PASCO ES-9080B Basic Electrostatics System Instruction Manual

Table of Contents

• Equipment List

• Introduction

• Equipment Description

• Electrometer Operation and Setup Requirements

• Suggested Demonstrations

• Technical Support, Copyright and Warranty Information

• Product End of Life Disposal Instructions

Introduction

Demonstrations of electrostatic phenomena have traditionally been limited to the simplest experiments due to equipment and technique challenges, often yielding qualitative rather than quantitative results. The PASCO ES-9080B Basic Electrostatics System is designed to address these issues, providing a comprehensive set of tools for mastering demonstration techniques. This manual covers material typically presented in an undergraduate unit on electrostatics.

Key principles for electrostatic demonstrations include:

• Equipment Description: Familiarize yourself with the equipment's usage.
• Equipment Orientations: Arrange apparatus clearly and separated for student visibility. Using a computer with a PASCO interface to display electrometer readings is recommended. Ensure the electrometer is visible if a computer is unavailable. Consider how arrangement affects charge distribution. Always stand to avoid obstructing views.
• Earth Grounds: Connect the demonstrator to an earth ground to prevent stray charges. Keep the electrometer grounded unless otherwise specified.
• Avoid Unnecessary Movement: Minimize movement to prevent charge buildup on clothing.
• Humidity: The electrometer is designed to minimize humidity effects. However, high humidity can cause charge leakage. Keep equipment clean and dry. Low humidity can cause static buildup; minimize movement.
• Practice: Familiarity with equipment and procedures is crucial for successful demonstrations.

Before starting, students and instructors should be aware of:

• The theory and use of the Faraday Ice Pail.
• Potential distortion of charge density due to improper proof plane use.
• Residual charge buildup on plastic insulators; ground these parts before experiments.
• The electrometer's internal capacitance must be considered for quantitative charge calculations.

Following these principles and practicing will lead to successful demonstrations and valuable educational outcomes.

Equipment Description

Electrometer (ES-9078A)

The Model ES-9078A Electrometer is a voltmeter for measuring voltage, current, and charge. Its high impedance (10¹⁴ Ω) makes it ideal for electrostatic experiments. It offers sensitivity approximately one thousand times greater than a gold-leaf electroscope, a center-zero meter for polarity indication, and a digits display. It can measure charges as low as 10^-11 coulombs. The electrometer includes a shielded signal input cable, a banana plug patch cord, a signal output (interface) cable, and a grounding cable.

Diagram Description: Figure 1 shows the front panel controls of the electrometer, labeling the meter display, digits display, zero button (for grounding and removing excess charge), output for interface, range-indicator LEDs, voltage range selection button, and power ON/OFF button, with connections for signal input and earth ground.

The electrometer is powered by four AA-alkaline batteries. A blinking LED indicates low battery. When replacing batteries, avoid touching internal components due to static sensitivity.

Electrostatics Voltage Source (ES-9077)

The ES-9077 is a high-voltage, low-current power supply for electrostatics experiments. It provides 30 VDC for capacitor experiments and 1 kV, 2 kV, and 3 kV outputs for Faraday ice pail and conductive sphere experiments. Outputs (except 30 V) have series resistance limiting short-circuit current to approximately 8.3 microamps. The 30 V output is regulated but delivers only about 1 milliamp before losing regulation. An AC adapter is included.

Diagram Description: Figure 2 shows the Electrostatics Voltage Source with terminals for ground, 30 V, 1 kV, 2 kV, and 3 kV.

Variable Capacitor (ES-9079)

This variable capacitor features two conductive plates, 20 cm in diameter, adjustable to various separations. A calibrated slide indicates plate separation in centimeters. Binding posts are provided for electrical connection. Three plastic spacers ensure a 1 mm plate separation when the movable plate touches them. A low-capacitance cable connects the plates to the electrometer; keep leads separated to minimize capacitance. It is crucial that the plates remain parallel; adjustments can be made using screws on the back of the movable plate. Keep plate supports clean to prevent charge leakage.

Diagram Description: Figure 3 shows the Variable Capacitor with its fixed and movable plates, binding posts, and the calibrated slide.

Charge Producers and Proof Plane (ES-9057B)

These components generate charges by contact. The charge producers are two wands with dark and white material on conductive disks. Rubbing these surfaces together results in the white surface acquiring a positive charge and the dark surface a negative charge. The proof plane samples charge density on a charged surface.

Care and Use Guidelines for Charge Producers:

• Ground the conductive disk to discharge. Breathing on the non-conductive neck can help remove stray charge.
• Avoid touching the neck with bare hands to prevent charge leakage. Clean with soap and water if leakage occurs. Clean disk surfaces with alcohol occasionally.
• New or recently cleaned producers may require vigorous rubbing of the white surface on the proof plane disk to generate charge.
• The producers are designed for the ES-9078 Electrometer and may not produce sufficient charge for a standard electroscope.

Diagram Description: Figure 4 shows the Charge Producers, illustrating the handle, non-conductive neck, and conductive knob/disk.

The Proof Plane

The proof plane is an aluminum-covered conductive disk attached to an insulated handle. The conductive disk is carbon-filled black polycarbonate (approx. 10³ Ω) with an aluminum surface; the neck is white polycarbonate (approx. 10¹⁴ Ω). It samples charge density on conductive surfaces. The sampled charge can be measured using a Faraday Ice Pail and Electrometer (Figure 6). When the proof plane touches a surface, it acquires the same charge distribution. To minimize distortion, hold the proof plane flat against the surface, tangent to it.

Diagram Description: Figure 5 shows the Proof Plane, detailing its handle, non-conductive neck, and conductive disk.

Diagram Description: Figure 6 illustrates the Proof Plane being used within a Faraday Ice Pail, connected to an electrometer.

Diagram Description: Figure 7 demonstrates the correct method for using the proof plane to sample charge on a conductive sphere, showing the plane being tangent to the surface.

The conductive knob can be used to sample charge density inside hollow spheres (e.g., ES-9061 Conductive Shapes).

Faraday Ice Pail (ES-9042A)

The Faraday Ice Pail operates on the principle that charge placed inside a conductor induces an equal charge on its outer surface. It consists of two nested wire mesh cylinders on a plastic base. The outer cylinder (shield) allows visibility and helps eliminate stray charges when grounded. The inner cylinder (pail) is mounted on insulators. When a charged object is placed inside without touching, an equal charge is induced on the outer surface of the pail. An electrometer connected between the pail and shield detects a potential difference proportional to the induced charge.

Diagram Description: Figure 8 shows the Faraday Ice Pail, illustrating the shield, pail, and insulators.

To prevent erroneous results, the Faraday Ice Pail must be momentarily grounded before each experiment. The demonstrator should also remain grounded during experiments.

Conductive Spheres (ES-9059C)

These 13 cm diameter spheres, made of nickel-plated ABS plastic, store electrical charge. Each is mounted on a non-conductive polycarbonate rod attached to a stable support base. A thumbscrew terminal on the lower half allows connection for grounding or voltage source leads. Keep spheres and rods clean to minimize charge leakage.

Diagram Description: Illustrations show a conductive sphere on a support base with a thumbscrew terminal and non-conductive rod.

Conductive Shapes (ES-9061)

These are special objects for storing electrical charges, made of nickel-plated ABS plastic. The Conductive Hollow Sphere (13 cm diameter) has a 3.8 cm hole for access. The Conductive Conical Shape is spherical on one side and tapers to a bulbous shape on the other. Both are mounted on non-conductive polycarbonate rods with thumbscrew terminals. The hollow sphere allows measurement of charge on the inside of a charged sphere. The conical shape allows measurement of charge density differences.

Diagram Description: Illustrations show a conductive hollow sphere and a conductive conical shape, each mounted on a support base with a thumbscrew terminal and non-conductive rod.

Electrometer Operation and Setup Requirements

The electrometer's controls are detailed in Figure 1. The setup procedure should be followed each time the electrometer is turned on, whether measuring voltage, current, or charge.

Warning: To avoid electrical shock or injury:

• Never measure potentials above 100 volts.
• Never connect the electrometer to electrostatic generators like Van de Graaff or Wimshurst machines.
• Do not touch signal input leads until you are grounded. Static charges can build up on people in dry conditions.

Setup

1. Connect the signal input test lead to the electrometer's BNC connector.
2. Connect the electrometer's ground post to an earth ground.
3. Turn the power ON. An indicator LED will blink twice.
4. Press the ZERO button to zero the meter. The display should read "0.0".
5. Use the push button to select the desired voltage range. The range setting indicates the voltage required for full-scale meter deflection (e.g., a setting of 30 means 30 volts for full scale).

Important Points for General Operation:

• Always press the ZERO button between measurements to discharge current.
• Shorting test leads is insufficient; stray charges may remain within the circuitry.
• Connect the electrometer to an earth ground (e.g., water pipe, grounded outlet, or COM port) for sufficient charge drainage. Grounding the experimenter by touching an earth ground before or during measurements is also helpful.

Suggested Demonstrations

Demonstration 1: Faraday Ice Pail and Charge Production

Equipment Required: Electrometer (ES-9078A), Charge Producers (ES-9057B), Earth ground connection, Faraday Ice Pail (ES-9042A), Signal Input Cable (test leads), Proof plane (optional).

Suggestions for Introducing the Experiment

Begin by demonstrating the electrometer measuring a battery's voltage. Explain that when using the ice pail, charge is measured indirectly through voltage. Changes in LED deflection indicate charge polarity. This helps students understand the type of charge in the ice pail.

Equipment Setup

Diagram Description: Figure 1.1 shows the setup for Demonstration 1, with the Electrometer connected to the Faraday Ice Pail. The electrometer's controls (meter display, digits display, ZERO button, range select, ON/OFF) are visible. Connections are shown from the electrometer's signal input cable to the ice pail's shield (black clip) and pail (red clip), with an earth ground connection to the electrometer.

Introduction

This demonstration investigates the relationship between induced charge on the ice pail and the charge of an object placed inside. It also explores charging by contact versus induction and demonstrates charge conservation.

Grounding the Ice Pail

Before experiments, the ice pail must be momentarily grounded. Pressing the ZERO button on the electrometer discharges both the pail and electrometer when they are connected and grounded. Keeping a hand on the shield or ground connector helps maintain the demonstrator's ground during experiments.

Warning: Ensure the electrometer is connected to earth ground for proper grounding of the pail to avoid electrical shock or injury.

Diagram Description: Figure 1.2 illustrates grounding the ice pail by touching both the pail and the shield simultaneously, then lifting the finger from the pail, then the shield.

Procedure 1A: Charging by Induction vs. Charging by Contact

1. Connect the electrometer to the Faraday Ice Pail as shown in Figure 1.1. Ensure both are grounded. The electrometer should read zero. Press ZERO to remove any residual charge.
2. Start with the voltage range set to 100 V, adjusting lower if needed. Analog meters are most accurate between 1/3 and 2/3 of full scale.
3. Charge producers: Remove stray charge from necks/handles by touching them to the grounded shield (demonstrator must also be grounded). Breathing on the neck can help remove residual charge. Rub the white and blue surfaces together to separate charges. Keep only the producer in use in hand, away from the ice pail surfaces.
4. Before inserting a charged disk into the ice pail, ensure you are touching the grounded shield.
5. Carefully insert the charged object into the ice pail, ensuring it does not touch the pail. Note the electrometer reading.
6. Remove the object and note the reading again. If the handle did not touch the pail, the reading should be zero.

Question: Why was there a potential difference between the pail and shield only while the charged object was inside?

6. Press ZERO to remove residual charge. Insert the object again, allowing it to touch the ice pail. Ensure students observe this contact.
7. Remove the object and note the electrometer reading.

Questions: Why is there now a permanent potential difference? Where did the charge on the ice pail come from?

8. To show charge transfer, ground the ice pail to remove all charge. Press ZERO. Insert the charge producer again. Does any charge remain on it?

Procedure 1B: Conservation of Charge

1. Start with uncharged producers. Rub blue and white materials together, keeping them separate after charging.
2. Use the Faraday Ice Pail to measure the magnitude and polarity of each producer by inserting them one at a time. Note the electrometer reading.

Questions: What is the relation between the magnitudes and polarities of the charges? Was charge conserved?

3. Ground the charge producers to remove all charge, including stray charge from necks and handles.
4. Insert both producers into the ice pail and rub them together inside. Note the electrometer reading. Do not let them touch the pail.
5. Remove one producer, note the reading, then replace it and remove the other. Note its reading. Comment on charge conservation based on magnitudes and polarities.

Extra Things to Try

• Repeat Procedure 1A with the opposite charged wand.
• Rub the white charge producer with a proof plane; measure the charge magnitude and polarity.
• Rub the blue material with a proof plane; measure the charge magnitude and polarity.
• Create a list of materials where rubbing a lower material with a higher material always results in the higher material being positive.

Demonstration 2: Charge Distribution

Equipment Required: Electrometer (ES-9078A), Electrostatic Voltage Source (ES-9077), Conductive Spheres (2) (ES-9059B), Earth ground connection (patch cord), Faraday Ice Pail (ES-9042A), Proof Plane, Signal Input cable (Test leads), Conductive Shapes (ES-9061).

Equipment Setup

Diagram Description: Figure 2.1 shows the setup for Demonstration 2. The Electrometer is connected to the Faraday Ice Pail. The Electrostatic Voltage Source powers a charged sphere. Various conductive shapes (spheres, conical, hollow) are positioned for sampling with the proof plane.

Introduction

This demonstration investigates charge distribution by measuring charge density variations. A charged surface is sampled with a proof plane, and the charge is measured using the Faraday Ice Pail. By sampling different sections, relative charge density can be observed, revealing uniform or non-uniform distributions. Charge conservation is also examined, noting that grounding the proof plane after each measurement depletes the surface charge.

If the proof plane is not grounded and does not touch the ice pail, the charge is not depleted and is returned to the surface during subsequent sampling.

Note: When the proof plane disk touches the surface, it becomes part of it. Hold the proof plane flat and tangent to the surface to minimize shape distortion.

Procedure

1. Ensure the Faraday Ice Pail is grounded, with its shield connected to earth ground. The electrometer, connected to the pail, must also be grounded (e.g., via the electrostatics voltage source COM port). Follow Figure 2.1 setup: black lead over the shield's edge, red lead over the ice pail's edge.
2. Place two conductive spheres at least 50 cm apart. Connect one sphere to the +2000 VDC port of the Electrostatic Voltage Source (ES-9077), ensuring the source is grounded to the same earth ground as the shield and electrometer. This sphere acts as the charged body.
3. Momentarily ground the other sphere to remove residual charge.
4. Sample and record the charge at various points on the sampling sphere (grounded in step 2) to represent the surface.
5. Bring the +2000 VDC charged sphere close (approx. 1 cm apart) to the grounded sphere. Turn the voltage source ON, then sample and record charge at the same points.
6. Momentarily ground the sampling sphere again (touching the grounded ice pail shield and the sphere). Sample and record charge at the same points.
7. Move the +2000 VDC charged sphere at least 50 cm away. Sample and record charge at the same points.

Analysis

1. What produced the charge distributions at each step?
2. Why did charge remain on the second sphere even after grounding?

Conductive Conical Shape

1. Remove the two conducting spheres. Connect the conductive conical shape to the +2000 VDC port on the Electrostatics Voltage Source.
2. Use the proof plane to sample charge at the larger rounded end and then at the narrow end.

Analysis

1. Which end has higher charge density?
2. Why?

Conductive Hollow Sphere

1. Remove the conductive conical shape. Connect the conductive hollow sphere to the +2000 VDC port on the Electrostatics Voltage Source.
2. Use the proof plane to sample charge on the outside surface of the sphere. Then use the conductive knob end of the proof plane to sample charge inside the sphere.

Analysis

1. How do charges compare between the outside and inside of the hollow sphere?

Extra Things to Try

1. To show charge resides on the outside surface, bend a metal sheet into a cylinder. Charge it and measure charge density on inner and outer surfaces.
2. To show how surface shape affects charge density, touch two charged proof planes together symmetrically and asymmetrically. Measure charge in each case and compare. Ensure necks and handles are free of stray charges.

Demonstration 3: Capacitance and Dielectrics

Equipment Required: Electrometer (ES-9078A), Charge Producers (ES-9057B), Electrostatic Voltage Source (ES-9077), 13 cm Conductive Spheres (2) (ES-9059B), Capacitor (approx. 30 pF) (ES-9043), Faraday Ice Pail (ES-9042A), Proof Planes (ES-9057B), Signal Input cable (Test leads), Variable Capacitor (ES-9042A), Sheet of dielectric material.

Introduction

This series of demonstrations investigates the relationship between charge (Q), voltage (V), and capacitance (C) for a parallel plate capacitor. The formula for capacitance is C = (εA)/d, where ε is the dielectric coefficient, A is the plate area, and d is the plate separation. Different materials can be inserted between plates to measure their dielectric coefficients.

Note: Students should understand capacitors in parallel. If not, refer to Procedure D.

The electrometer can be considered an infinite impedance voltmeter in parallel with a capacitor (CE), representing its internal capacitance and lead capacitance (Figure 3.1).

Diagram Description: Figure 3.1 is an ideal schematic showing a Voltmeter connected in parallel with an external capacitor (C_ext), and this combination in parallel with the electrometer's internal capacitance (C_E). The internal capacitance is noted as 25 pF without a cable.

Procedure 3A: Measuring the Electrometer's Capacitance

This procedure precisely measures the capacitance of the electrometer and its cables. It is not necessary for qualitative experiments.

When a capacitor of known capacitance C is charged by voltage V, the charge is Q=CV. Connecting this capacitor to the electrometer places it in parallel with the electrometer's internal capacitance (CE), making the total capacitance C + CE. The capacitor discharges, and the electrometer reads a voltage VE. Since total charge is conserved, CV = (C + CE)VE.

1. Obtain a low-leakage capacitor (approx. 30 pF).
2. Charge the capacitor with a known voltage V (not exceeding 100 V).
3. Remove the capacitor from the power supply without grounding it.
4. Connect the charged capacitor across the electrometer input leads and note the reading VE.
5. Calculate the electrometer's internal capacitance using the formula: CE = C * (V - VE) / VE.

Procedure 3B: Measuring C, V and Q for a Parallel Plate Capacitor

These experiments qualitatively study the relationship between C, V, and Q for a parallel plate capacitor. Readings from the electrometer are used for relative comparisons. The electrometer can connect to a computer via a PASCO interface for graphical display.

3B.1: V Measured, Q Variable, C Constant

Diagram Description: Figure 3.2 shows the setup: the Basic Variable Capacitor connected to the Electrometer, which is grounded. One sphere is connected to the +2000 VDC port of the Electrostatics Voltage Source. The capacitor is placed away from the sphere and source to prevent induction.

1. Press the ZERO button to remove residual charge from the electrometer and capacitor plates.
2. Set the plate separation to approximately 2 mm. Use a proof plane to transfer charge from the charged sphere to the capacitor plates by touching the sphere and then a plate. Equal charges are transferred if contact points are consistent.

Question: Why is touching only one plate sufficient?

4. Observe how the electrometer's potential difference reading changes as more charge is added to the capacitor.
5. Double the plate separation to 4 mm and repeat. Compare the new potential values to the previous ones.

3B.2: Q Measured, C Variable, V Constant

Diagram Description: Figure 3.3a illustrates the setup, similar to Figure 3.2. The Basic Variable Capacitor has an initial 6 cm separation and is connected to the +2000 VDC port. The Faraday Ice Pail is connected to the electrometer, which is grounded.

1. Momentarily ground a proof plane. Use it to examine the capacitor's charge density via the ice pail. Investigate charge density at various points on the plates (inner and outer surfaces) and how it varies across the plate.
2. Choose a point near the center of a capacitor plate. Measure charge density at different plate separations (varying capacitance). How does the charge vary with capacitance?

3B.3: Q Measured, V Variable, C Constant

Diagram Description: Figure 3.3b shows a setup identical to 3B.2. The Variable Capacitor has an initial 6 cm separation and is connected to the +3000 VDC port. The Faraday Ice Pail is connected to the electrometer, which is grounded.

1. Keep plate separation constant. Change the potential across the plates by moving the connecting cable from the +3000 V to the +2000 V port. Examine charge density near the center of a capacitor plate. How does charge vary with voltage? Repeat with +1000 VDC.

3B.4: V Measured, C Variable, Q Constant

Diagram Description: Figure 3.4 shows the setup. The Variable Capacitor is connected to the Electrometer and grounded. The voltage source is used only to momentarily charge the capacitor.

1. With a 2 mm plate separation, momentarily connect the plates to the 30 V source to charge them. Adjust electrometer sensitivity so readings are about 1/5 scale.
2. Increase plate separation and note electrometer readings at various separations. How does the potential vary with capacitance?

Note: An alternative method involves charging a sphere and transferring charge to the capacitor.

Procedure 3C: Dielectric Coefficients

The dielectric coefficient (κ) is a dimensionless factor indicating how much capacitance increases when a dielectric material is inserted between capacitor plates. It's a fundamental property of the material.

Ideally, measure κ by inserting a dielectric between charged plates and noting potential changes. However, sliding a dielectric into close plates can induce static charge. The recommended procedure is:

Note: If only one plate is movable, fix the other.

1. Connect the electrometer across the capacitor plates, set separation to approx. 3 mm.
2. Place a block (approx. 3 cm high) under the side nearest the movable plate (Figure 3.5).
3. Momentarily touch the plates with the voltage source to charge them to approx. 4/5 scale. Record the initial voltage (V_i).
4. Carefully increase plate separation enough to insert the dielectric sheet against the stationary plate without forcing it. Ensure the dielectric is free of residual charge.
5. Return plates to the original 3 mm separation and record the new electrometer reading (V_f).
6. Pull plates apart, remove the dielectric sheet.
7. Return plates to 3 mm separation and verify the electrometer reading matches the original V_i.

Analysis

The calculations for dielectric constant involve:

Diagram Description: Figure 3.6 shows circuit diagrams: 'before' with capacitor Cp and electrometer capacitance CE charged to Vi, and 'after' with new capacitance C'p and charges q'p, q'E, and voltage Vf.

Before dielectric: q_p + q_E = (C_p + C_E)V_i

After dielectric: q'_p + q'_E = (C'_p + C_E)V_f

Since total charge is conserved (q_p + q_E = q'_p + q'_E), then (C_p + C_E)V_i = (C'_p + C_E)V_f.

Rearranging yields the formula for κ:

κ = C'_p / C_p = [C_E(V_i - V_f) + C_pV_i] / [C_pV_f]

Table 3.1: Some Dielectric Coefficients

Procedure 3D: Capacitors in Series and in Parallel

This demonstration examines the effects of connecting capacitors in series and parallel. Requires two capacitors (200-400 µF to ignore electrometer capacitance), a DC voltage source, the electrometer, cables, and a double-throw switch.

Diagram Description: Figure 3.7 shows circuit diagrams: 3.7a illustrates capacitors C1 and C2 in series with a voltage source V and switch. 3.7b shows C1 and C2 in parallel with V and a switch.

3D.1: Capacitors in Series

Ensure capacitors are uncharged before connecting. Use a short wire to momentarily short each.

1. Set up the series circuit as in Figure 3.7a.
2. Connect to the 30 VDC output and close switch A to charge C1.
3. Calculate the initial charge on C1 (Q₀ = C₁V).
4. Throw the switch to position B; C1 and C2 are now in series.
5. Use the electrometer to measure voltage drops across C1 (V₁) and C2 (V₂).
6. Determine the charge in each capacitor (Q₁, Q₂) using known capacitances.

Questions: Find a relation between V₁, V₂, and the source voltage. How do Q₁ and Q₂ relate to the original charge on C₁?

3D.2: Capacitors in Parallel

1. Ensure capacitors are uncharged.
2. Set up the parallel circuit as in Figure 3.7b.
3. Set the voltage source to 30 VDC and close the switch to charge the capacitors.
4. Use the electrometer to measure the potential difference across each capacitor. Compare it to the source voltage.
5. Determine the charge in each capacitor using known capacitances. How are the charges related?

Analysis

1. Compare series and parallel capacitors regarding charges, voltages, and capacitance.

Demonstration 4: Charging and Discharging Capacitors

Equipment Required: Electrometer (ES-9078A), Power Amplifier (CI-6552A), Capacitors (200-400 µF), Computer with PASCO interface, Faraday Ice Pail (ES-9042A), Signal Input cable (Test leads), Resistors (10-90 kΩ; 10-1000 Ω), DataStudio® software.

Introduction

This demonstration investigates how voltages across a capacitor and resistor vary during charging and discharging, and determines the capacitive time constant (τ = RC). When a capacitor charges from a DC supply, voltage increases until it equals the source voltage. Both charging and discharging are characterized by the time constant τ = RC.

Use recommended capacitor values so electrometer capacitance is negligible. Adjust resistance for a convenient RC constant. Two variations are presented: one using a DC voltage source for a voltage vs. time graph (higher resistances, 10-90 kΩ), and another using a signal generator with a square wave (lower resistances, 100-1000 Ω).

Equipment Setup

The electrometer's signal output cable connects to a PASCO interface as an analog sensor.

1. Open the software and select the electrometer from the sensor list.

Diagram Description: Figure 4.1 shows the experimental setup: a resistor (R) and capacitor (C) in series with a 30 VDC source and a double-throw switch. The electrometer output connects to an analog channel of the PASCO interface.

3. Set up the computer display to plot voltage vs. time.
4. With the switch open, press Start. Throw the switch to position A to begin charging the capacitor; observe the voltage on screen.
5. When the capacitor reaches the source voltage (30 VDC), flip the switch to position B to discharge it; observe the voltage.
6. Experiment with different R values to observe changes in charging time.

Analysis

When a capacitor charges through a resistor from a DC supply, voltage increases over time according to V = V₀(1 - e^-t/RC). After one time constant (t = RC), voltage reaches 63% of maximum (V = 0.63V₀).

1. Calculate 63% of the source voltage. Locate this value on the graph and determine the time taken. This time is the RC constant. (PASCO DataStudio's Smart Tool can assist.)
2. Compare the measured time constant with the calculated value from known C and R.

When discharging, voltage decreases according to V = V₀e^-t/RC. After one time constant, voltage drops to 37% of maximum.

3. Determine 37% of the total voltage. Locate this point on the discharge plot and find the time taken.
4. Compare this measured RC constant with the known value.

Procedure 4B: Charging/Discharging Capacitors with Signal Generator

Applying a positive square wave to an RC circuit causes periodic charging and discharging (Figure 4.2). The period of a full charge-discharge cycle equals the wave period.

Note: The specified R, C, and frequency values work well. Adjust frequency if using different values. Ensure the voltage remains constant long enough for full charging (approx. t = RC[lnV₀ - ln0.01]). The wave period should be at least double this charging time.

Diagram Description: Figure 4.2 shows a graph of voltage (V) versus time, illustrating the charging and discharging curves of a capacitor in an RC circuit driven by a square wave signal.

Experimental Setup

1. Set up the circuit shown in Figure 4.3, connecting the resistor and capacitor in series to the PASCO 750 Interface's signal output. Use a 200 µF capacitor and a 1000 Ω resistor. The electrometer reads voltage across the capacitor and connects to an analog channel.

Diagram Description: Figure 4.3 shows the experimental setup: a computer connected to a PASCO interface, which is connected to an electrometer. The electrometer is part of a circuit with a resistor and capacitor connected to a signal generator.

2. Using DataStudio software, create a voltage vs. time display for the electrometer readings.
3. Set the signal generator to produce a positive square wave (approx. 4 V maximum, 0.45 Hz frequency) and set it to AUTO.
4. Start recording data. Observe the capacitor voltage. Stop data collection after several cycles.
5. Analyze one full charge-discharge cycle.

Analysis

The analysis is similar to Procedure A.

Extra Things to Try

• Check the voltage across the resistor during capacitor charging and discharging.

Appendix A: Copyright and Warranty Information

Copyright Notice

The PASCO scientific 012-07227G Basic Electrostatics System Manual is copyrighted. Non-profit educational institutions may reproduce parts for laboratory use without charge, provided reproductions are not sold for profit. Other reproduction requires written consent from PASCO scientific.

Limited Warranty

PASCO scientific warrants the product against defects in materials and workmanship for one year from shipment. PASCO will repair or replace defective parts at its option. Warranty excludes damage from abuse or improper use. PASCO scientific determines the cause of failure. Customers are responsible for packing and shipping equipment for warranty repair, prepaid. PASCO scientific covers return shipping costs after repair.

Credits: Author: Cecilia Hernandez

Appendix B: Technical Support

For assistance with the Basic Electrostatics Systems or other PASCO products, contact PASCO scientific:

Address: PASCO scientific, 10101 Foothills Blvd., Roseville, CA 95747-7100

Phone: (916) 786-3800

FAX: (916) 786-3292

Web: www.pasco.com

Email: techsupp@pasco.com

Product End of Life Disposal Instructions

This electronic product is subject to disposal and recycling regulations that vary by country and region. It is your responsibility to recycle electronic equipment according to local environmental laws to protect human health and the environment. Contact your local waste disposal service or the place of purchase for recycling drop-off locations.

The European Union WEEE (Waste Electronic and Electrical Equipment) symbol on the product or packaging indicates it must not be disposed of in standard waste containers.

Symbol Description: A symbol depicting a crossed-out waste bin with a circular arrow, indicating proper disposal and recycling.