Parallel Plate Capacitance Calculator
Dielectric reference table
| Material | εr | Strength (MV/m) | C (1 cm², 1 mm) |
|---|
Typical room-temperature values; real parts vary with grade, frequency, temperature and thickness.
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Variables
| Symbol | Quantity | Unit |
|---|---|---|
| C | Capacitance | Farads |
| ε | Permittivity | F/m |
| A | Plate area | m² |
| d | Distance between plates | m |
What it means
The capacitance of a parallel‑plate capacitor is given by C = εA/d, where ε is the permittivity of the dielectric material between the plates, A is the area of each plate, and d is the separation distance. Permittivity ε = ε₀ * ε_r, where ε₀ is the vacuum permittivity (8.85×10⁻¹² F/m) and ε_r is the relative permittivity (dielectric constant) of the material. This formula shows that capacitance is directly proportional to plate area and inversely proportional to plate separation. Increasing the area or decreasing the distance increases capacitance. The formula also shows that inserting a dielectric (ε_r > 1) multiplies the capacitance. This is the basis for the design of variable capacitors (by changing plate overlap) and for high‑value capacitors using thin dielectric films. Understanding parallel‑plate capacitance is fundamental in circuit design, filter design, and energy storage. It also helps in understanding parasitic capacitance in circuit boards. Example: With ε=8.85×10⁻¹² F/m, A=0.1 m², d=0.001 m, C = (8.85e-12 * 0.1)/0.001 = 8.85×10⁻¹⁰ F (885 pF).
Worked example
Parallel Plate Capacitance – Practical Example
Real‑World| Parameter | Value |
|---|---|
| ε₀ | 8.85 pF/m |
| A | 10 cm² = 10×10⁻⁴ m² |
| d | 1 mm = 10⁻³ m |
| Formula | C = ε₀·A / d |
Common mistakes
- Permittivity ε: Use the absolute permittivity of the dielectric (ε = ε₀·ε_r).
- Area A: The overlap area of the plates – not the total surface area.
- Distance d: The separation between plates – in metres.
- Edge effects: The formula assumes infinite plates – for finite plates, fringe fields cause deviations.
- Dielectric breakdown: If the voltage is too high, the dielectric may break down – the formula gives capacitance only.
Applications
Parallel‑plate capacitance is determined by the dielectric permittivity, plate area, and separation distance; larger area and smaller gap increase capacitance. This formula is essential for designing capacitors, touch sensors, and many electronic components. Engineers use it to calculate the capacitance of printed circuit board traces, to design capacitive sensing interfaces, and to model the behaviour of dielectric materials. In power electronics, it helps determine the capacitance required for filtering and energy storage. By understanding the dependence on geometry and material, professionals can optimise capacitor performance and size. This fundamental equation is also used in the design of MEMS capacitive sensors and in the study of dielectric breakdown.
- Capacitor design for power supplies and filters
- Capacitive touch sensing and proximity detection
- PCB trace capacitance modelling for high‑speed signals
- Dielectric material characterisation and selection
- MEMS capacitive sensors and actuators
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