1. What is the Capacitance Formula?

Definition: This formula calculates the capacitance of a parallel-plate capacitor based on the permittivity of the dielectric, plate area, and distance between plates.

Purpose: It helps engineers and students determine the capacitance of a capacitor design.

2. How Does the Formula Work?

The formula is:

Where:

• \( C \) — Capacitance (farads)
• \( \epsilon \) — Permittivity of the dielectric (farads per meter)
• \( A \) — Area of one plate (square meters)
• \( d \) — Distance between plates (meters)

Explanation: Capacitance increases with larger plate area or higher permittivity, and decreases with greater plate separation.

3. Importance of Capacitance Calculation

Details: Accurate capacitance calculation is crucial for circuit design, energy storage systems, and signal processing applications.

4. Using the Calculator

Tips: Enter the permittivity (default is vacuum permittivity 8.8541878128×10⁻¹² F/m), plate area in m², and plate separation in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is permittivity?
A: Permittivity is a measure of how much electric field is reduced by the dielectric material between the plates.

Q2: What's a typical plate area?
A: Plate areas vary widely from mm² in small capacitors to m² in large industrial capacitors.

Q3: How does distance affect capacitance?
A: Capacitance is inversely proportional to distance - halving the distance doubles the capacitance.

Q4: What if I use a different dielectric?
A: Multiply vacuum permittivity by the dielectric's relative permittivity (εᵣ) - e.g., ~3.9 for silicon dioxide.

Q5: Why is the result in ×10⁻¹² farads?
A: Because we're using the vacuum permittivity value in ×10⁻¹² F/m, which keeps results in a practical range.