Experiment to determine the absolute capacity of a capacitor
Answers
A storage oscilloscope enables the voltage/time graph for a capacitor charging through a resistor to be displayed and, from the print-out, a value of the time constant for the circuit to be calculated. This provides all the information required for calculating the value of the capacitor.
Equipment required
A PC oscilloscope such as the 2205 with PicoScope Education software.
A capacitor of unknown value (approximately 1 µF for the values used here).
A battery (a 9 V PP3 was used but any type or value can be used)
Suitable leads and connectors.
Equipment setup
graph
Background theory
When an uncharged capacitor is connected to a DC supply through a resistor, the potential difference across its plates (Vc) increases rapidly at first but then slows down until the value is equal to that of the DC supply (Vs). When Vc = Vs then there is no current flowing through the resistor and the capacitor is fully charged. The time constant of the circuit, t, is defined as the time taken for the value of Vc to reach 63.2% of the final value which can be taken as Vs. We also have that t = RC where R is the value of the resistor in ohms and C is the capacitor value in farads. For a full treatment of the mathematics behind this definition see the Appendix at the end of this note.
Practical considerations
The PicoScope 2205 oscilloscope can give a time axis of almost any value and so the values of R and C can be any convenient value. It should be noted however that the input impedance of the PicoScope 2205 is approximately 1 MΩ and will be connected in parallel with the capacitor. If this input impedance is not to significantly change the maximum value of Vc then the charging resistor should have a value < 1 MΩ by a factor of about 100.