sum of the voltages around each loop. You must keep track of the signs of all currents and voltages.
4. Do the same calculations as above (steps 2 and 3) for the circuit corresponding to the case
when the switch S is open (II).
5. Redraw the circuit for the case when the switch is open and solve the circuit currents in
the cricuit using Kirchhoff’s rules. Use your measured values of the resistances in this calculation.
Compare your calculated results for currents through each of the resistors with your experimental
results.
Questions to be answered in the Report:
1. Do your measurements agree, within experimental errors, with Kirchhoff’s rules? Discuss
your results.
2. For the circuit in which switch S is open, how do your measured values of the currents
compare with the calculated values? What might account for any discrepancies?
3. If the voltage source had a significant internal resistance, would this affect the results?
Explain.
4. For each circuit (I and II), what is the total power dissipated in the resistors? Show how you
calculated this result.
5. For each circuit (I and II), which resistor dissipates the most power? Justify your answer.
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Data Sheet
Date experiment performed:
Name of the group members:
Tables 1. Switch closed
Switch closed
R (ohms)
V (volts)
R1
Vbc =
R2
Vcd =
R3
Vbd =
R4
Vde =
Rdecade
Vab =
I (milliamps)
P (milliwatts)
I (milliamps)
P (milliwatts)
Table 2. Switch open
Switch open
R (ohms)
V (volts)
R1
Vbc =
R2
Vcd =
R3
Vbd =
R4
Vde =
Rdecade
Vab =
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