Every capacitor, cable, transformer and circuit board depends on a dielectric — a material that does not conduct, yet responds strongly to an electric field. Questions on dielectric constant, dielectric strength, loss tangent and polarization appear regularly in BCS (EEE), PGCB, BPDB, BREB, DPDC and electrical-materials university exams. This post explains what happens inside a dielectric with an animation, then covers every property, type and application you need.
- A dielectric is an insulating material that becomes polarized in an electric field and can store electric energy.
- Dielectric constant (relative permittivity) εr = ε/ε0 = C/C0 — how much a material increases capacitance compared with vacuum.
- Dielectric strength = maximum field before breakdown (kV/mm). Air ≈ 3 kV/mm.
- Polarization types: electronic, ionic, orientation (dipolar), space-charge. εr falls with frequency as slower mechanisms drop out.
- Dielectric loss P = ωCV² tan δ; a good insulator has a small loss tangent tan δ.
1. What Is a Dielectric?
A dielectric is an electrically insulating material with very few free charges, in which an applied electric field displaces bound charges slightly from their equilibrium positions instead of making them flow. This displacement — polarization — lets the material store electrical energy.
When a dielectric fills the space between capacitor plates, capacitance rises from C0 (vacuum) to
C = ε0 εr A / d = εr C0, ε0 = 8.854 × 10⁻¹² F/m2. Polarization (Animation)
Without a field, polar molecules (shown as ellipses with + and − ends) point in random directions, so their dipole moments cancel. When a field E is applied, each dipole experiences a torque and turns so that its negative end faces the positive plate. Inside the material the charges still cancel, but a layer of bound negative charge appears at the surface next to the + plate and bound positive charge at the surface next to the − plate. These bound charges produce a field opposing E, so the net field inside is reduced. For the same voltage the plates can hold more charge — capacitance increases by εr.
Quantitatively, the polarization P (dipole moment per unit volume, C/m²) is:
P = ε0 (εr − 1) E = ε0 χe E, D = ε0E + P = ε0 εr Ewhere χe = εr − 1 is the electric susceptibility, and the dipole moment of one dipole is p = q·d.
3. Types of Polarization
| Type | Mechanism | Occurs in | Speed / frequency limit | Temperature dependence |
|---|---|---|---|---|
| Electronic | Electron cloud shifts relative to nucleus | All materials (atoms) | Fastest, up to ~10¹⁵ Hz (optical/UV) | Independent |
| Ionic (atomic) | Positive and negative ions shift in opposite directions | Ionic solids (NaCl, ceramics) | Up to ~10¹³ Hz (infrared) | Almost independent |
| Orientation (dipolar) | Permanent dipoles rotate to align with E | Polar materials (water, PVC, nitrobenzene) | Up to ~10⁹–10¹¹ Hz (microwave) | Decreases with temperature (thermal agitation) |
| Space-charge (interfacial) | Charge carriers pile up at grain boundaries / interfaces | Multiphase, impure or composite materials | Slowest, up to ~10³ Hz | Increases with temperature |
Polar dielectrics (water, PVC, castor oil) contain permanent dipoles; non-polar dielectrics (H₂, N₂, polyethylene, transformer oil) have none and show only electronic (and ionic) polarization, so they usually have low εr and low loss.
4. Effect of Frequency on Dielectric Constant
Each mechanism needs time to respond. As the frequency of the applied field rises, the slow mechanisms cannot follow and stop contributing, so εr falls in steps. Each drop is accompanied by a peak in dielectric loss.
This is why water has εr ≈ 80 at low frequency but a refractive index of only ≈ 1.33 (εr = n² ≈ 1.77) at optical frequencies.
5. Important Properties of Dielectrics
5.1 Dielectric constant (relative permittivity) εr
Ratio of the permittivity of the material to that of free space; dimensionless. High εr → smaller capacitors for the same capacitance. Low εr → less charging current and lower signal delay in cables and PCBs.
5.2 Dielectric strength
Maximum electric field a material can withstand without breakdown, in kV/mm. It depends on thickness, temperature, moisture, impurities, frequency and duration of voltage. Example: air ≈ 3 kV/mm; good transformer oil should withstand at least 30 kV across a standard 2.5 mm gap (≈ 12 kV/mm); mica exceeds 100 kV/mm.
5.3 Dielectric loss and loss tangent (tan δ)
In a real dielectric the current leads the voltage by slightly less than 90°. The small angle δ = 90° − φ is the loss angle, and the power lost as heat is:
Ploss = V I cos φ ≈ ω C V² tan δtan δ is also called the dissipation factor; power factor of the insulation ≈ tan δ for small δ. Measuring tan δ (with a Schering bridge or a tan-δ test set) is a standard condition check for cables, bushings and transformers — a rising tan δ signals moisture or ageing.
5.4 Other properties
- Insulation resistance (volume and surface resistivity) — should be very high.
- Thermal stability — insulation classes Y (90 °C), A (105 °C), E (120 °C), B (130 °C), F (155 °C), H (180 °C), C (>180 °C).
- Mechanical strength, moisture resistance, chemical stability and resistance to partial discharge.
6. Dielectric Breakdown
When the field exceeds the dielectric strength, the material suddenly conducts — breakdown. Solid dielectrics break down by:
- Intrinsic (electronic) breakdown — very fast (~10⁻⁸ s); free electrons gain enough energy to cause an avalanche.
- Thermal breakdown — dielectric loss heats the material faster than it can cool; resistance falls, loss rises, and it runs away.
- Electro-mechanical breakdown — electrostatic force between electrodes compresses the material until it fails.
- Electrochemical breakdown and ageing — slow chemical changes, treeing and partial discharges in voids gradually erode the insulation.
Gases break down by Townsend avalanche and streamer mechanisms (Paschen’s law: breakdown voltage depends on pressure × gap). Liquids break down mainly due to impurities, moisture and gas bubbles — that is why transformer oil is filtered and dried.
7. Classification and Common Dielectric Materials
| State | Material | Typical εr | Typical use |
|---|---|---|---|
| Gas | Air | 1.0006 | Overhead lines, air capacitors, air-break switches |
| SF₆ | ≈ 1.002 | Gas-insulated switchgear, circuit breakers (strength ≈ 2.5–3 × air) | |
| Liquid | Mineral transformer oil | ≈ 2.2 | Transformers, oil circuit breakers, cables |
| Solid | Polyethylene / XLPE | ≈ 2.3 | Power and coaxial cable insulation |
| Paper (dry / impregnated) | 2 – 4 | Paper capacitors, transformer windings | |
| PVC | 3 – 5 | LV wiring insulation | |
| SiO₂ (silicon dioxide) | 3.9 | MOSFET gate oxide, IC insulation | |
| FR-4 (glass-epoxy) | ≈ 4.4 | Printed circuit boards | |
| Mica, porcelain, glass | 4 – 8 | Capacitors, insulators, bushings | |
| Barium titanate (BaTiO₃) | 1000 – 10 000 | Ceramic (MLCC) capacitors, piezo/ferroelectric devices |
Water (εr ≈ 80) is a strong dielectric but a poor insulator because of dissolved ions — moisture is the main enemy of insulation.
8. Applications
- Capacitors: ceramic, mica, paper, polypropylene film, and electrolytic (thin Al₂O₃ or Ta₂O₅ oxide layer).
- Power equipment insulation: transformer oil and pressboard, XLPE cables, porcelain and polymer insulators, SF₆ in GIS.
- Electronics: PCB substrates, gate oxides (SiO₂ and high-k HfO₂), microwave substrates.
- Special dielectrics: piezoelectric quartz (oscillators), ferroelectric BaTiO₃, electrets (microphones), pyroelectric sensors.
9. Solved Problems
Problem 1. A parallel-plate capacitor has plate area 0.01 m² and separation 1 mm. Find C with air and with a dielectric of εr = 5.
- C0 = ε0A/d = 8.854 × 10⁻¹² × 0.01 / 0.001 = 88.5 pF
- C = εrC0 = 5 × 88.5 = 442.7 pF
Problem 2. Find the polarization in a dielectric of εr = 5 in a field of 10⁶ V/m.
P = ε0(εr − 1)E = 8.854 × 10⁻¹² × 4 × 10⁶ = 35.4 µC/m²
Problem 3. A cable has a capacitance of 0.5 µF per phase and tan δ = 0.002. Find the dielectric loss per phase on an 11 kV, 50 Hz system.
- Vph = 11 000/√3 = 6351 V; ω = 314.16 rad/s
- P = ωCV² tan δ = 314.16 × 0.5 × 10⁻⁶ × 6351² × 0.002 ≈ 12.7 W per phase
10. Practice MCQs (click to see answer)
1. The dielectric constant of vacuum is: (a) 0 (b) 1 (c) 8.854 × 10⁻¹² (d) ∞
2. Which polarization exists in all dielectrics? (a) Ionic (b) Orientation (c) Electronic (d) Space-charge
3. Orientation polarization ______ with increase in temperature. (a) Increases (b) Decreases (c) Remains constant (d) Becomes infinite
4. Dielectric strength of air is approximately: (a) 3 kV/mm (b) 30 kV/mm (c) 300 V/mm (d) 3 V/mm
5. Dielectric loss is proportional to: (a) tan δ (b) sin δ only (c) 1/ω (d) 1/V²
6. When a dielectric with εr = 4 replaces air in a capacitor, capacitance becomes: (a) 1/4 (b) Same (c) 4 times (d) 16 times
7. The relation between polarization and electric field is: (a) P = ε0εrE (b) P = ε0(εr − 1)E (c) P = E/ε0 (d) P = χe/E
8. As frequency increases, the dielectric constant generally: (a) Increases (b) Decreases (c) Stays the same (d) Becomes negative
9. The gas used in modern high-voltage circuit breakers is: (a) CO₂ (b) N₂ (c) SF₆ (d) H₂
10. Breakdown caused by heat generated from dielectric loss is called: (a) Intrinsic (b) Thermal (c) Electromechanical (d) Avalanche
11. Insulation class F corresponds to a maximum temperature of: (a) 105 °C (b) 130 °C (c) 155 °C (d) 180 °C
11. বাংলায় দ্রুত রিভিশন
- ডাইইলেকট্রিক: অন্তরক পদার্থ যা বৈদ্যুতিক ক্ষেত্রে পোলারাইজড হয় এবং বৈদ্যুতিক শক্তি সঞ্চয় করতে পারে।
- ডাইইলেকট্রিক ধ্রুবক εr = C/C₀; ক্যাপাসিট্যান্স εr গুণ বাড়ে। ডাইইলেকট্রিক শক্তি = ভাঙন ছাড়া সর্বোচ্চ ক্ষেত্র (বাতাস ≈ ৩ kV/mm)।
- পোলারাইজেশনের ধরন: ইলেকট্রনিক (সব পদার্থে, দ্রুততম), আয়নিক, অরিয়েন্টেশন/ডাইপোলার (তাপমাত্রা বাড়লে কমে), স্পেস-চার্জ (ধীরতম)।
- কম্পাঙ্ক বাড়লে εr কমে, কারণ ধীর প্রক্রিয়াগুলো সাড়া দিতে পারে না।
- ডাইইলেকট্রিক লস P = ωCV² tanδ; tanδ বাড়লে বোঝা যায় ইনসুলেশনে আর্দ্রতা বা বার্ধক্য।
- ব্যবহার: ক্যাপাসিটর, ক্যাবল (XLPE), ট্রান্সফরমার অয়েল, SF₆ সার্কিট ব্রেকার, PCB।
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References: A. J. Dekker, Electrical Engineering Materials; C. L. Wadhwa, High Voltage Engineering; IEC 60156 (insulating liquids – breakdown voltage). Images and animations: original work by Totalecer.