Dielectric Capacitance Calculator
Dielectric Capacitance Calculator computes capacitance of a parallel-plate capacitor, visualizing effect of dielectric constant.
Formulas Used in Dielectric Capacitance Calculator
The calculator uses the following formula for a parallel-plate capacitor with a dielectric:
Capacitance:
\\[ C = \kappa \epsilon_0 \frac{A}{d} \\]Where:
- \\( C \\): Capacitance (F)
- \\( \kappa \\): Dielectric constant (dimensionless)
- \\( \epsilon_0 = 8.854187817 \times 10^{-12} \, \text{F/m} \\): Permittivity of free space
- \\( A \\): Plate area (m²)
- \\( d \\): Plate separation (m)
Example Calculations
Example 1: Vacuum (No Dielectric)
Input: A = 0.01 m², d = 0.001 m, κ = 1
\\[
C = 1 \cdot 8.854187817 \times 10^{-12} \cdot \frac{0.01}{0.001} \approx 8.854 \times 10^{-11} \, \text{F}
\\]
Result: C = 8.854e-11 F
Example 2: With Dielectric
Input: A = 0.01 m², d = 0.001 m, κ = 2.5
\\[
C = 2.5 \cdot 8.854187817 \times 10^{-12} \cdot \frac{0.01}{0.001} \approx 2.214 \times 10^{-10} \, \text{F}
\\]
Result: C = 2.214e-10 F
Example 3: Larger Area
Input: A = 0.05 m², d = 0.001 m, κ = 1
\\[
C = 1 \cdot 8.854187817 \times 10^{-12} \cdot \frac{0.05}{0.001} \approx 4.427 \times 10^{-10} \, \text{F}
\\]
Result: C = 4.427e-10 F