How to Calculate the Capacitance of a Parallel-Plate Capacitor with Dielectric?

What is the formula for calculating the capacitance of a parallel-plate capacitor filled with a dielectric?

The formula for calculating the capacitance of a parallel-plate capacitor with a dielectric is given by: C = K²Co, where K is the dielectric constant and Co is the capacitance of the empty capacitor (without the dielectric).

Understanding Capacitance of Parallel-Plate Capacitor with Dielectric

Capacitance is the ability of a component to store electrical charge when a voltage difference exists between its terminals. In a parallel-plate capacitor, the capacitance can be increased by adding a dielectric material between the plates. The dielectric constant (K) of the material determines how much the capacitance will increase.

Calculation Formula

The formula for calculating the capacitance of a parallel-plate capacitor with a dielectric is C = K²Co, where:

  • C is the capacitance with dielectric
  • K is the dielectric constant
  • Co is the capacitance of the empty capacitor

Example Calculation

Let's say we have a parallel-plate capacitor with the following parameters:

  • Dielectric constant (K) = 4
  • Plate area (A) = 3 m2
  • Plate separation (d) = 2 mm

First, we calculate the capacitance of the empty capacitor (Co):

Co = πυA/d

Substitute the values and simplify to find Co = 13.275 nF.

Then, use the formula C = K²Co to find the capacitance with the dielectric: C = 212.4 nF.

Conclusion

By understanding the formula and calculations involved, you can determine the capacitance of a parallel-plate capacitor with a dielectric. Adding a dielectric material increases the capacitance, providing important functionalities in electronic circuits.

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