Capacitance Formula
Reference for capacitance: C = Q/V, parallel plate C = e0*A/d, and energy E = 0.5CV2.
Covers series, parallel, RC time constants, and dielectrics.
The Formulas
Capacitance: C = Q / V
Parallel Plate: C = ε₀ × A / d
Energy Stored: E = ½ × C × V²
Parallel Plate: C = ε₀ × A / d
Energy Stored: E = ½ × C × V²
Capacitance measures a capacitor's ability to store electric charge. A larger capacitance means more charge can be stored at the same voltage.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| C | Capacitance | Farads (F) |
| Q | Charge stored | Coulombs (C) |
| V | Voltage across the capacitor | Volts (V) |
| ε₀ | Permittivity of free space (8.854 × 10⁻¹² F/m) | F/m |
| A | Area of each plate | m² |
| d | Distance between plates | m |
| E | Energy stored | Joules (J) |
Example 1
A capacitor stores 0.006 C at 12 V. What is the capacitance?
C = Q / V = 0.006 / 12
= 0.0005 F = 500 μF
Example 2
How much energy does a 100 μF capacitor store at 50 V?
E = ½ × C × V² = 0.5 × 0.0001 × 50²
= 0.5 × 0.0001 × 2500
= 0.125 J
When to Use It
Use the capacitance formula when:
- Designing electronic circuits with capacitors
- Calculating energy stored in capacitor banks
- Analyzing timing circuits (RC circuits)
- Understanding camera flashes, defibrillators, and other charge-discharge devices
Key Notes
- One Farad is an enormous capacitance — practical capacitors range from picofarads (pF, 10⁻¹²) in radio circuits to thousands of microfarads (μF, 10⁻⁶) in power supplies; the gap from pF to F spans twelve orders of magnitude
- Capacitors in series combine as 1/C_total = 1/C₁ + 1/C₂ + … (like resistors in parallel); in parallel, C_total = C₁ + C₂ + … — this is the opposite of resistor combinations and a common exam trap
- Inserting a dielectric material (ceramic, mica, polymer) between the plates multiplies capacitance by the relative permittivity κ: C = κε₀A/d — κ ranges from 2 (PTFE) to over 10,000 (some ceramics), which is why ceramic capacitors are so compact
- The RC time constant τ = RC gives the time for a capacitor to charge to 63% (or discharge to 37%) of its final value; after 5τ the capacitor is considered fully charged — used in timing circuits, filters, and debounce logic