---
title: "Capacitor plate spacing and dielectric breakdown"
subject: "Electrical Engineering Material"
chapter: 3
key: "semester_3/electrical_engineering_material:plate-spacing-breakdown"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/plate-spacing-breakdown
site: BCT Engineering
---

# Capacitor plate spacing and dielectric breakdown

Electrical Engineering Material · Chapter 3: Dielectric Materials

- Asked in: 2082 Kartik (new course), 2 marks; 2076 Chaitra, 4 marks (asked 2 times)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/plate-spacing-breakdown
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-3

## Question

Explain how, if the spacing between parallel plates of a capacitor is less, the dielectric breakdown will occur soon.

## Short answer

E = V/d, so smaller spacing gives higher field for the same voltage. The field reaches dielectric strength E_br at a lower voltage, causing sooner breakdown. Also higher field promotes electron avalanche and thermal heating.

## Answer

Dielectric breakdown occurs when the electric field in the insulator exceeds its **dielectric strength** $E_{br}$ (the maximum field it can withstand, e.g. about 3 kV/mm for air, 20–40 kV/mm for oil and polymers).

For a parallel-plate capacitor with voltage $V$ and plate spacing $d$, the field in the dielectric is

$$
E = \frac{V}{d}
$$

So for a given voltage, the field is **inversely proportional** to the spacing. The breakdown voltage is

$$
V_{br} = E_{br}\,d
$$

#### Why small spacing breaks down sooner

1. When $d$ is reduced, the same voltage produces a larger field, so $E$ reaches $E_{br}$ at a lower voltage.
2. A higher field gives the few free electrons more energy between collisions ($e E \lambda$), so they can ionize atoms and start an **avalanche** at a lower voltage.
3. A higher field also means more leakage current and dielectric heating per unit volume ($\propto E^2$), leading to **thermal breakdown** sooner.
4. In thin soft films, the electrostatic pressure $\frac{1}{2}\varepsilon E^2$ is larger and can cause **electromechanical** collapse.

#### Example

For air ($E_{br} \approx 3\ \text{kV/mm}$):

| Spacing $d$ | Breakdown voltage $V_{br}$ |
|---|---|
| 10 mm | 30 kV |
| 1 mm | 3 kV |
| 0.1 mm | 300 V |

So a capacitor with closer plates fails at a much lower voltage. This is why high-voltage capacitors use either larger spacing or a dielectric with very high strength (mica, polypropylene), and each capacitor has a rated working voltage. (Very thin films often show a slightly higher $E_{br}$ because they contain fewer defects, but their breakdown voltage $E_{br}d$ is still lower.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For a given voltage V, how does the field E in a parallel-plate capacitor depend on spacing d?
   A. E = Vd
   B. E = V/d, so smaller d gives larger E
   C. E is independent of d
   D. E = V/d^2
   Answer: B. E = V/d is inversely proportional to spacing. (Key point: Field in capacitor)

2. If air has E_br = 3 kV/mm, the breakdown voltage for a 0.1 mm gap is:
   A. 30 kV
   B. 3 kV
   C. 30 V
   D. 300 V
   Answer: D. V_br = E_br d = 3 kV/mm x 0.1 mm = 0.3 kV = 300 V. (Key point: Breakdown voltage)

3. Why does a higher field start an avalanche at a lower voltage?
   A. Electrons gain more energy (eE*lambda) between collisions and ionize atoms
   B. The dielectric becomes thicker
   C. The permittivity of air becomes zero
   D. The electrons slow down
   Answer: A. Higher field gives free electrons more energy per mean free path, so impact ionization begins at lower voltage. (Key point: Why smaller gap fails sooner)

## Related in Electrical Engineering Material

- [Thermal and electromechanical dielectric breakdown](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Athermal-electromechanical-breakdown) — Electrical Engineering Material, chapter 3, asked 4×
- [Types of dielectric breakdown](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adielectric-breakdown-types) — Electrical Engineering Material, chapter 3, asked 2×
- [Dielectric strength and types of breakdown](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Adielectric-strength-breakdown) — Electrical Engineering Material, chapter 3
- [Breakdown mechanisms; electronic vs orientational polarization](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Abreakdown-and-polarization-types) — Electrical Engineering Material, chapter 3
- [Power loss in a glass dielectric](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aglass-dielectric-power-loss) — Electrical Engineering Material, chapter 3

## Related in other subjects

- [Parallel plate capacitor with mica](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Amica-capacitor-field-free-charge) — Engineering Physics, chapter 7
- [Displacement current in parallel plate capacitor](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adisplacement-current-circular-plates-b-integral) — Engineering Physics, chapter 9
- [Capacitance of parallel plate capacitor](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Apoisson-parallel-plate-capacitance) — Electromagnetism, chapter 2
- [Viscosity of oil between parallel plates](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Aviscosity-parallel-plates) — Hydro Power, chapter 1