lab

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 1/12

UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment

Assignment # 5B Name Lab 5 Experiment I worked in a group with

Evan Hathaway - Jun 30, 2020, 11:33 AM CDT

Update and Submit

Equipment

Content LA Thirteen - Jun 12, 2020, 1:19 AM CDT

1 Basic Electrometer ES – 9078

1 Basic Variable Capacitor ES – 9079

1 Electrostatics Voltage Source ES – 9077

1 Short Patch Cords (set of 8) SE-7123

1 Resistor/Capacitor/Inductor Network UI-5210

1 Voltage Sensor UI-5100

1 Short Patch Cord Set SE-7123

1 850 Universal Interface UI-5000

1 PASCO Capstone UI-5400

1 Digital Storage Oscilloscope TBS-1052

1 Oscilloscope

1 Arbitrary Waveform Generator SDG 810

1 BNC Male-Dual Banana Adaptor

Content LA Thirteen - Jun 12, 2020, 1:20 AM CDT

Setup A: Capacitance

Content LA Thirteen - Jun 12, 2020, 1:20 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 2/12

Figure A1: Setup Figure A2: Indicator Foot

1. Move the Variable Capacitor plates so they are about 2 mm apart. 2. Adjust screws on the back of the moveable plate to make the plates parallel. 3. Position the movable plate so the leading edge of the indicator foot (see Fig. A2) is at the 0.2 cm position. The gap between the two

plates should be 2 mm all the way around. 4. Attach the twin lead (red & black) connector to the Signal Input jack on the Basic Electrometer. 5. Attach the black spade end of the twin lead to the fixed plate 6. Attach the red spade end of the twin lead to the movable plate 7. Attach a black banana/banana wire as shown from the common (com) terminal on the Electrostatic Voltage Source to the ground

terminal on the Electrometer. 8. Attach the red banana/banana lead to the +30V terminal and leave one end free. 9. Attach an adaptor cable from the Electrometer signal output to the universal interface analog input A.

10. Plug in the power supply for the Electrostatic Voltage Source. 11. Shift the switch on the back to the On position. The green Power On light should glow.

Important Note:

The edge effects are significant if the approximation of large plates relative to the gap size is not fulfilled. If the gap increases the dependence of potential difference of initially charged capacitor versus the gap size bend from linear dependence.

If the edge effects are significant the measured potential difference will be sensitive to environment near the capacitor, for example: how the wires are routed and how far away from where your hand and your body will be. Note, people are conducting plates and have a significant amount of capacitance.

The charges in this experiment all small so static discharge will result in the decreasing of measured voltage in time

Basic Variable Capacitor

The PASCO experimental Variable Capacitor consists of two metal plates 17.7 cm (7 in) in diameter with a plate area A = 2.46 x 10-2 m2.

Content LA Thirteen - Jun 12, 2020, 1:24 AM CDT

Procedure A1: The Effect of the Plate Separation

Content LA Thirteen - Jun 12, 2020, 1:24 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 3/12

1. Set the capacitor plates 0.3 cm apart by setting the movable plate so leading edge of its indicator foot is at the 0.3 cm mark. 2. Turn on the electrometer and set the range button to the 100 V scale. 3. Remove any charge from the capacitor by momentarily touching both plates at the same time with a wire. 4. Zero the electrometer by pressing the ‘ZERO’ button until the needle goes to zero. 5. Momentarily connect a cable from the +30-V outlet in the voltage source to the stud on the back of the movable capacitor plate. This

will charge the capacitor. 6. Remove the charging cable. 7. Read all of the following steps. They need to be performed quickly since the charge will slowly escape from the electrometer,

especially if the humidity is high. One person should run the computer while one moves the capacitor plate. Everyone else should stay back. Everyone should try to be in the same position for each reading. Anybody too close can make the readings change.

8. Open the Data Tab, but read the rest of this page first. 9. Slide the movable plate so it is at 8.0 cm (leading edge of the indicator foot). Once the plate is in position, the person moving the plate

should move away 50 cm or so and try to be in the same position for each measurement. 10. Click the PREVIEW button at the lower left to begin collecting data. Colored numbers will appear in first row of the table. The person

doing the computer should click the Keep Sample (red checkmark in the lower left) button. The number in the first row will turn black and the colored number will move to the second row. The person at the computer should read the next separation (7 cm) out loud and wait.

11. Move the plate to 7.0 cm and repeat the process until 0.3 cm. 12. Click the STOP button to end the data collection. 13. Examine the graph. If the data looks like a smooth curve, continue to analysis. If not, repeat the process until the data is a smooth curve. 14. Record the data in Table 1.

Table 1: Air Gap Capacitor Data

Separation (cm) Voltage (V)

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.5

1.0

0.5

0.3

Content LA Thirteen - Jun 12, 2020, 1:28 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 4/12

Analysis A1: The Effect of the Plate Separation

Content LA Thirteen - Jun 12, 2020, 1:28 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 5/12

This analysis will use equations 4 and 5 to show how our capacitor responds for a distance larger than the square of the plate area. The data obtained in procedure A1 is clearly not linear. If the large plate approximation was valid for this system, (Equation 3) V would be directly proportional to distance. The Voltage vs. Separation graph on the data page would be a straight line. When the gap distance became greater than a certain size the large plate approximation fails and Equation 4 must be used. To verify Equation 4 for the case where C is not zero, Q and Csys must be known. This will be

determined by fitting a math model (Equation 4) to the data. The calculator in the software will be used to fit a model to the data obtained in procedure A1. There are 4 lines in this calculator.

Line 1 is the charge of the system in Coulombs. Line 2 contains the physical parameters for this particular plate capacitor. Line 3 is the capacitance of the system in Farads. Line 4 is the voltage output from the model (Equation 5). Initial values for both line 1, 2, and 3 are already entered. The initial values for lines 1-3 have been calculated assuming an ideal 30 volts, no charge loss, and ideal capacitance for the system. Each system will be different due to charge loss, and slight deviations in capacitance and voltage. Lines 1 and 3 need to be modified as to fit the software model to the obtained data. Do not modify Line 2 as it is the calculated constants in this system!

1. Click open the Curve Fit Page 2. Use the Run Select button on the graph toolbar to select the best run 3. Modify the coefficient before the power of both lines 1 and 3 until the software generated model fits the data from procedure A1. 4. Record the Values for lines 1-3 in table 2. 5. Observe the potential decrease in time due to static discharge, if all the settings are the same. 6. Observe the edge effects when the V vs. d is not linear with the gap size.

Table 2: Software model

Line # Value Units

Line 1 Coulomb

Line 2 F Cm

Line 3 Farad

Figure A4: Calculator Setup

Content LA Thirteen - Jun 12, 2020, 1:36 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 6/12

Procedure A2: The Effect of a Dielectric between the Plates

Content LA Thirteen - Jun 12, 2020, 1:36 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 7/12

This procedure will verify equations 6 and 7

1. You will use paper as the dielectric to be inserted between the plates. Use 0.5 cm of paper in a lab manual. 2. Position the movable plate of the capacitor at 0.5 cm. 3. Turn on the electrometer and set the range button to the 100 V scale. 4. Remove any charge from the capacitor by momentarily touching both plates at the same time with a wire. It is also best practice to keep

hands away from the capacitor. 5. Zero the electrometer by pressing the ‘ZERO’ button. The needle must be at zero. 6. Momentarily connect a cable from the +30 V outlet in the voltage source to the stud on the back of the movable capacitor plate. This

will charge the capacitor. Remove the charging cable. 7. Move the movable plate to 8 cm. 8. Click on the PREVIEW button below. 9. One student holds the paper directly above the gap between the capacitor plates so that the long side of the paper is vertical.

10. Hold the paper with one hand and keep the other hand on the metal connector attached to the signal input of the Electrometer so that there is no static charge on the student holding the paper.

11. Press the Keep Sample button to record the voltage when the paper is not between the plates. 12. Lower the paper between the two plates until it touches the base. Do not let the paper touch either plate! Keep your hand as far above the

plates as possible. 13. Press the Keep Sample button to record the voltage when the paper is between the plates. 14. Pull the paper back above the plates and repeat steps 4 more times. 15. Click the STOP button to stop monitoring the data. 16. If the final voltage with the paper out is much different from the initial paper out value, you probably touched the plates and should

repeat the experiment. 17. Record the data in Table 3.

Table 3: Dielectric Data

Trial Paper Position Voltage (V)

1 Out

2 In

3 Out

4 In

5 Out

6 in

7 Out

8 in

9 Out

Content LA Thirteen - Jun 12, 2020, 1:38 AM CDT

Part B: RC time constant

Content LA Thirteen - Jun 12, 2020, 1:39 AM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 8/12

1. Assemble the circuit in Figure B1, using R2 = 3.3 kΩ and C2 = 560pF. Set the function generator to the following parameters:

Vpp = 2 V f = 1 kHz

DC offset = +1 V Waveform: Square

Figure B1. RC Circuit Diagram

2. Connect the oscilloscope probe across the capacitor (orientation does not matter). Turn on the output of the function generator. You should see a distorted wave similar to a square wave like that pictured below.

3. Connect the oscilloscope probe across the capacitor (orientation does not matter). Turn on the output of the function generator. You should see a distorted wave similar to a square wave like that pictured below.

Figure B1. Typical growth and decay curves for RC charging and discharging

Cory Nook - Aug 04, 2020, 11:02 PM CDT

Procedure B1: Measuring the RC time constant

Content LA Thirteen - Jun 12, 2020, 10:39 PM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 9/12

We will now measure the RC time constant of this RC combination by utilizing the cursors on the oscilloscope.

1. Adjust the volts/div (vertical scale) and time/div (horizontal scale) to see one rising portion of the signal, then position the curve with the horizontal and vertical positioning knobs such that the majority of the display is used.

We wish to measure the time it takes for the signal to decay from 2V to 1V or from 1V to 0.5 V. This time is the half-life.

Figure B2. Horizontal axis (time) magnified five times such that growth behavior can be clearly assessed.

2. Open the Cursor menu and set the mode to “Track.” Cursor A and B should both have CH1 as their input. Now move cursor A along the curve to the minimum point just before the signal begins to decay. Move cursor B to as close to half of it as possible. Record these fall times in Table 4.

On the other hand, when we measure the rise time, we need to measure the time it takes the signal to rise to half of its maximum value. In other words, the time that it takes for the signal to rise from 0V to 1V or from 1V to 1.5V, since the maximum voltage is 2V.

Record these rise times in Table 4.

3. Calculate the theoretical half-life by using equation 13. Take the average of the four measured values and compare to the theoretical value using a percent difference.

Table 4

Half Life Second

Decay

T1/2 (2V-1V)

T1/2 (1V-0.5V)

Rise

T1/2 (0V-1V)

T1/2 (1V-1.5V)

Average T1/2

T1/2 : Equation 13

% difference

Cory Nook - Aug 04, 2020, 10:58 PM CDT

Procedure B2: Varying Voltage

Content LA Thirteen - Jun 12, 2020, 10:41 PM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYu… 10/12

1. Set the function generator output now to 4 V peak-to-peak, with a + 2.0 V DC offset.

2. Adjust oscilloscope to again view one cycle. Repeat previous steps to measure the rise time and fall time, and average the two and record your data in Table 5.

Table 5

Half Life Second

Decay T1/2 (4V-2V)

Rise T1/2 (0V-2V)

Average T1/2

3. Turn OFF the output of the function generator and disconnect the oscilloscope probe from the capacitor.

Content LA Thirteen - Jun 12, 2020, 10:42 PM CDT

Procedure B3: Varying Capacitance

Content LA Thirteen - Jun 12, 2020, 10:42 PM CDT

1. Set the function generator back to original setting of 2 V peak-to-peak and + 1 V DC offset.

2. Replace C2=560pF with C1 = 3900 pF (in other words, increase/decrease capacitance)

3. Connect the oscilloscope probe across the new capacitor, and repeat the measurements of rise and fall times and record your data in Table 6.

Table 6

Half Life Second

Decay

T1/2 (2V-1V)

T1/2 (1V-0.5V)

Rise

T1/2 (0V-1V)

T1/2 (1V-1.5V)

Average T1/2

T1/2 : Equation 12

% difference

4. Turn the function generator output OFF.

Cory Nook - Aug 04, 2020, 10:59 PM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYuM… 11/12

Procedure B4: Varying Resistance

Content LA Thirteen - Jun 12, 2020, 10:46 PM CDT

1. Now use C2 = 3900 pF and R1 = 47kΩ in the RC circuit.

2. Use the same function generator settings as before, and switch the output ON. The oscilloscope should still be connected to the capacitor from the part B3. You will notice that the maximum and minimum values of the wave are not the same as before. We ask that you record these values and use the modified table below.

Maximum V=_______ Minimum V=_______

3. Repeat the time measurements once again and fill out table 7: (We know that you will not be able to reach 0 and 2V, but use the minimum and maximum of the wave for your cursor locations for 0 and 2V.)

4. Turn the function generator output OFF.

Table 7

Half Life Second

Decay

T1/2 (2V-1V)

T1/2 (1V-0.5V)

Rise

T1/2 (0V-1V)

T1/2 (1V-1.5V)

Average T1/2

T1/2 : Equation 12

% difference

Cory Nook - Aug 04, 2020, 11:01 PM CDT

Conclusions

Content LA Thirteen - Jun 12, 2020, 10:50 PM CDT

3/7/2021 UNT PHYS 2240 Lab SPRING 2021 - Alymjan Rejepov/Experiment 5: Capacitance and RC Circuit/Experiment - LabArchives, Your Electr…

https://mynotebook.labarchives.com/entries/print_page/ODkwOTE2LjB8Njg1MzIwLzY4NTMyMC9Ob3RlYm9vay8yNjQyODEzODIwfDIyNjE1NTYu… 12/12

Capacitance

1. What happened to the voltage vs. gap dependence as the plates got far from each other ( d increasing)? Why did this happen?

2. Basing the conclusion on the data in Table 3, what does a dielectric do?

RC Circuit

3. Summarize how changing the capacitance changes the rise and fall times. How does changing the voltage change the rise and fall times?

4. Using the values found for the ∆Taverage compute the % differences between this and the time constant defined by RC. Are the percent

differences between theory and experimental data reasonable? Explain what causes the differences, and any sources of error.

Content LA Thirteen - Jun 12, 2020, 10:53 PM CDT