Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. You may wish to label each package of resistors so as to differentiate them for future storage.
2. The color code in the bands for the 220 Ω resistor is Red-Red-Brown-Gold.
3. The color code in the bands for the 620 Ω resistor is Blue-Red-Brown-Gold.
4. The color code in the bands for the 1.1 k Ω resistor is Brown-Brown-Red-Gold.

Safety Precautions

Although 9-V batteries are generally not strong enough to deliver an electric shock, remind students to handle batteries appropriately. Inspect batteries first for signs of cracks and leaking before using; do not use batteries that are compromised. Remind students to follow all laboratory safety precautions.

Disposal

All materials may be saved and stored for future use. Discard depleted batteries according to local regulations.

Lab Hints

• Enough materials are provided in this kit for 30 students working in pairs or for 15 groups of students. All materials are reusable. Two extra LEDs are included.
• Both parts of this laboratory activity can reasonably be completed in one 50-minute class period. The prelaboratory assignment may be completed before coming to lab, and the data compilation and calculations may be completed the day after the lab.
• Diodes are circuit components that only allow current to pass in one direction. Light emitting diodes are a special type of diode that will light up when a critical voltage is reached. Because of the low current requirement, they are ideal for use in this application, requiring only their critical voltage to remain illuminated. The critical voltage of these red light emitting diodes is 1.7–2.2 V.
• It is advisable to check students’ circuits to ensure there will be no short circuit that could possibly damage some of the electronic components, such as the LED.
• If your classroom lacks a voltage probe but you still wish to do a quantitative experiment, you may modify Part A to accomplish this goal. As the measured battery voltage may be approximated as “V_o” and the LED will no longer remain lit around 1.7–2.2 V, this gives approximate data points that students can compare to the theoretical calculation of the voltage decay curve. Plug the average time into Equation 2, and compare the theoretical voltage to the LED’s voltage range of 1.7–2.2 V. Note that because real world capacitors will steadily lose their charge, the theoretical voltage will be higher than the LED voltage range.
• If switches are not available for classroom use, they may be omitted from the circuit. Simply instruct students not to attach one of the cords until they are ready to begin data collection.
• Although 9-V batteries are generally not sufficient to deliver an electric shock, it is advisable to remind students of proper safety precautions when working with electricity. Never allow battery terminals to touch or short circuit, as this may create a fire hazard. Never handle batteries or electrical components with wet hands; or allow electric cords to run over or near a sink.
• The following figure is a graphical representation of a discharging capacitor. The table shows the approximate voltage after each time constant.
  {12150_Hints_Figure_4}

Teacher Tips

• This activity fits well within any electronics unit.
• Properties of capacitors may be further studied by combining the capacitors into both series and parallel circuits, to demonstrate the equivalent capacitance of three capacitors hooked in series versus in parallel. Equation 3 shows the equivalent capacitance of three capacitors connected in parallel.
  {12150_Tips_Equation_3}
  Equation 4 shows the equivalent capacitance of three capacitors connected in series.
  {12150_Tips_Equation_4}
  Have students compare three capacitors connected in series versus in parallel against their single capacitor.
• For further study of electronics, consider the Simple Circuits Kit (Flinn Catalog No. AP6302) and the Resistance Mystery Kit (Flinn Catalog No. AP7417). An assembled circuit requiring a capacitor can be put together in the Build a Shake Flashlight Kit (Flinn Catalog No. AP7320).

Answers to Prelab Questions

1. The units for the time constant, RC, are seconds. Derive this from the units for capacitance and resistance.
   {12150_PreLabAnswers_Equation_5}
2. 1. Given a 750 μF capacitor connected in series with a 2.10 kΩ resistor and a 9.00-V battery, what is the time constant (RC)?
   2. Use Equation 2 to solve for the potential across the capacitor after 1 RC.

      Time constant: 750 μF x 2.1 kΩ = 0.00075 C/V x 2100 V/A = 1.58 (C/V)(V/(C/s) = 1.58 s
      After 1 RC: V_c = 9 x (1 – e^–1.58/1.58) = 9 x (1 – e^–1) = 5.69 V

3. Label the components in the following circuit diagram. Hint: Look up any unfamiliar symbols in your physics textbook or research online.
   {12150_PreLabAnswers_Figure_5}
4. In this diagram, what will happen when the switch is closed in the left position? In the right?

   When the switch is closed in the left position the capacitor will charge. When the switch is closed to the right, the capacitor will release its charge and the LED will light.

Sample Data

Draw and label the circuit setup.

Battery voltage: ___8.18___ Qualitative Observations: Discharging a Capacitor
Record your observations of the circuit and LED for each resistor.

Resistor, 220 Ω
Observation—The LED Starts out very bright, but goes out fairly quickly
LED “On” time ___2.73,2.11,2.37___ Average ___2.40___

Resistor, 620 Ω 
Observation—The LED does not stay bright for very long, but takes longer to go out.
LED “On” time ___4.22,4.39,4.13___ Average ___4.24___

Resistor, 1.1 kΩ 
Observation—The brightness of the LED quickly fades, but it remains faintly lit for a long time.
LED “On” time ___6.97,6.23,6.86___ Average ___6.69___

Quantitative Observations
Record the best-fit line for each of the resistors.

Answers to Questions

1. Compare the RC constant for each resistor with your observations. Was there a correlation between the amount of time the LED was lit and the RC value? What about the brightness of the LED?

   The RC value seems to be correlated with how long the LED stayed lit—the higher the RC, the longer it was lit. However, the LED was not as bright with a higher RC as when the RC was lower.

2. Quantitative: Identify the constants in your best-fit lines, and compare them to Equations 2 and 3. Calculate the average time constant using the charging and discharging data. Does the time constant in your best-fit lines match the expected values?

   The time constants according to the best-fit line were all close to the data, although they were all slightly higher than expedted.

3. You’ve come upon a lab where most of the components are not properly labeled. You find a capacitor and want to know its capacitance. You happen to have a 9-V battery and find a resistor whose color code indicates that it’s a 780 Ω resistor. You also have a 1.6-V LED. Based on this information, is it possible to calculate the approximate capacitance of the capacitor? If so, explain how and calculate the capacitance. If not, explain what other information is needed, and how you would calculate it.

   Yes, it is possible to calculate the capacitance of the capacitor. Allow the capacitor significant time to charge to ensure it is fully charged at 9 V. When connected with the LED, the amount of time between the switch being closed and the LED turning off will give you a value for T at V_c = 1.6 V. This eliminates all but one variable in the equation, capacitance. The equation would be 1.6 V = 9 × e^{–t/780 × C}

References

Halliday, D., Resnick, R., Walker, J. Fundamentals of Physics, 7th ed. John Wiley & Sons, Inc.: DeKalb, IL, 2005; pp 657–664 and pp 720–724.

Introduction

Capacitors are simple circuit components that store electrical energy. They are ubiquitous in electronics; most electronic devices built today incorporate capacitors in a variety of ways. Learn more about the properties and function of capacitors by using them to build and test simple circuits.

Concepts

• Capacitors
• RC circuits
• Capacitor half-life
• Circuit diagrams

Background

With their ability to store charge, capacitors function similarly to rechargeable batteries. Once a voltage has been supplied, a capacitor will hold that voltage until some complete circuit loop is made, at which point the stored charge is released.

Capacitors consist essentially of two conductors, called plates. The plates are placed in close proximity to each other but do not make electrical contact—an insulating dielectric between them prevents charge from directly conducting from one plate to another. A dielectric is any sort of traditionally insulating material that does not easily allow current to flow; examples include glass, wool, rubber, ceramic, and even air. The function of the dielectric is simple—to stop a charge from leaping from one plate to another. When a voltage, such as from a battery, is applied across a closed circuit, a charge builds up on one plate as electrons attempt to flow but cannot pass the gap between the plates. This induces the opposite charge in the other plate as electrons are driven away, and creates an electric field between the two plates. When the switch is opened, breaking the complete circuit, and the battery is removed, the charge will remain in place. In an ideal capacitor this charge will remain indefinitely but, in real capacitors, the charge will leak off over time. When the switch is closed once more to complete the circuit, the capacitor will release its stored electrical energy.

A capacitor’s capacitance is a measure of its ability to hold a charge. With a greater capacitance, more charge will be stored for the same potential difference. Capacitance (C) is the proportionality constant between the amount of charge on the plates and their corresponding voltage. The equation for capacitance is

where

q is the charge on the plates (in coulombs)
V is the potential difference between them (in volts).

The units of capacitance are “farads” (F). One farad is equal to one coulomb per volt.

The rate at which a capacitor will release its charge depends on the circuit setup, specifically on the resistor with which it is in series. A resistor is a common circuit component designed to limit current flow by producing a voltage drop. Consider a simple circuit consisting of a switch, capacitor, resistor and battery. When the switch is closed, the battery will charge the capacitor (see Figure 1). When the battery is removed from the circuit, the capacitor will store its charge. Closing the switch will allow it to release that charge, at a rate determined by both the capacitance of the capacitor and the resistance of the resistor. When the voltage is removed, the capacitor can be made to drain the charge by closing the circuit. The time required for the capacitor to discharge its stored charge depends on the product RC of the resistance R and the capacitance C(R x C). For any given circuit RC is a constant and is referred to as the time constant of the capacitor. The voltage drain of the capacitor—the decrease in voltage V as a function of the initial voltage V_o and the time t—can be determined using Equation 2. Voltage drain is exponential, much like radioactive decay. A higher resistance will cause less current to flow, thus it will take longer for the charge to drain from the capacitor.

Capacitors come in many shapes and sizes and most today have a very efficient design, such as two plates tightly curled around a middle dielectric. They are used in most electronics applications and are found in almost every circuit. They are as useful as resistors when it comes to building an electrical circuit. Their ability to store a charge means they can function as batteries, but the rate at which they supply energy can be tightly controlled and modified to suit the purposes of the circuit. For example, camera flashes rely on capacitors. A battery provides energy slowly to the capacitor—the tedious “charge” time on older disposable cameras—while the capacitor is able to release energy very quickly, allowing for the bright flash of light energy. Capacitors are critical components in many other types of circuits, allowing for complex behaviors, such as electric resonance and smoothing power output. Without capacitors, computers, MP3 devices and cell phones would not be possible.

Experiment Overview

This experiment will demonstrate the basic properties of capacitors and their discharge half-life, by connecting a 1000 μF capacitor with different resistors. This will be seen visually using a light emitting diode (LED), which is a circuit component that requires very little current, but a specific amount of voltage to light. The capacitor will also be explored quantitatively using a voltage probe.

Materials

Prelab Questions

1. The units for the time constant, RC, are seconds. Derive this from the units for capacitance and resistance.
2. Given a 750 μF capacitor connected in series with a 2.10 k Ω resistor and a 9.00-V battery:
   1. What is the time constant (RC)?
   2. Use Equation 2 to solve for the potential across the capacitor after 1 RC.
3. Label the components in the following circuit diagram. Hint: Look up any unfamiliar symbols in your physics textbook or research online.
   {12150_Pre-Lab_Figure_3}
4. In this diagram, what will happen when the switch is closed in the left position? In the right?

Safety Precautions

Although 9-V batteries are not powerful enough to deliver an electric shock under normal conditions, please follow all proper safety precautions when working with electronics. Check completed circuits with the instructor to ensure that you have not created a short circuit. Please follow all laboratory safety guidelines.

Procedure

Part A. Qualitative Analysis

1. Obtain the battery, capacitor, connector cords, switch and the 220 Ω resistor. Note: The color code in the bands for the 220 Ω resistor is Red-Red-Brown-Gold.
2. Using a multimeter, measure the voltage of the battery and the resistance of the resistor. Record these values in the data table. Note: It is important to measure experimentally the resistance of a resistor, even though this value is theoretically known. Resistors will often have a tolerance range, indicated by the gold or silver band. The gold bands indicate these resistors have a 5% tolerance, meaning their value will be within 5% of 220 Ω.
3. Calculate the RC value for this resistor–capacitor combination, and record this value on the worksheet.
4. Inspect the capacitor to determine which lead is the negative lead. Note: This will be represented by a black band with a “–” symbol, along with arrows to point in the direction of the negative lead.
5. Inspect the LED to determine which lead is the negative lead. The shorter lead is negative.
6. Connect the connector cords, battery, resistor, LED and capacitor together according to Figure 3 from the Prelab Questions. Note: Ensure the switch is open; that is, not connected to either terminal.
7. Have your instructor approve your circuit setup to ensure the polarity is correct and there is no short circuit. Draw the circuit setup on the worksheet.
8. Obtain the stopwatch.
9. When ready, close the switch toward the left, in order to complete the battery loop circuit. Leave this circuit closed/connected for at least 20 seconds to ensure the capacitor is sufficiently charged.
10. Have one partner prepare to flip the switch to the LED loop, and another to measure the amount of time from when the switch is closed to when the LED flickers out.
11. When ready, close the switch toward the right, in order to complete the LED loop circuit. Time how long the LED remains lit.
12. Once the LED goes out, leave this circuit closed/connected for at least 30 seconds to ensure the capacitor is sufficiently discharged.
13. Record your observations and the time on the worksheet.
14. Repeat steps 8–13 twice more to average the results.
15. Repeat steps 2–14 for the 620 Ω resistor. Note: The color code in the bands for the 620 Ω resistor is Blue-Red-Brown-Gold.
16. Repeat steps 2–14 for the 1.1 kΩ resistor. Note: The color code in the bands for the 1.1 kΩ resistor is Brown-Brown-Red-Gold.
17. If voltage probes are available, move on to Part B in the Procedure. Otherwise, disconnect all circuit components and finish filling out the data and calculations on the worksheet.

Part B. Quantitative Analysis (optional)

18. Follow steps 4–6 in the Part A Procedure to prepare the circuit. The switch should be open.
19. Attach voltage probes across the capacitor, or according to the instructor’s directions.
20. Open the corresponding software on a computer or calculator, and prepare it to record voltage data for 30 seconds.
21. Start data collection and close the switch toward the left, as in step 9.
22. Save this data. (Optional) If available, use a curve-fitting program to find the equation for the resulting graph of voltage vs. time. Be sure to use only the data from when the capacitor was charging.
23. Start data collection and close the switch toward the right, as in step 11.
24. Save this data. (Optional) If available, use a curve-fitting program to find the exponential equation for the resulting graph. Be sure to use only the data from when the capacitor was charging.
25. Save and/or print the data according to the instructor’s direction. Label the printout.
26. Repeat steps 18–26 for the other two resistors.
27. When finished, disconnect all circuit components and store them according to the instructor’s directions.

Student Worksheet PDF

12150_Student1.pdf