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.