Part A: STANDING WAVES ON A STRING Using PhET simulation
Part A: STANDING WAVES ON A STRING Using PhET simulation
(Part A: STANDING WAVES ON A STRING Using PhET simulation) 12/27/2019
OBJECTIVE
To study standing waves on a string and see the effects of changing the tension in the string,
EQUIPMENT
PhET Simulation Wave on a String: https://phet.colorado.edu/en/simulation/wave-on-a-string
You can also reach this simulation by going to PhET, and looking for Wave on a String.
Theory: Standing Waves in Strings
For any wave with wavelength λ and frequency f, the speed, v, is
v = λf (1)
The speed of a wave on a string is also related to the tension in the string, T, and the linear density (=mass/length), μ, by
v2 = T/μ = λ2f2 (2)
L is the length of the string and n is the number of segments, antinodes, or harmonics. Since a segment is 1/2 wavelength then
λ = 2L/n where n = 1, 2, 3, … (3)
Solving Equation 2 for the tension yields:
T = μλ2f2 (4)
Which can also be written as:
(5)
PROCEDURE
Constant Tension
1. Open the software. Select: Oscillate, Amplitude = 0.10 cm, Damping = 0, Tension = Lowest, Fixed End.
2. Turn on the oscillator by pressing the large blue button with the arrow. You will see the wave going from left to right, hit the fixed end and reflect. The reflected waves will interfere with the waves going to the right.
3. Now adjust the frequency in the Signal Generator until you get a standing wave in one segment (i.e. the first harmonic). Note this frequency, and measure the wavelength by using the ruler tool. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
4. Increase the frequency gradually until you obtain a standing wave in the 2nd, 3rd, 4th, and 5th harmonic. Record each frequency and wavelength.
5. Calculate the wavelength by using equation (3).
6. Calculate the velocity of the waves by using equation (1)
7. Change the oscillator to Pulse. Keep the pulse width small. Measure the time taken by the pulse to travel from the left to the right ends, and hence calculate the velocity of the pulse in the string. Repeat three times and take the average. Use this value as a second value of the speed of the wave.
8. Calculate the percent difference between the two speeds.
| Number of Harmonic
( n ) |
Number of nodes | Wavelength
λ = 2L/n
( m ) |
Frequency
f
( Hz ) |
Speed of wave
V = λ*f
( m/s ) |
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
9. Repeat for the other two available tensions of the string. Case A: Lowest Tension
DATA TABLE
Length of the string: _________
Speed of the wave
| Trial number | Time for pulse to reach other end | Speed of the wave |
| Average speed of the wave |
Length of the string: ____________
Case B: Medium Tension
| Number of Harmonic
( n ) |
Number of nodes | Wavelength
λ = 2L/n
( m ) |
Frequency
f
( Hz ) |
Speed of wave
V = λ*f
( m/s ) |
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
Speed of the wave
| Trial number | Time for pulse to reach other end | Speed of the wave |
| Average speed of the wave |
Length of the string: ____________
Case C: Highest Tension
| Number of Harmonic
( n ) |
Number of nodes | Wavelength
λ = 2L/n
( m ) |
Frequency
f
( Hz ) |
Speed of wave
V = λ*f
( m/s ) |
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 |
Speed of the wave
| Trial number | Time for pulse to reach other end | Speed of the wave |
| Average speed of the wave |
Part B E-39-0 Electric Charges and Electric Fields ONLINE
6-21-2020 Adapted from manual from Dr. Kam Chu
Objective
To study the electric field and electric potential around different charges.
Equipment
PhET Simulation:
https://phet.colorado.edu/sims/html/charges-and-fields/latest/charges-and-fields_en.html
Theory
There is an electric field surrounding a charge, in which another charge would experience an electric force. The strength of the electric field at a distance from a point charge is given by:
(1)
Where is the Coulomb Constant, q is the charge, and r is the distance from the charge. The unit vector points away from a positive charge, and towards a negative charge. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
The electric potential due to a point charge is given by the equation:
(2)
Where is the electric potential (in volts), and is a scalar quantity.
In this Lab, we will use a PhET simulation to study the electric field and electric potential surrounding single and multiple point charges.
Procedure
Play with the simulation (Charges and Fields) and get oriented with all the different options. This should help you understand the lab better. Note that you have positive and negative point charges, an electric field sensor (yellow circle), a tape measure and a voltmeter, that also makes the equipotential lines. For each case, take a screenshot and attach with your report. You may alsoturn on ‘gridlines’ if desired. Each small square of the grid is 10 cm wide and high. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
Activity 1: Electric Field Lines and Equipotential Lines
1: Have one positive and one negative charge placed symmetrically in the field. Get the Electric field lines. Use the voltmeter to draw about ten equipotential lines (Figure 1 shows a related situation with a few equipotential lines)
2: Repeat with both charges being negative.
3: Repeat with both charges being positive.
4. Repeat with 4 positive charges (on top of each other, to create 4q) and one negative charge.
5. Parallel Plates: Put a large number of positive charges in a straight row (to look like a solid line). Make a negative line in the same way (parallel to the first). As an example, see figure 2. Get the electric field lines and Equipotential Lines between and surrounding the parallel plates.
6. Attach screenshot of the simulations in your report. Figure – 1
Figure-1: Parallel “plates”.
ACTIVITY 2
1) Turn on ‘gridlines’.
2) Select positive point charge of any magnitude (you do this by placing the point charges on top of each other). Place the charge at the intersection of two thick gridlines, somewhere in the left half of the screen.
3) Use the tape measure and Voltmeter to find the voltage at different locations along the horizontal line on which the charge is placed. Enter values in Table 1.
4) Plot a graph in Excel between the voltage (y-axis) and the distance (x-axis).
5) Use Excel to determine the value of the Coulomb Constant (see eqn. (2). Find the percent error between the calculated and accepted values.
6) Use the tape measure and the yellow Electric Field sensor to measure the electric field at different distances in the horizontal direction from the charge. Enter the data in Table 2.
7) Plot a graph in Excel between the Electric Field (on y-axis) and distance (on x-axis)
8) Use Excel to determine the value of the Coulomb Constant (see eqn. (1)). Find the percent error between the calculated and accepted values.
9) Attach the screenshots, graphs and calculations to your report. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
DATA
Table 1
Charge = _________
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| distance | |||||||
| voltage |
Value of k found from the graph: ___________
Percent error in k: ________________
Table 2
Charge = __________
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| distance | |||||||
| Electric Field |
Value of k found from the graph: ___________
Percent error in k: ________________
Part C E-35-O CAPACITORS IN CIRCUITS ONLINE LAB
7/1/2020
OBJECTIVES
The purpose of this lab will be to determine how capacitors behave in R-C circuits by measuring the time for charging and discharging. The manner in which capacitors combine will also be studied.
EQUIPMENT
PhET interactive simulation tool [Circuit Construction Kit: (AC+DC) – Virtual Lab]
https://phet.colorado.edu/en/simulation/legacy/circuit-construction-kit-ac-virtual-lab
PROCEDURE
1. Open the simulation by ctrl+click the link, or copy paste the link to the browser. The simulation should look like that shown in Fig.6
2. Since this simulation is in java (and not web based as some of the others), you may have to download the simulation. If you cannot run the simulation, you may need to follow the following PhET help guidelines: https://phet.colorado.edu/en/help-center/running-sims
Then click “Why can Irun some of the simulations but not all?”
3. Run the simulation, and you will see a page like that shown in Fig.7.
4. You would not set up the circuit. For assistance in setting up the circuit, see the manual: 00PhET Simulation Tool Instructions for Electric Circuits Labs.
5. This experiment requires you to measure the voltage as a function of time. The timer can be easily controlled by using the Pause/Play button (►) and/or the step button (|►) (these are at the bottom of the page).
Figure 6. Figure 7.
Case-A: charging the capacitor.
1. Set up the circuit as shown in figure 8. Once set up, it should look something like that shown in figure 9.
2. Set the resistance to 100 Ω, capacitance to 0.05 F, and Battery to 10.0 V.
3. Before charging the capacitor, make sure that it has no charge (the voltmeter reads zero). Otherwise you need to discharge the capacitor first until the voltage across the capacitor becomes zero. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
4. Put switch S1 in the ON state and switch S2 to the OFF state.
5. Set the Pause/Play button (►) to pause and the timer to zero. Before 5 seconds, use the step button (|►) to increase time by 0.5 second intervals and record the voltage values in Table I. After 5 seconds, use the Pause/Play button (►/||) to record the voltage at around 7.00, 10.0, 15.0, 20.0, and 25.0 seconds.
6. Using equation (5), obtain the charge at each time, and enter in Table 1.
7. Draw a graph between charge on y-axis and time on x-axis. It should look like Fig. 3.
8. Use the known values of resistance and capacitance to calculate the time constant and the maximum charge by using eqn. (2) and eqn. (3), and enter in Table 2.
9. Calculate the charges equal to one time constant, two time constants, and five time constants and enter in Table 2. Compare these with the experimental values using % error. Put your calculation in the table II.
C
Figure 8
Volt-meter
Figure 9.
Case-B: Discharging capacitor
1. Set up the circuit as shown in figure 8.
2. Set the resistance to 100 Ω, capacitance to 0.05 F, and Battery to 10.0 V.
3. Before discharging the capacitor, make sure the capacitor has been fully charged (the voltmeter reading is very close to 10.0 V).
4. Set switch to off and switch to on.
5. Set the Pause/Play button (►) to pause, and the stopwatch to zero. For time less than 5 seconds, use the step button (|►) to increase time by 0.5 second intervals. Record the voltage values in Table 3. After 5 seconds, use the Pause/Play button (►/||) to record the voltage at about 10.0, 15.0, 20.0, and 25.0 seconds.
6. Using equation (5), obtain the charge at each time, and enter in Table 3.
7. Draw a graph between charge on y-axis and time on x-axis. It should look like Fig. 5.
8. Use the known values of resistance and capacitance to calculate the time constant and the maximum charge by using eqn. (2) and eqn. (3), and enter in Table 4.
9. Calculate the charges equal to one time constant, two time constants, and five time constants and enter in Table 4. Compare these with the experimental values using % error. Put your calculation in the table II.
Case-C: Capacitors in Series.
1. Set up the circuit as shown in figure 10.
2. Set the resistance to 100 Ω, each capacitance to 0.05 F, and Battery to 10.0 V.
3. Before charging the capacitor, make sure that it has no charge (the voltmeter reads zero). Otherwise you need to discharge the capacitor first until the voltage across the capacitor becomes zero.
4. Put switch S1 in the ON state and switch S2 to the OFF state.
5. Now calculate the value of the time constant by using the equation for sum of capacitors in series.
6. Start charging the capacitors and note the voltage difference across both capacitors. Note the time it takes for the voltage to reach 63.2 % of Vmax. This is the measured value of time constant. Note this in Table 5.
7. Now charge the capacitors to full charge, and by using proper switching, measure the time for the voltage across them to fall BY 63.2% of Vmax. This is the measured time constant for discharging the capacitors.
8. Compare the measured and calculated values of the time constant for capacitors in series. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
Figure 11
Volt-meter
C1
C2
Volt-meter
C2
C1
Figure 10
Case-D: Capacitors in parallel.
1. Set up the circuit as shown in figure 11.
2. Set the resistance to 100 Ω, each capacitance to 0.05 F, and Battery to 10.0 V.
3. Repeat the steps needed to measure the time constant while charging and while discharging, and compare with the calculated value for capacitors in parallel.
4. Enter the results in Table 5.
DATA
Case-A: Data for charging a single capacitor
Table-1
Resistance R = _________ Capacitance C = ________
| Time
(s) |
Measured Voltage (VC) | Charge on Capacitor
q(t) (eqn. (5) |
Time (s) | Measured Voltage (VC) | Charge on Capacitor q(t)
(eqn. (5) |
Time (s) | Measured Voltage (VC) | Charge on Capacitor q(t)
(eqn. (5) |
||
| 0.50 | 3.00 | 7.00 | ||||||||
| 1.00 | 3.50 | 10.0 | ||||||||
| 1.50 | 4.00 | 15.0 | ||||||||
| 2.00 | 4.50 | 20.0 | ||||||||
| 2.50 | 5.00 | 25.0 |
Make a graph between q(t) and time.
Table 2
Maximum Charge from eqn (2) = Q = ___________
RC time constant from eqn (3) = τ = ___________
| Calculated value
eqn (1) |
Experimental value
eqn (5) |
% error | |
| Charge at t = 1 τ | |||
| Charge at t = 2 τ | |||
| Charge at t = 3 τ |
Case-B: Data for Discharging a single capacitor
Table-3
Resistance R = _________ Capacitance C = ________
| Time
(s) |
Measured Voltage (VC) | Charge on Capacitor
q(t) (eqn. (5) |
Time (s) | Measured Voltage (VC) | Charge on Capacitor q(t)
(eqn. (5) |
Time (s) | Measured Voltage (VC) | Charge on Capacitor q(t)
(eqn. (5) |
||
| 0.50 | 3.00 | 7.00 | ||||||||
| 1.00 | 3.50 | 10.0 | ||||||||
| 1.50 | 4.00 | 15.0 | ||||||||
| 2.00 | 4.50 | 20.0 | ||||||||
| 2.50 | 5.00 | 25.0 |
Make a graph between q(t) and time.
Table 4
Maximum Charge from eqn (2) = Q = ___________
RC time constant from eqn (3) = τ = ___________
| Calculated value
eqn (4) |
Experimental value
eqn (5) |
% error | |
| Charge at t = 1 τ | |||
| Charge at t = 2 τ | |||
| Charge at t = 3 τ |
Case C and D: Data for Two Capacitors in Series and Parallel:
Table 5:
Resistance: ____________ Capacitance 1: _____________ Capacitance 2: _____________
| Type of Circuit
Capacitors in: |
Calculated values of
τC and τD |
Measured Charging time τC | Measured Discharging time τD | Percent error in time of charging | Percent error in time of discharging |
| Series | |||||
| Parallel |
τC : Time constant for charging
τD : Time constant for discharging
Part D Lab 2 Ohm’s Law
Objective
Learn to build a simple circuit with one resistor and one DC source.
Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build circuits and verify Ohm’s Law.
Theory
Ohm’s Law states that the electric current passing through a resistor with resistance is proportional to the voltage (electric potential difference) across the resistor and inversely proportional to the resistance
Equipment
Ⓐ
Figure-1
PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab
For guidance on how to use the simulation, tool, see PhET Simulation Tool Instructions for Electric Circuits Labs.
Procedures
1. Build the circuit as shown in Figure 1 using the PhET Simulation Tool.
2. Set the DC Power Source to 12.0 V.
3. Create three resistors 10.0 Ω, 20.0 Ω, and 30.0 Ω. Putting each resistor into the circuit one at a time, measure voltage using the voltmeter and record the values on Table 1. Note that the volt-meter should be parallel with the resistor.
4. With the power source still set at 12.0 V, measure the current of each resistor and record the values on Table 1. The ammeter should be in series with the resistor. You must first cut the circuit and open it with two disconnected ends and then plug in the ammeter. Please refer to “PhET Simulation Tool Instructions for Electric Circuits Labs” for how to measure current.
5. Avoid the common mistake of connecting the ammeter directly to the power supply’s two terminals.
6. Compare the calculated and measured currents in Table 1 and find the percentage difference.
7. Put the 10.0 Ω resistor in the circuit and increase the voltage of the power supply from to using increments. Using the method outlined in step 4, measure the current at each step. Record the voltage and current values in Table 2.
8. Plot the voltage-current curve and find the slope of the line. The slope of the line will be the resistance.
9. Compare the measured with the known values of the resistance values and find the percentage error.
In you report, include screenshots of the circuits that you make for doing this Lab. (Part A: STANDING WAVES ON A STRING Using PhET simulation)
Data Table 1
DC Power Source: 12.0 V
| Resistance | Measured Voltage | Calculated Current (Equation 1) | Measured Current | % difference in the current |
| 10.0 Ω | ||||
| 20.0 Ω | ||||
| 30.0 Ω |
Data Table 2
Resistance: 10.0 Ω
| Voltage
(volt) |
Measured Current
(ampere) |
Slope (equals resistance)
(ohm) |
% error in resistance |
| 1.00 V | |||
| 2.00 V | |||
| 3.00 V | |||
| 4.00 V | |||
| 5.00 V |
Part E Series and Parallel Circuit
(Using PhET Simulation Tool)
Objective
1. Learn to build up series circuit and a parallel circuit with three resisters.
2. Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build the circuits and Verify Ohm’s Law
Theory
The relations for two resisters in series and parallel circuits are the following:
| Series Circuit | Parallel Circuit
|
|
|
|
|
Figure 1 Two resister in series |
Figure 2 Two resister in parallel |
Equipment
PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab
Procedures
Build the circuit as shown in Figure 1 by using PhET Simulation Tool
1. Click the above http link, you will see
2. Click ▲, you will see
3. Now you build your circuit by using “wire”, “Battery” and “Resistor”
4. You can tap the circuit elements to change it value by adjust
5. You can also toggle between the battery and the battery symbol as shown above.
6. Use the circuit board, build the series circuit by using three resisters as shown in the following figure 3: set up , , ,
Figure 3
7. Measure the voltage across each resister, the voltage across over the two and (resister) and the voltage across over all the resisters (). Record the values on the table 1.
How to use the circuit board tool Voltmeter to measure the voltage
Simple drag the Voltmeter to the necessary location as shown in the following figure.
8. Using Ohm’s law calculate the currents for each resister and put the values on table 1.
9. Using circuit board tool Ammeters measure the current passing through each resister and record the values on the table 1. Note that the Ammeters should be in series with the resister. (The figure below show you how to cut a circuit open and then put the Ammeters)
10. Compare the current in table 1, and find the percentage difference.
11. Use the circuit board, build the parallel circuit by using three resisters as shown in the following figure 4.
Figure 4
12. Repeat procedures from 7 to 10, record the data in table 1, and find the percentage difference.
Data Table 1
| Resistance: | :___________ | :____________ | :____________ |
| Series | Parallel | |||||||
| Measured Voltage |
(Ohm law) |
Measured Current | % difference | Measured Voltage |
(Ohm law) |
Measured Current | % difference | |
Your Lab Report Should Include the Following
1. Lab theory
2. Your build circuit photo
3. Procedures
4. Your circuit setup photo which shows voltage [across the two and (resister)] measurement; and circuit setup photo which shows current [pass through the two resistor and (resister)] measurement.
5. Data Table 1
6. Conclusion
Part F Combination of Series and Parallel Circuit
(Using PhET Simulation Tool)
Objective
3. Learn to build up a combination of series and parallel circuit with three resisters.
4. Use PhET interactive simulation tool (Circuit Construction Kit AC Prototype) to build the circuits and Verify Ohm’s Law
Theory
| Combination of Series and Parallel Circuit | |
|
Figure 1 Two resister in series |
|
|
|
Equipment
PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab)
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab
Procedures
Build the circuit as shown in Figure 1 by using PhET Simulation Tool
13. Click the above http link, you will see
14. Click ▲, you will see
15. Now you can build your circuit by using “wire”, “Battery” and “Resistor”
16. You can tap the circuit elements to change it value by adjust
17. You can also toggle between the battery and the battery symbol as shown above.
18. Use the circuit board, build a combination of series and parallel circuit by using three resisters as shown in the following figure 2: set up , , ,
Figure 2
19. Measure the voltage across each resister, and the voltage across over the two and (resister) Record the values on the table 1.
How to use the circuit board tool Voltmeter to measure the voltage
Simple drag the Voltmeter to the necessary location as shown in the following figure.
20. Using Ohm’s law calculate the currents for each resister and put the values on table 1.
21. Using circuit board tool Ammeters measure the current passing through each resister, and the current going through the two and (resister). Record the values on the table 1. Note that the Ammeters should be in series with the resister. (The figure below show you how to cut a circuit open and then put the Ammeters)
22. Compare measured current in column 3 and calculated current in column 4 in the table 1, and find the percentage error.
Data Table 1
| Resistance: | :___________ | :____________ | :____________ |
| 1 | 2 | 3 | 4 | 5 | |
| Measured Voltage | Calculated Current
(Using Ohm’s Law) |
Measured Current | Calculated Current
(Using Equation 1-6) |
% error (compare column 3 and 4) | |
Your Lab Report Should Include the Following
7. Lab theory
8. Your build circuit photo
9. Procedures
10. Your circuit setup photo which shows voltage [across the two and (resister)] measurement; and circuit setup photo which shows current [pass through the two resistor and (resister) measurement.
11. Data Table 1
12. Calculation details in column 4
13. Conclusion
Part G E-34-O KIRCHHOFF’S RULES ONLINE LAB
7/01/2020
OBJECTIVE
The purpose of this lab will be to experimentally demonstrate Kirchhoff’s Rules for electrical circuits.
EQUIPMENT
PhET interactive simulation tool (Circuit Construction Kit: DC – Virtual Lab):
https://phet.colorado.edu/en/simulation/circuit-construction-kit-dc-virtual-lab
For an introduction on using the PhET Circuit Construction simulation, see: 00-PhET Simulation Tool instructions for Electric Circuits Labs.
THEORY (Part A: STANDING WAVES ON A STRING Using PhET simulation)
Electronic circuits that cannot be reduced to simple series of parallel circuits can be analyzed by different methods. As an example, consider the circuit of figure 1. The currents and voltage drops across the resistances cannot be found by a simple application of Ohm’s Law. In this circuit, points A and D are called Junctions, since more than two wires connect there. A closed loop is any path that starts at some point in the circuit, passes through the elements of the circuit, and arrives back at the same point, without passing through any element more than once. There are three such closed loops in the circuit of Figure 1. These are Loop 1: A-B-C-D-A, Loop 2: A-D-E-F-G-A, and Loop 3: B-C-D-E-F-G-A-B. The junctions and loops are used in two Kirchhoff’s rules to analyze the circuit.
KCR- Kirchhoff’s Current Rule: The sum of the currents entering a junction = sum of currents leaving a junction. Or equivalently: the net current entering a junction is zero.
KVR-Kirchhoff’s Voltage Rule: The algebraic sum of the voltage changes around any closed loop is zero.
We would usually know the values of the battery voltages and resistances. As a first step, we label and assign directions (arbitrarily) to the currents in each section of the circuit (i.e. between each junction). We then write the junction equation (assuming a current entering the junction is positive, and leaving the junction is negative) at node D as:
i1 + i3 – i2 = 0 (1)
We now traverse the closed loops in any direction (clockwise or counter-clockwise, the resulting equations are equivalent) and add up all the changes in the voltages and set them to zero, i.e.
ΣΔV = 0 (2)
The voltage change across a resistor is found by Ohm’s Law as
ΔV = I R (3)
The sign of ΔV is positive if we are crossing the resistance in a direction that is against the direction of the current in that resistor, and it is negative if we go across the resistor in the same direction as the current. The ΔV across the battery is positive if we cross it from its negative to its positive side. With these, the equations for the three loops become:
Loop 1 (starting at the point A and going clockwise):
V1 – i1*R1 – i1*R2 + i3*R3 = 0.0 (4)
Loop 2 (starting at A and going clockwise):
-i3*R3 – i2*R4 + V2 – i2*R5 = 0.0 (5)
Loop 3 (starting at A, and going clockwise):
+V1 – i1*R1 – i1*R2 – i2*R4 + V2 – i2*R5 = 0.0 (6)
Note that equation (6) is simply the sum of equations (4) and (5), and is therefore not an independent equation. The same would apply to the junction rule applied at node A. So the useful (or independent) number of Junction equations that we can use are one less than the number of junctions, and the Loop equations are one less than the number of loops.
We then simultaneously solve equation (1) and any two out of equations (4), (5) and (6) to obtain the values of the currents i1, i2 and i3. In case any of the currents comes out to be negative, it simply means that we had choses then wrong direction for that current.
PROCEDURE (Part A: STANDING WAVES ON A STRING Using PhET simulation)
1 Select five resistors and measure and note their resistances. Label them as R1, R2, … , R5. Select resistors that are in the range of 10.0 Ω to 100.0 Ω.
2 Connect the resistors on the PhET simulation to make the circuit as shown in Figure 1. Attach the two batteries to appropriate points on the circuit. Set their voltages between 6.0 to 10.0 volts each. (The two voltages may or may not be the same). Note the positions of the resistors R1, R2, … R5. Measure the voltages across the batteries and note these as V1 and V2 in the Data Sheet.
3 Using the values of the resistances and battery voltages, calculate the currents i1, i2 and i3 by using the two Kirchhoff’s Rules. Use the same notation and directions of the currents as used in Figure 1. Use the calculated currents to calculate the potential difference across each resistor by using Ohm’s Law.
4 Once the calculations are done, you have an idea of what values to expect. First measure the voltages across each of the resistors and note it.
5 Now measure the currents i1, i2 and i3. For this you would need to break the circuit and insert the ammeter in series with the wires to complete the loop.
6 Calculate the percent errors in the calculated and measured values of the currents and voltages. Check to see if the Kirchhoff’s Junction rule and Loop Rules are verified.
DATASHEET: KIRCHHOFF’S RULES
| V1 = |
| V2 = |
| RESISTANCE | CURRENT | VOLTAGE | ||||||
| CALCULATED | MEASURED | % ERROR | CALCULATED | MEASURED | % ERROR | |||
| R1 = | ||||||||
| R2 = | ||||||||
| R3 = | ||||||||
| R4 = | ||||||||
| R5 = |
Part H: Geometrical Optics Using PhET SIMULATIONS (Part A: STANDING WAVES ON A STRING Using PhET simulation)
Rev 3-14-2020
OBJECTIVE
To study the reflection of light on flat and curved surfaces, and refraction of light though different shapes, and to find the focal length of a convex lens.
EQUIPMENT
PhET simulation Bending Light: https://phet.colorado.edu/en/simulation/bending-light
PhET simulation Geometric Optics: https://phet.colorado.edu/en/simulation/legacy/geometric-optics
You can also get to the simulations by entering in your browser: Phet, then select Physics. Then select Bending Light, and Geometric Optics simulations.
PROCEDURE (Part A: STANDING WAVES ON A STRING Using PhET simulation)
The procedure for all experiments will be to track a laser beam as it reflects or refracts. In the simulations that we will use, we have a laser that can be turned on or off by clicking the red button on it. It can also be moved and rotated. The laser will give a narrow ray of light which we will follow as it reflects or refracts. This can be done for several points in the beam’s path.
In most cases, you would need to measure the angle, which is done from the normal to the surface. You can turn on the normal by selecting it in one of the menu boxes on the page. You can measure the angle by using the protractor tool. Complete the Results section at the end.
CASE A: Reflection from a Plane Mirror (see figure 1)
1. After opening the simulation, select “INTRO”.
2. Select the material where the laser is as “AIR”, and that on the lower side as “WATER”.
3. Set the laser to any arbitrary angle. Turn on the laser.
4. Use the Protractor to measure the angle of the incident ray and angle of the reflected ray (this is dimmer than the incident ray). (ignore the ray going into the water). Repeat for different angles.
5. Repeat for AIR and GLASS as the materials.
6. Enter the results in Table A, and verify that the angle of incidence = angle of reflection.
CASE B: Refraction (see figure 2)
1. After opening the simulation, select “INTRO”.
2. Select the material where the laser is as “AIR”, and that on the lower side as “WATER”.
3. Set the laser to any arbitrary angle. Turn on the laser.
4. Use the Protractor to measure the angle of the incident ray and angle of the refracted ray (i.e. the one entering the water). (ignore the reflected ray). Repeat for different angles.
5. Repeat for AIR and GLASS as the materials.
6. Repeat with AIR and MYSTERY A as the two materials.
7. Enter the results in Table B, and calculate the refractive indices of water, glass and Mystery A by using equation 1.
CASE C: Refraction Again (see figure 7)
1. After opening the simulation, select “PRISM”.
2. From the bottom panel, select the Square. Set Reflections Off. Turn on Normal.
3. Select the Environment as AIR. Select Objects as GLASS.
4. Set the laser to any arbitrary angle, pointing to the square. Turn on the laser.
5. Use the Protractor to measure the angle of the incident ray and angle of the refracted ray (i.e. the one entering and inside the square). Make sure that the ray inside the square does not reflect form the side surface.
6. Use these angles to calculate the refractive index of the material by using equation 1. Repeat with different angles.
7. Repeat for MYSTERY B as the material of the square.
8. Enter the results in Table C.
CASE D: Total Internal Reflection (Part A: STANDING WAVES ON A STRING Using PhET simulation)
1. After opening the simulation, select “INTRO”.
2. Select the material where the laser is as “WATER”, and that on the lower side as “AIR” (i.e. the laser beam is going from water into air)
3. Set the laser to a small angle (i.e. close to the normal). Turn on the laser.
4. Increase the angle slowly and observe the refracted ray. At some angle, the refracted ray will become parallel to the water-air surface. Beyond this point, when the angle is further increased, there is no refracted ray, only a reflected ray. This is Total Internal Reflection. The angle that the incident ray makes at the point at which the refracted ray becomes parallel to the glass surface (i.e. angle of refraction = 90), is called the Critical Angle. Use the Protractor to measure the angle of incidence at this point. Use equation 3 to compare the calculated and measured values of the Critical Angle.
5. Repeat to find the critical angle for the GLASS – AIR interface.
6. Enter the results in Table D.
CASE E: Total Internal Reflection Again (see figure 6)
1. After opening the simulation, select “PRISM”.
2. Select the semi-circular object, and bring it to the middle of the screen. Its straight side should be vertical.
3. Select the Environment as Air, and semi-circular object as Glass. Turn on Normal. Turn off Reflections.
4. Turn on the laser. Set the laser to an angle about 40° with the horizontal.
5. Now place the cursor in the object, with left click hold the object and move it (it should not rotate) to a position so that the laser beam entering it is at zero degrees to the surface. This is when the beam is directly over (i.e. parallel to) the normal. It will now be exiting the object from center of the flat side, which is also the center of the circle forming the curved side. Now rotate the Object by holding it from the little thing at its bottom. The object must not move, only rotate. This will rotate it about its center so that the beam is always exiting from the center of the flat side.
6. Keep rotating the object slowly, until the exiting beam is parallel to the flat surface. If you turn it a bit more, the beam will have Total Internal Reflection. Use the protractor to measure the angle on incidence inside the object at the flat surface at the point of Total Internal Reflection. The angle of refraction should be 90°. Use equation 3 to compare the calculated and measured values of the Critical Angle.
7. Repeat for Mystery A. Use the refractive Index found in Case B for calculating the percent error.
8. Enter the results in Table E.
CASE F: Refraction Light Ray Shift (see figure 7)
1. After opening the simulation, select “PRISM”.
2. From the bottom panel, select the Square. Set Reflections Off. Turn on Normal.
3. Select the Environment as Air. Select Objects as Glass.
4. Set the laser to any arbitrary angle, pointing to the square. Turn on the laser. The laser beam should come out from the back side.
5. Note (figure out how), the position of the refracted ray coming out of the glass on the other side.
6. Change the material of the Object to “Air”. This will cause the ray to go straight (since refractive indices of environment and square are the same). Note the position of this ray.
7. Measure the distance that the ray shifts when the Object is Air and when it is Glass (figure out how to do this). Enter the results in Table 6.
8. Measure the thickness of the square. Enter all data in Table F.
9. Use equation 6 to calculate the shift, and compare with your measured value.
h
d
(6)
CASE G: Deviation of light by a prism (see figure 3)
1. After opening the simulation, select “PRISM”.
2. From the bottom panel, select the Triangle (prism). Set Reflections Off. Turn on Normal.
3. Select the Environment as Air. Select Objects as Glass.
4. Set the laser to any arbitrary angle, pointing to the prism. Turn on the laser. The laser beam should come out from the other side.
5. Use the protractor to measure the angle of incidence θi , angle of refraction θr, angle of the prism A , and angle of Deviation δ, and record them in Table G.
6. Calculate the angle of deviation by using equation (4), and compare with measured value. Use the refractive index of glass found in Case C.
CASE H: Focal Length of a Convex Lens (see figure 4) (Part A: STANDING WAVES ON A STRING Using PhET simulation)
1. Open the simulation: Geometric Optics.
2. Select Principal Rays and Screen. Select some values of Curvature, Refractive Index and Diameter of the lens.
3. Place the lamp al some position on the principal Axis (the horizontal line passing through the center of the lens).
4. Move the screen until the image becomes a small dot. The image of the object is now in focus on the screen.
5. Select the Ruler, and measure the distance from the center of the lens to the light source. (Measure to the point where the rays join together). This is the Object distance ‘p’. Now measure the image distance ‘q’ from the lens to the screen (to the point where the rays join). You may have to select a pencil or an arrow as the object to do this.
6. Note the data in Table H, and calculate the focal length, ‘f’, of the lens.
7. Repeat for several different positions of the object. Have at least one position where you get a virtual image (i.e. when object is between lens and the focal length).
8. Measure the focal length (this is the distance from lens to the ‘X’ on the Principal Axis.
RESULTS
All values are measured values unless mentioned. Attach at least one image of each case with your report.
TABLE A: LAW OF REFLECTION
| Trial number | Angle of Incidence | Angle of Reflection | Percent Difference |
TABLE B: LAW OF REFRACTION (Part A: STANDING WAVES ON A STRING Using PhET simulation)
| Material | Trial number | Angle of Incidence | Angle of Refraction | Refractive Index (equation 1) | Average of three values | Percent Error in refractive index |
| Water | ||||||
| Water | ||||||
| Water | ||||||
| Glass | ||||||
| Glass | ||||||
| Glass | ||||||
| Mystery A | ||||||
| Mystery A | ||||||
| Mystery A |
TABLE C: LAW OF REFRACTION AGAIN
| Material | Trial number | Angle of Incidence | Angle of Refraction | Refractive Index (equation 1) | Average of three values | Percent Error in refractive index |
| Glass | ||||||
| Glass | ||||||
| Glass | ||||||
| Mystery B | ||||||
| Mystery B | ||||||
| Mystery B |
TABLE D: TOTAL INTERNAL REFLECTION
| Material | Trial number | Angle of Incidence | Angle of Refraction | Critical Angle
Calculated |
Percent Error in Critical Angle |
| Water-Air | |||||
| Glass-Air |
TABLE E: TOTAL INTERNAL REFLECTION AGAIN
| Material | Trial number | Angle of Incidence | Angle of Refraction | Critical Angle
Calculated |
Percent Error in Critical Angle |
| Water-Air | |||||
| Mystery-Air |
TABLE F: REFRACTION LIGHT RAY SHIFT
| Trial Number | Angle of Incidence | Angle of Refraction | Thickness ‘h’ of the square | Measured Value of Shift in the Ray | Calculated Value of the Shift | Percent error in shift |
TABLE G: DEVIATION OF LIGTH FROM A PRISM
| Trial Number | Angle of Incidence | Angle of Refraction | Angle of Prism | Angle of Deviation | Calculated Angle of Deviation | Percent error in angle of Deviation |
| No | Distance from Lens to Object
p |
Distance from Lens to Image
q |
Calculated Focal Length by equation 1
f |
| Average value of Focal Length | |||
| Percent error |
TABLE H: FOCAL LENGTH OF A CONVEX LENS (Part A: STANDING WAVES ON A STRING Using PhET simulation)
