# Datalogging in Science

## Capacitor storage

Electricity

Capacitor - - - time constant

Overview
In this experiment the time taken for a capacitor to charge and discharge through resistors will be measured and used to determine the time constant of the capacitor.

Background
Capacitors are devices that can store electric charge; they do not produce the charge. A capacitor is traditionally made from two metal plates separated by an insulating material called a dielectric.
When a voltage is applied to a capacitor the voltage across the plates increases as charge flows in. The charge ceases to flow when the voltage across the plates is equal to the supply voltage. The capacitor in this state is charged. Shorting the terminals of the capacitor will cause it to discharge.
Adding a resistance into the charging circuit increases the time taken to reach a full charge. If a resistance is used to discharge the capacitor the time taken will also increase.

Precaution
If you are using an electrolytic capacitor check that the polarity of the capacitor is followed

Procedure
1. Assemble the circuit as shown above. Connect to the power supply but do not turn the power on. Connect the Voltage Sensor to the datalogger.

2. Write down the values of the resistor and capacitor used.

3. Launch the
Graphing software.

4. Measure the voltage (emf) of the supply with no current flowing, using the
meters function on the EasySense unit or Test mode. You can do this by temporarily connecting the Voltage Sensor across the supply terminals. Replace the Sensor into the circuit after taking this measurement.

5. Put the switch in the discharge position to make sure the capacitor is fully discharged before starting. If necessary finish the discharge by shorting across the terminals of the capacitor with a piece of wire.

6. Start datalogging.

7. Immediately close the switch and watch the recording, if the voltage is not rising put the switch into its alternate position.

8. When the line of the graph shows no further change in value, swap the switch to the other position to discharge the capacitor.

9. If there is enough time repeat the charge / discharge cycle.

10. If a complete cycle is not obtained on the graph, repeat the recording.

11. When finished, use the switch to make sure the capacitor is discharged fully.

Theory

The time constant of a resistor - capacitor circuit is used as a measure of the length of time needed to charge a capacitor to within a percentage of its final maximum value.
The time constant =
C x R
R = the value of the charging resistor
C = the capacitance of the capacitor
The time constant is defined as the time taken to reach 63% of its final maximum voltage when charging.
When discharging the time constant is the time taken to fall by 63% from the maximum value i.e. to fall to 37% of the maximum value.

Results
Finding the time constant for charge mode
1. The maximum voltage is the emf of the supply measured at the beginning of the experiment.

2. Multiply the maximum voltage by 0.63 to find the 63% voltage.

3. Use the
Interval tool to find the time taken to go from zero volts to the 63% value.

4. Expose the results table and check that the data selected by the Interval Selection has correctly identified the beginning and end of the time period.
Finding the time constant for discharge mode.
1. Use the 63% voltage value determined above.
2. Use
interval  to find the time taken to go from the maximum value to 0.37 of the maximum value, i.e. to reduce the voltage by 63%. The Interval command will show this value as an increasing negative number.
Theoretically the two values for charge and discharge should be the same, in practice they will be slightly different. Explain why there is a difference (hint: think of energy losses).

Questions
1. How long did it take for the capacitor to reach 95% of its maximum voltage? (Multiply the emf  value by .95 to calculate the 95% of maximum voltage).

2. How does the value of the time constant relate to the time for reaching 95% of the maximum voltage?

3. If there is unlimited time available, when will the capacitor reach full charge? Explain your reasoning.

4. Where / how could you apply the knowledge of time constants?

Extension
1. How does increasing
a. The value of R
b. The value of C
c. The supply Voltage
affect the time constant?

2. What happens if resistors of different values are used on the charge and discharge sides of the circuit?
Note: these experiments are best done using the
Overlay mode.

Data Harvest users

1. Connect the sensor to the datalogger and the logger to the computer
2. Then click the Set Up icon to the right of this message.
3. When the software opens, click the Play button.

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