Experiment 5 - Capacitive I

process of the experiment

Please use your time in the lab to conduct the different experiments. Calculations for this experiment should be done at home after all data has been collected. You can use the oscilloscope screenshot to USB-Flashdrive function to make sure you have all data available later.

Further information on the use of the oscilloscope for this experiment can be found here.

If you want to print this description, the pdf export might not work properly, so you can download one here: MLP-Experiment 5 - Capacitive I-281125.pdf (version Nov 28, 2025 )

1.      Context of the Experiment

This experiment concerns capacitive sensors. These can be found all around us. For using them, it is necessary to be able to measure a capacitance, which is this experiment’s main topic.

 

2.      Learning Goals of this Experiment

• Knowing: electrical measurement circuits, basics of electric circuits

• Abilities: understand physical concept of capacitive sensors, handling of oscilloscope and function generator

• Understand: possible measurement accuracy of measurement method

3.      Literature

[1] Lectures: Electrical Measurement Technology, Capacitive Sensors

[2] Oscilloscope Introduction Video (Video on EDUX1052G) → Please watch this video and make sure you understand how the oscilloscope is working before coming to the experiment!

[3] P. L. Regtien, Hg., Sensors for Mechatronics. Amsterdam: Elsevier, 2012.

[4] https://www.electronics-tutorials.ws/rc/time-constant.html

[5] how-to-measure-inductance-or-capacitance-using-oscilloscope

[6] https://www.tek.com/en/blog/what-is-an-oscilloscope-probe

[7] https://learn.sparkfun.com/tutorials/how-to-use-an-oscilloscope/all 

[8] https://learn.sparkfun.com/tutorials/how-to-use-a-multimeter/all

[9] User's guide for the EDUX1052G

4.      Basics/Fundamentals

The most known capacitance is a plate capacitance, where two plate electrodes are being charged. For these it is possible to change the capacitance by changing the displacement of one plate, the dielectric, the effective area or deforming the plates as the capacitance depends on the permittivity ε due to the dielectric, the area A and the distance of the plates d: 

Capacitive sensors can be used for a lot of different applications, for example for measuring pressure, distance, proximity, acceleration, humidity, filling levels, gaps, angles, hygrometer applications and moisture. Advantages of capacitive sensors are their low costs, simple setup, their ability to withstand high temperature and pressure and their high reliability. One disadvantage is, that measuring materials with low dielectric constants can be challenging.

There are multiple ways to measure unknown capacitance, some of them are introduced in the following sections,

4.1 Tau-method (τ) 

Tau is the time constant of an RC circuit that takes to change from one steady state condition to another steady state condition when subjected to a step change input condition [4]. τ is the time taken for the capacitor from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage. The change of state from one stable condition to another generally occurs at a rate determined by the time constant of the circuit which itself will be an exponential value. The time constant of an RC circuit could be used to measure the value of the unknown capacitance, given that the resistance is known:

 

therefore:

4.2 AC signal phase shift

Another method is to use the phase shift of an applied AC voltage signal to an RC circuit.  The capacitance could be calculated from the reactance:

4.3 Resonance 

One way to measure unknown capacitance is done using the resonance frequency of a special circuit called the resonant circuit. This circuit is composed of an inductor and a capacitor connected in series. At resonance frequency, the effect of the capacitor is diminished by the effect of the inductor. Given the value of the inductance, one can calculate the value of the capacitance as follows:

Where 

 is the resonance frequency and 

 is the value of the inductance.

5.      Technical Basics & preparations

• have all measurement devices at hand and familiarize yourself with them: oscilloscope, internal function generator of the oscilloscope, multimeter.

5.1 Oscilloscope

One of the basic components of this experiment is the oscilloscope. The basics of how to use an oscilloscope is found in [7]. 

 5.2 Multimeter

Another basic component is the multimeter. Further details on how to use the multimeter are found in [8]                                                           

Preparations:

• Gather all the necessary measurement objects and instruments:

  • Clamps, cables, breadboard

  • Resistors/potentiometers

  • Inductances

  • Multimeter

  • Oscilloscope

  • Function-generator

 

CAUTION!

Be careful with the polarisation of the capacitor and the inductor, usually the terminals are marked with +/- or one pin is longer than the other, in this case the longer pin is the positive terminal.

Always make sure to unload your capacitor, before you connect it. Make sure that the capacitor is not loaded by connecting a resistor to the terminals and short-circuiting it across it.

6.     Resetting the Oscilloscope

This week requires extensive work with the oscilloscope. When problems with the settings of it arise it might help to reset them. To do so press the button indicated on the picture below.