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Calculating the Capacitance and Energy Stored in a Parallel Plate Capacitor



  • Introduction

    When parallel conductive plates are separated by a dielectric, a capacitor is formed. Capacitors are able to store electric charge allowing them to act as an energy storage device. However, the amount of energy that can be stored in a capacitor is limited by the dielectric strength of the dielectric material used. Applying a voltage that results in an electric field that exceeds the dielectric strength of the dielectric will cause a breakdown of the dielectric material. This EngineeringPaper.xzy sheet shows how to calculate the capacitance and maximum energy storage for a parallel plate capacitor. The image below shows the critical dimensions that will be used in the calculations.

    Inputs

    In order to perform the calculation, we need to first defined the electrode area, A, and the dielectric thickness, d:







  • Next wee need to specify the dielectric material since the capacitance depends on the relative permitivity, ε_r, of the dielectric material. The table below allows us to select the dielectric material. Note that currently only the selected table row is displayed. To see all table rows and select a different material, click the button. We also need the dielectric strength value, U_d, in order to determine the maximum amount of energy that can be stored by the capacitor.


    Note that the table dielectric properties are for room temperature and the relative permittivity values are for frequencies less than 1 kHz. When a range of values are specified in the data sources, the lowest value in the range is chosen for both relative permittivity and dielectric strength.

    Data sources: https://en.wikipedia.org/wiki/Relative_permittivity and https://en.wikipedia.org/wiki/Dielectric_strength



  • Air


  • We are now ready to calculate capacitance using the following equation. We also need to specify the vacuum permittivity, ε_0, so that the relative permittivity values from the table above can be converted to absolute permittivity values.









  • Next, we'll calculate the maximum voltage that be applied across the electrode by multiplying the dielectric strength, U_d, by the dielectric thickness, d:







  • Finally, we can use the equation for the energy store in a capacitor to find the upper limit for the amount of energy that can be stored by this capacitor: