reports for general physics lab 106

Transcription

GERMAN - JORDANIAN
UNIVERSITY
SCHOOL OF BASIC SCIENCE AND HUMANITIES
REPORTS FOR GENERAL PHYSICS LAB
Phys106
MECHANICS
Experiment 1: Part B
Measurements and Calculation of Errors
Name: ……………………
Reg. No.: ………………
Section: …………
Table no. (
Partner’s Name: …………...
Instructor: ………………….
Date: ……………......
)
*Finding Density of a Cylinder
Data Table
Trial
1
Mass (g)
Height (cm)
Diameter (cm)
Volume (cm3)
Density(g/cm3)
2
∆m =
g
∆h=
cm ∆D =
cm
Calculations
1. Calculate the error in the density (∆ρ) for each trial.
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
2. Find the average value of the calculated densities and compare it with the standard value
of stainless steel density (  = 7.7 g/cm3)?
[find the percent difference]
………………………………………………………………………………………
………………………………………………………………………………………
3. Which quantity contributes more to the error in the density; the mass, the diameter or
the height? Why?
………………………………………………………………………………………
………………………………………………………………………………………
………………………………………………………………………………………
3 / 39
Experiment 2: Part A
Velocity and Speed
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
* Velocity of a Motorized Cart (Motion Sensor)
* DataStudio file: 06 Constant Velocity.ds
Data Table
Run
1
2
3
Slope
Y-intercept
Data
Sketch in Fig. 2A.1 your graph of Position versus Time (for all the three trials, and label
each one). Write the axis title and its units
Questions
1. What does the y-intercept of each graph represent?
2. What physical quantity does the slope of each plot represent?
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3. What are the units for the slope of each plot?
4. Write an equation for each plot on your graph using the form y = mx + b. Include numbers
for the slope and y-intercept.
Run
1
2
3
Equation (y = mx + b)
5. Knowing the physical quantities represented by the slope and Y-intercept, what variables
could you put in your equation in place of ‘y’, ‘m’, ‘x’, and ‘b’ to make it more specific for
the motion of the cart?
y:……………..
m:……………..
x:……………..
b:……………..
6. How long was the motorized cart moving during each data run?
Run
Time of Motion (s)
(Graph)
1
2
3
7. Why is the time of motion different for each data run?
5 / 39
Linear Motion: Acceleration
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
Part 1: Constant Velocity and Constant Acceleration
* DataStudio file: 07 Vel and Acc.ds
Data
Sketch in Fig. 2B.1 your graph of Position versus Time for the motion of the two carts. Write
the axis title and its units.
Questions: Cart Motion
1. Which cart was moving with constant velocity? What is the approximate velocity of this
cart?
2. Is there a moment when each cart has travelled the same distance at the same time? When?
3. Examine the point on the graph where the two plots cross. Which cart was going faster at
that moment? How can you tell?
6 / 39
 Select the plot of data for the fan cart’s motion. Click the ‘Fit’ button in the Graph
toolbar and select a curve fit that you think will match the plot of data. (If your
selection is not a ‘good fit’ for your data, try another curve fit.)
4. Which curve fit is the best for your data?
Interpret Graphs
EXAMPLE 1: The following graph represents
the motion of a cart. Write a description of the
motion by answering the questions.
1. What happens during the first 3 seconds of
motion?
2. What happens during the time interval
between 3 and 5 seconds?
3. What happens after 5 seconds? How is the
motion of the car after 5 seconds different
from the motion during the first 3 seconds?
EXAMPLE 2:
4. Find the speed of the cart at the moments:
t=2s, and t=4s.
5. What is the cart doing in EXAMPLE2?
7 / 39
Part 2: Graph Position, Velocity, and Acceleration of a Fan Cart
* DataStudio file: 08 Fan Cart.ds
Data
Sketch in Fig. 2B.2 your graph of Position, Velocity, and Acceleration versus Time for the
motion of the fan cart. Write the axis title and its units.
Questions
1. Consider the position versus time graph, describe the graph.
2. Consider the velocity versus time graph, describe the graph.
How to Find the Acceleration from Position versus
Time
1. Highlight a smooth part of the position graph.
2. Click the ‘Fit’ menu and select ‘Quadratic Fit’.
The "A" is the coefficient of the squared term in the
curve fit formula. Record the coefficient “A”.
A = ___________
How to Find the Acceleration from Velocity versus
Time
1. Highlight a smooth part of the velocity graph.
2. Click the ‘Fit’ menu and select ‘Linear Fit’.
The "m" value is the slope. Record the slope
as the acceleration.
m = _________
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Compare the Acceleration Values
Multiply the value of “A” number by "2" to get the acceleration based on position versus
time. Record the value of 2 x "A".
2 x A = _____________
Compare this value to the slope (“m”) of the Linear Fit for the velocity versus time graph.
(This is the acceleration based on velocity versus time.)
Verification
Compute the percent difference of your two values for acceleration.
9 / 39
Linear Motion with Constant Acceleration (g sinθ)
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
* DataStudio file: 10 g sin theta.ds
Data Table
Run Angle(degrees) Sin(theta) Acceleration (m/s2)
1
10
2
8
3
6
4
4
5
2
Data
Sketch in Fig. 3A.1 your graph of data from the Acceleration Sensor for Acceleration versus
sin θ for the cart in each data run and write the axis title and its units.
Questions
1. Describe the acceleration versus sinθ plot of the Graph display.
2. Calculate the value of “g” using the acceleration of the cart.
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3. What is the percent difference between your measured value for “g” and the accepted value
for “g”?
11 / 39
Linear Motion, Free Falling Bodies
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
Part 1: Acceleration of a Freely Falling Ball
* DataStudio file: 11 Falling Ball.ds
Data
Sketch in Fig. 3B.1 and Fig. 3B.2 your graph for position and velocity versus time, write the
axis title and its units.
Data Table
‘g’ (slope of velocity versus time) = ___________
Questions
1. How does your value for ‘g’ (slope of velocity versus time) compare to the accepted
value of the acceleration of a free falling object (9.8 m/s2)? “Find the percent error”
2. What factors do you think may cause the experimental value to be different from the
accepted value?
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3. Mark on both Figures 3B.1 and 3B.2, the position versus time and the velocity versus time
graphs, the point corresponding to the moment of the first rebound and the moment when the
ball was at its maximum height after its first rebound.
Part 2: Acceleration of a Freely Falling Picket Fence
* DataStudio file: 12 Free Fall Fence.ds
Questions
1. Find the slope of the velocity versus time from Fig. 3B.2. How does it compare to the
accepted value of the acceleration of a free falling object (g = 9.8 m/s2)? “Find the percent
error”
2. What factors do you think may cause the experimental value to be different from the
accepted value?
3. Determine whether releasing the Picket Fence from just several centimeters above the
Photogate makes any difference in the value of the acceleration.
13 / 39
Experiment 4:
Projectile Motion
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
Part 1: Horizontal Launch
* DataStudio file: 13A Projectile Motion 1.ds
Data Table
Range Initial Speed (m/s) Time of Flight (s)
Short
Middle
Long
Questions
1. How do the values for the time of flight for the short, middle, and long-range distances
compare when the ball was launched horizontally? State your conclusion.
2. Measure the height of the starting point and use it to compute the time of flight.
Height of the starting point =
m
3. Compare the value you found in the previous question with the values in the table; [find
the percentage error]
4. What is the reason behind the small differences in the time of flight values in the table.
14 / 39
Launching with Angle 30°
* DataStudio file: 13B Projectile Motion 2.ds
1) Data Table
Arrangement
Initial
Speed (m/s)
Measured Time of
Flight (s)
Calculated Time of
Flight (s)
Percent
Error
Short range
Mid range
2) Measure the range, the horizontal distance between the launching point and the landing
point and record it.
Arrangement
Initial
Speed (m/s)
Measured
Range (m)
Calculated
Range (m)
Percent
Error
Short range
Mid range
Questions
1. Why would time of flight depend on the angle of launch?
2. Compute the time of flight for each range and compare it to the measured time by finding
the percent difference. Record your values in the table. Write down, as an example, the
calculation for the short range.
3. Why would range depend on the angle of launch?
4. Compute the range for each initial velocity and compare it to the measured range by finding
the percent difference. Record your values in the table. Write down, as an example, the
calculation for the short range.
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5. If you want to change the angle of launch (only) but you want your projectile to land on
the same point, what must be the new angle? Why?
_______________________________________________________________________
6. What are the quantities that differ between the cases when the angle was 30° and the new
angle in question (5) above?
16 / 39
** Graph papers are necessary for this experiment.
Experiment 5
Newton’s Second Law
Name: ……………………
Reg. No.: ………………
Table no. (
Date: ……………......
)
Part 1: Constant Mass, Changing Force
* DataStudio file: 15A Newton’s 2nd Law 1.ds
Data
Make a sketch in Fig. 5.1 your graph of velocity versus time for the first run of data, Write
the axis title and its units.
Data Table 1
Masshanger=
g Massloaded (on cart) =
Total mass of the system (MT) =
g
g=
Massempty cart = 500 g
kg
atheoritical
(m/s2)
Percent Difference
%
Data Table 2
Run
m hanger
(kg)
Fdriving
(N)
aexperimental
(m/s2)
#1
#2
#3
17 / 39
1. What does the slope of the sketch above represent?
2. What happens to the value of the acceleration as you increase the value of the driving force
but the system's mass remains constant?
3. Plot the Fdriving vs. aexperimental graph, calculate the slope, say what does it represent? and
describe the graph.
[Use a graph paper]
The slope represents:
The graph is:
Part 2: Constant Force, Changing Mass
* DataStudio file: 15B Newton’s 2nd Law 2.ds
Data Table 1
mhanger= 45 g = 0.045 kg
Fdriving = mhanger × g = 0.045 kg × 9.8 m/s2 = 0.44 N
Mloaded → changing (0g, 500g, 1000g) ; MT = (mhanger + mcart)
(constant)
(constant)
(changing)
Data Table 2
Run
mloaded
(kg)
Total mass
of the cart
mcart (kg)
MT of the
system(kg)
aexp.
(m/s2)
atheor.
(m/s2)
Percent
Diff. (%)
1/aexp.
(s2/m)
#1
#2
#3
Questions
1. What happens to the acceleration as you increase the mass of the object and keep the driving
force constant?
2. Plot mcart vs. 1/aexp. [Use a graph paper]
18 / 39
Extension Problem
3. The motor of the toy cart shown has a thrust of F and a mass of
M. Other toys of mass m can be added to the cart and hence its
acceleration decreases since the acceleration is inversely
proportional to the total mass. The Fig. 5.2 besides shows the
relation between the added mass and the inverse of the
acceleration of the cart. Use the graph below (m vs 1/a) to find:
a) F, the thrust of the cart’s motor.
b) M, the mass of the empty cart.
19 / 39
m
M
Friction
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
Part 1: Coefficients of Static and Sliding (Kinetic) Friction

DataStudio file: 20 Friction Forces.de
Data
Make a sketch in Fig. 6.1 of one run of the frictional force versus time data
20 / 39
 Sketch in Fig. 6.2 the static force and
felt.
sliding force versus normal for
Data Table
Record the coefficient of friction (slopes) in the table below
Material
Felt
Coefficient of Static Friction, µs Coefficient of Sliding Friction, µk
Cork
Questions
1. What happens to the static friction force as the mass is increased when applying a
force ?
-------------------------------------------------------------------------------------------------2. What happens to the static friction force as the mass is increased ?
-------------------------------------------------------------------------------------------------3. Think about your experience with the friction trays. When a car skids to a stop (with
wheels “locked”), which friction force is at work? How do you know?
-------------------------------------------------------------------------------------------------Prediction : If the mass of the block is increased, will the force of kinetic friction increase?
Will the coefficient of kinetic friction increase? Explain.
------------------------------------------------------------------------------------------------21 / 39
Momentum and Collisions
Name: ……………………
Reg. No.: ………………
Table no. (
)
Date: ……………......
Part 1: Momentum in an Inelastic Collision
* DataStudio file: 23A Momentum 1.ds
Observations
What happens to the carts during the inelastic collision?
Calculations
Use the mass and the change in velocity of each cart to calculate the momentum of each cart
before collision. Find the total momentum before the collision.
The momentum after collision is the product of the combined mass and the velocity after
collision. Use the total mass and the final velocity to determine the momentum of both carts
after collision.
Data Table
Before Collision
Mass
Cart
(kg)
1
2
Initial
Velocity (m/s)
Momentum Before
(kg m/s)
Total Momentum
Before
After Collision
Mass (kg) Final Velocity (m/s) Momentum After
Cart1+Cart2
Questions
1. How does the momentum before the collision compare to the momentum after the
collision?
22 / 39
2. What factors do you think may cause a difference between the momentum before and the
momentum after collision?
Part 2: Momentum in an Elastic Collision
* DataStudio file: 23B Momentum 2.ds
Observations
Describe the motion of the carts during the elastic collision.
Calculations
Use the mass and the change in velocity of each cart to calculate the change in momenta of
Cart 1 and Cart 2.
Data Table
Cart
Run#1
Mass
(kg)
Change in velocity
(m/s)
Change in momentum
(kg m/s)
1
2
Questions
1. How does the change in momentum of Cart 1 compare to the change in momentum of Cart
2?
23 / 39
Experiment 7
Charging and Charge Distribution
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: _____________________
Table #:____________________
Date: _________________________
___________________________________________________________________
 Open the DataStudio file: 64 Charging.ds
Part One: Electrostatic Charging
Questions:
1. What polarity is the white Charge Producer? What polarity is the blue Charge Producer? Is
the change of the charge on the ‘Ice Pail’ permanent or temporary? Sketch in the Fig. 7.1 the
resulting graph.
White:………………………………………….
Blue: …………………………………………..
Part Two: Electrostatic Charge Distribution
on a Conductive Sphere:
Graph:
Sketch in the Fig. 7.2 your graph of Charge and Location for the sphere:
24 / 39
Questions:
1. What happens to the charge on the Conductive Sphere when it is connected to a source of
charge such as the Electrostatic Voltage Source?
………………………………………………………………………………………………..
………………………………………………………………………………………………..
Part Three: Charging a Conductive Sphere:
A. Charging a Conductive Sphere by Conduction:
Questions:
1. What is the polarity of the charge on both spheres?
Sphere A:……………………………………………..
Sphere B: ……………………………………………..
2. What is the relation between the values of the charge on each sphere?
…………………………………………………………………………………………………
…………………………………………………………………………………………..
B. Charging a Conductive Sphere by Induction:
Questions:
1. For step 5 in the procedure above, draw schematic diagram for the two spheres and determine the
polarity on each sphere?
2. According to step 8 in the procedure above, what is the charge on both sides of sphere B?
………………………………………………………………………………………….
3. According to step 13 in the procedure above. What is the polarity of the charge on the sphere
B?
………………………………………………………………………………………
………………………………………………………………………………………
25 / 39
4. According to step 13 in the procedure above. Is the charge on the sphere permanent?
………………………………………………………………………………………
………………………………………………………………………………………
5. How does the result of charging by contact differ from the result of charging by induction?
………………………………………………………………………………………
………………………………………………………………………………………
26 / 39
Experiment 8
Resistors and Resistors Connections
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: ____________________
Table #:____________________
Date: _________________________
__________________________________________________________________
 Open the DataStudio file: 67 Ohm’s Law.ds
Part (1): Ohm’s Law
Graph:
Make a sketch in the Fig. 8.1 of the Scope display screen for voltage and current for the given
Resistors.
Questions & Calculations:
1. From your graphs use the smart tool to calculate the resistance in each case.
Resistor (1) = ………………………Ω
Resistor (2) = ……………………….Ω
2. Show how did you calculate the resistance of R2?
……………………………………………………….………………………...………………
……………………………………………………………………............................................
.......................................................................................................................................
27 / 39
3. Use the DMM to measure the values of R1 and R2 and consider that as the accepted value
for each resistor.
Resistor (1) = …………………….Ω
Resistor (2) = …………………….Ω
4. Calculate the percentage error for both resistors R1 and R2.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
Part (2): Resistors Connections
Graph:
Make a sketch in the Fig. 8.2 of the Scope display screen for voltage and current for the series
and parallel connections of the given set of resistors.
1. Use the smart tool to calculate the slope of each line in the graphs above.
Series connection: …………………………
Parallel connection: ……………………….
2. What does the slope represent in each case?
28 / 39
3. Calculate the theoretical value of the equivalent resistance for the two types of connections
below.
Series connection: …………………………
Parallel connection: ……………………….
4- Calculate the percentage error for both cases:
5- What factors do you think that may contribute to the errors?
29 / 39
Experiment 9
Kirchhoff's Laws
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: _____________________
Table #:____________________
Date: _________________________
___________________________________________________________________
 Open the DataStudio file: 70 Kirchhoff.ds
Data:
* Measure the voltage across each resistor, and record the measured values on the diagram
9.1 above.
* Measure the current across each branch then fill in the table below.
1. Calculate the sum of the measured voltages around any two loops in the circuit to verify
Kirchhoff’s voltage law.
………………………………………………………………………………...…………….
………………………………………………………………………………………………
……………………………………………………………………………………………….
30 / 39
3. Using your measured values of current and their direction of flow on one of the nods,
calculate the sum of currents entering the junction and the sum of currents leaving the
junction.
………………………………………………………………………………...………………
…………………………………………………………………….................................
………………………………………………………………………………...………………
………………………………………………………………………………………….
4. Using kirchhoff's laws calculate the currents (I1, I2, I3), and insert your calculated values in
the table then calculate the % error.
………………………………………………………………………………...………………
…………………………………………………………………….................................
………………………………………………………………………………...………………
……………………………………………………………………...…………………………
……………………………………………………...…………………………………………
…………………………………………................................................................
………………………………………………………………………………...………………
…………………………………………………………………….................................
………………………………………………………………………………...………………
…………………………………………………………………….................................
………………………………………………………………………………...………………
…………………………………………………………………….................................
……………………………………………………………………….................................
Quantity
I1
I2
I3
Measured Values
Calculated Values
% error
5. What are the main sources of error in this experiment?
………………………………………………………………………………...………………
………………………………………………………………………………………….
31 / 39
Experiment 10
Capacitors and Capacitors Connections
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: ____________________
Table #:____________________
Date: _________________________
__________________________________________________________________
 Open the DataStudio file: 71 RC Circuit.ds
Part(1) Capacitance of a single capacitor:
From the V-t graph you got, write down the value of (t1/2) for each capacitor you have:
(t1/2) for capacitor (1) = __________ s
(t1/2) for capacitor (2) = __________ s
1. Use the relation
𝐶=
𝑡1/2
𝑅 × 0.693
to calculate the capacitance of each capacitor:
Capacitance for capacitor (1) = ___________ μF
Capacitance for capacitor (2) = ___________ μF
2. Calculate the percentage error for each capacitor:
5. What is the maximum theoretical charge (q0) each capacitor can have?
…………………………………………………………………………………………………
…………………………………………………………………………………………...
32 / 39
6. From your V-t Graph use the smart tool to determine τ (time needed for the capacitor to
charge to 63% of its maximum charge)
…………………………………………………………………………………………………
…………………………………………………………………………………………..
7. Calculate τ theoretically (τ = RC)
…………………………………………………………………………………………………
…………………………………………………………………………………………..
8. Calculate the percentage error for τ:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
Part (2) Capacitors connections:
(a) Series Connection:
(t1/2) for the series connection of the given capacitors = __________ s
7. Using your V-t graph, calculate the equivalent capacitance of the two capacitors connected
in series:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
8. Calculate theoretically the equivalent capacitance the two capacitors connected in series:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
9. Calculate the percentage error between the theoretical and the experimental value:
…………………………………………………………………………………………………
………………………………………………………………………………………….
(b) Parallel Connection:
(t1/2) for the parallel connection of the given capacitors = __________ s
33 / 39
10. Using your V-t graph, calculate the equivalent capacitance of the two capacitors connected
in parallel:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
11. Calculate theoretically the equivalent capacitance the two capacitors connected in parallel:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
12. Calculate the percentage error between the theoretical and the experimental value:
…………………………………………………………………………………………………
…………………………………………………………………………………………..
13. What major factors of error do you think that could account for the percentage error in all
the experimental results?
…………………………………………………………………………………………………
…………………………………………………………………………………………..
34 / 39
Experiment 11
Magnetic Field in a Current-Carrying Coil and
Magnetic Induction
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: _____________________
Table #:____________________
Date: _________________________
___________________________________________________________________
 Open the DataStudio file: 80 Mag Field Coil.ds
Part 1: Magnetic Field of an N turn coil:
Data:
Number of loops of wire:………………………………….
Radius of coil (m):……………………………………....
Sketch in the Fig. 11.1 your graph of Magnetic Field Strength versus Current.
35 / 39
Calculations:
1. To find the value of the permeability of free space, first convert your slope from gauss to
tesla by using the following conversion (1 gauss = 10-4 tesla).
Slope (gauss/A):…………………….
Slope (tesla/A):……………………...
2. Rearrange the equation (B = µ0NI /2R) to solve for the permeability of free space (μ0). How
can you relate the slope of your graph to this equation?
……………………………………………………………………………………….……….
……………………………………………………………………………………………….
3. Substitute your value of slope into your equation and calculate µ0
µ0 = ……………….
4. Compute the percent error between your value and the accepted value
(µ0 = 1.26 x 10-6 T m/A).
…………………………………………………………………………………………………
…………………………………………………………………………………………..
5. If we changed the number of loops of the wire or the diameter of the wire. What do you
expect about how the value of µ0 will change?
…………………………………………………………………………………………………
…………………………………………………………………………………………..
6. What are the sources of error in this experiment?
…………………………………………………………………………………………………
…………………………………………………………………………………………..
36 / 39
Part 2: Magnetic Induction:
 Open the DataStudio file: 79 Induction - Magnet.ds
1. Sketch in the Fig. 11.2 the voltage supplied to the primary coil in step 7 of the procedure.
5. Sketch in the Fig. 11.3 the EMF produced in the secondary coil in the same step 7 above.
6. What conclusion can you draw about the relation between the two graphs?
…………………………………………………………………………………………………
.…………………………………………………………………………………………..
37 / 39
Experiment 12
Transformer Basics
Name: _____________________
Partner’s Name: ________________
Section: ____________________
Instructor: _____________________
Table #:____________________
Date: _________________________
___________________________________________________________________
 Open the Data studio file: 81 Transformer.
Data and Calculations:
Table (1)
Number of Turns
Primary Coil
Secondary Coil
Input Voltage
(V)
Output Voltage
(V)
Core
None
Iron rod
U-Shaped
Closed
Table (2) (Assuming Ideal Transformer)
Number of Turns
Measured Input Current I1 =
Input
Output
Primary Secondary
Voltage
Voltage
V1 / V 2
N1 / N 2
Coil (N1)
Coil (N2)
(V1)
(V2)
38 / 39
Calculated
Output
Current I2
Questions & Analysis
Part 1: The Effect of the core in the Transformer:
1. Which core configuration gives the maximum transfer of electromagnetic effect to the
secondary coil? Explain why?
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
……………………………………………………………………………………..
Part 2: The effect of the number of turns in the secondary coil:
2. Calculate the ratios V1 / V2 and N1 / N2 Then insert your results in table 1.2. What
conclusion do you figure out from your results?
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………………...
3. State the major sources of error in this experiment?
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
…………………………………………………………………………………………………
………………………………………………………………………………..
39 / 39

reports for general physics lab 106

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