Physics
Electricity and Heat
Sensors:
Loggers:
Voltage, Current
Any EASYSENSE
Logging time: EasyLog
37 Charge stored on a capacitor
Read
Capacitors are devices that can store electric charge; they do not produce the charge. A capacitor was
originally made from two metal plates separated by an insulating material called a dielectric. They are now
made from a wide range of materials including ceramics, Mylar, polystyrene, tantalum and aluminium and
electrolyte. There are many different types of capacitor available and they come in a variety of shapes and
sizes. The unit of capacitance is the Farad and values will range from pico-Farads (10-12) to Farads.
Capacitors are used in: timing circuits, energy storage, frequency filters and smoothing voltages.
In this investigation, you are going to measure the charge that a capacitor can store and then deliver when
discharged.
A
B
Resistor
Capacitor
+
Voltage
Sensor
Red Lead
Take care with polarity of the wires from the sensors. The red and black in the diagram refers to the colour of
the leads from the sensors.
What you need
1.
2.
3.
4.
5.
6.
7.
8.
An EASYSENSE logger.
A Smart Q Current sensor ±100 mA or ±1 A.
A Smart Q Voltage sensor ±12 or 20 V.
Electric circuit kit or breadboard.
Capacitors and resistors, a 10,000 μF capacitor and a 1 kΩ resistor, are recommended.
SPDT switch.
d.c. power supply, dry cells in good condition work well. Refer to notes below for fuller advice.
Connecting wires and crocodile clips.
What you need to do
1. Assemble the circuit as shown but do not connect the power. If you are using electrolytic capacitors
ensure the correct polarity is observed.
2. Connect the Voltage and Current sensor to inputs of the logger.
3. Note down the values of the resistors used and the value of the capacitor
4. From the EasySense software’s Home screen select EasyLog.
5. Use Test Mode (Tools menu) to measure the voltage (e.m.f) of the supply with no current flowing.
You can do this by temporarily connecting the Voltage sensor across the supply terminals. Replace
the sensor into the circuit after taking this measurement.
Electricity and Heat
37 - 1 (V2)
6. 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.
7. Click Start.
8. Immediately close the switch and watch the recording, if the voltage is not rising put the switch into
its alternate position.
9. When the line of the graph shows no further change in value, swap the switch to the other position to
discharge the capacitor.
10. Repeat the charge / discharge cycle.
11. Click on Stop to finish logging.
12. If you did not manage to get a complete cycle on the graph, click on Start and repeat.
13. When you have collected all the data you need, use the switch to make sure the capacitor is
discharged fully.
Theory
The charge stored on the capacitor is given by the following equation:
Q=CxV
Q = the charge in Coulombs, C
C = the capacitance in farads, F
V = the voltage in volts, V
When a capacitor is charged a current flows, the relationship between charge and a steady current is:
Q=Ixt
I = the current flowing in amps.
If the current is variable, as in this experiment, then the charge flow is the AREA under the current time
graph.
Analysis of results
The graphs you obtained are Current and Voltage vs. Time. You will calculate the total charge stored from
the Current vs.Time graph.
Measuring Vmax
Using Values, measure the maximum voltage in the charge cycle of the voltage-time graph. This is Vmax,
write down this value.
Measuring the charge stored
The charge stored during the charge cycle and the charge delivered during the discharge cycle are found by
measuring the area under the current-time graph.
1. Make sure the Current scale is displayed on the y-axis.
2. Select the Area icon.
3. Go to the first charge cycle on the graph, click on the point where the current starts to increase, and
drag the cursor across to the point where current has fallen back to zero.
Electricity and Heat
37 - 2 (V2)
4. A value will appear in the blue data box showing mAs, i.e. millicoulombs (mC), in the example
66.589 mAs.
5. For comparison, the charge on the capacitor can be calculated from Vmax and the Farad rating of the
capacitor. Charge = V x C
6. Note the error rating of the capacitor; the farad rating can have a 20% tolerance. The result collected
from the graph will be the measured value for the device. The value written on the device will be its
design value.
Questions
1. Are there any general differences between the charge and discharge values? Explain why this
occurs.
2. A flash-gun lamp requires a charge of 0.004 coulombs at 6 volts. What sized capacitor (in
microfarads) is needed to store this charge?
Extension
Use fast logging to obtain more reliable results. Use Graph mode, and select a 30 s total recording time with
a 10 ms interval; this will be enough for two complete charge-discharge cycles.
Investigate the relationship between:
1. Charge vs. Voltage; does the charge stored vary with the charging voltage?
2. Charge vs. Capacitance; Measure the charge stored for different values of the capacitance,
maintaining the maximum voltage constant
Electricity and Heat
37 - 3 (V2)