Capacitance Calculator

Calculate capacitance from plate area and separation, analyze dielectric effects, and compute energy storage. Essential for electronics design and physics applications.

**Parallel Plate Capacitor:** C = ε₀ × εᵣ × A / d Where: • C = Capacitance (F) • ε₀ = Permittivity of free space = 8.854×10⁻¹² F/m • εᵣ = Relative permittivity (dielectric constant) • A = Plate area (m²) • d = Plate separation (m) **Charge-Voltage Relationship:** C = Q / V Where: • Q = Charge (C) • V = Voltage (V) **Energy Stored:** U = ½ × C × V² U = ½ × Q² / C U = ½ × Q × V **Series Combination:** 1/C_total = 1/C₁ + 1/C₂ + 1/C₃ + ... **Parallel Combination:** C_total = C₁ + C₂ + C₃ + ... **Common Dielectric Constants:** • Vacuum/Air: εᵣ = 1 • PTFE/Teflon: εᵣ = 2.1 • Paper: εᵣ = 3.7 • Glass: εᵣ = 5-10 • Ceramic: εᵣ = 100-10,000
**Example 1 (Air Capacitor):** Plate area = 0.01 m² (100 cm²) Separation = 0.001 m (1 mm) Dielectric = Air (εᵣ = 1) • C = 8.854×10⁻¹² × 1 × 0.01 / 0.001 • C = 8.854×10⁻¹¹ F = 88.54 pF **Example 2 (Paper Dielectric):** Area = 0.01 m², Separation = 0.0001 m (0.1 mm) Dielectric = Paper (εᵣ = 3.7) • C = 8.854×10⁻¹² × 3.7 × 0.01 / 0.0001 • C = 3.28×10⁻⁹ F = 3.28 nF = 3280 pF **Example 3 (Effect of Distance):** Area = 0.02 m², εᵣ = 5 Distance 1 mm: C = 885 pF Distance 0.5 mm: C = 1770 pF (doubled!) Distance 2 mm: C = 442.5 pF (halved!) **Example 4 (From Charge and Voltage):** Charge = 100 μC = 1×10⁻⁴ C Voltage = 50 V • C = Q/V = 1×10⁻⁴ / 50 • C = 2×10⁻⁶ F = 2 μF • Energy = ½ × 2×10⁻⁶ × 50² = 0.0025 J = 2.5 mJ **Example 5 (Flash Capacitor Energy):** Capacitance = 1000 μF = 0.001 F Voltage = 300 V • U = ½ × 0.001 × 300² • U = 45 J (enough to power LED flash!) • Q = 0.001 × 300 = 0.3 C **Example 6 (Ceramic Capacitor):** Area = 0.0001 m² (1 cm²) Separation = 0.00001 m (10 μm, very thin!) Dielectric = Ceramic (εᵣ = 1000) • C = 8.854×10⁻¹² × 1000 × 0.0001 / 0.00001 • C = 8.854×10⁻⁸ F = 88.54 μF (very high!) **Example 7 (Supercapacitor Comparison):** 1000 μF at 100 V: U = ½ × 0.001 × 100² = 5 J 1 F at 10 V: U = ½ × 1 × 10² = 50 J 100 F at 2.7 V: U = ½ × 100 × 2.7² = 364.5 J **Example 8 (Series vs Parallel):** Two 100 μF capacitors: • Series: 1/C = 1/100 + 1/100, C = 50 μF • Parallel: C = 100 + 100 = 200 μF

What is capacitance?

Capacitance is the ability to store electric charge. A capacitor with capacitance C stores charge Q = CV when voltage V is applied. Measured in farads (F), where 1 F = 1 coulomb per volt. Typical capacitors range from picofarads (pF) to millifarads (mF).

What is the parallel plate capacitor formula?

For a parallel plate capacitor: C = ε₀εᵣA/d, where ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space, εᵣ is the relative permittivity (dielectric constant), A is plate area (m²), and d is separation distance (m).

What is a dielectric material?

A dielectric is an insulating material placed between capacitor plates. It increases capacitance by a factor of εᵣ (relative permittivity). Common dielectrics: air (εᵣ ≈ 1), paper (εᵣ ≈ 3.7), glass (εᵣ ≈ 5-10), ceramic (εᵣ ≈ 100-10,000).

How does distance affect capacitance?

Capacitance is inversely proportional to plate separation: C ∝ 1/d. Halving the distance doubles the capacitance. Closer plates create stronger electric fields and store more charge at the same voltage.

How does area affect capacitance?

Capacitance is directly proportional to plate area: C ∝ A. Doubling the area doubles the capacitance. Larger plates can store more charge because there's more surface for charge distribution.

What is permittivity ε₀?

Permittivity of free space ε₀ = 8.854×10⁻¹² F/m (farads per meter) is a fundamental constant describing how electric fields interact with vacuum. It appears in Coulomb's law and capacitance formulas, relating charge to electric field.

How do I calculate energy stored in a capacitor?

Energy stored is U = ½CV² = ½Q²/C = ½QV, where C is capacitance, V is voltage, and Q is charge. This energy is stored in the electric field between the plates.

What are typical capacitance values?

Ceramic capacitors: 1 pF - 10 μF, Electrolytic capacitors: 1 μF - 10,000 μF, Supercapacitors: 1 F - 5000 F, Variable capacitors (tuning): 10-500 pF, Power factor correction: 1-100 μF, Camera flash: 100-1000 μF.

How do capacitors combine in series and parallel?

In parallel: C_total = C₁ + C₂ + C₃... (capacitances add). In series: 1/C_total = 1/C₁ + 1/C₂ + 1/C₃... (reciprocals add). Parallel increases capacitance; series decreases it.

What is dielectric breakdown?

Dielectric breakdown occurs when the electric field exceeds the dielectric strength, causing the insulator to conduct. For air: ~3×10⁶ V/m. Breakdown permanently damages capacitors. Voltage rating must exceed maximum operating voltage.

Why use dielectric materials instead of vacuum?

Dielectrics increase capacitance (higher εᵣ), increase breakdown voltage (higher dielectric strength), and provide mechanical support. A ceramic dielectric (εᵣ = 1000) gives 1000× more capacitance than vacuum in the same space!

What is the difference between capacitance and capacity?

Capacitance (measured in farads) is the ability to store charge per volt (C = Q/V). Capacity often refers to total energy storage or charge storage capability. Capacitance is an intrinsic property; capacity depends on operating conditions.

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