Capacitance Formula
Learn the capacitance formula C = Q/V and how capacitors combine in series and parallel.
Essential for circuit design and energy storage.
The Formula
Capacitance measures a capacitor's ability to store electric charge.
A higher capacitance means the component can store more charge at a given voltage.
The SI unit is the Farad (F), but most practical capacitors are measured in microfarads (μF), nanofarads (nF), or picofarads (pF).
Variables
| Symbol | Meaning |
|---|---|
| C | Capacitance (Farads, F) |
| Q | Stored charge (Coulombs, C) |
| V | Voltage across the capacitor (Volts, V) |
Series and Parallel Rules
Capacitors in series (total capacitance decreases):
Capacitors in parallel (total capacitance increases):
Example 1
A capacitor stores 0.006 C of charge at 12 V. What is its capacitance?
C = Q / V
C = 0.006 C / 12 V
C = 0.0005 F = 500 μF
Example 2
Two capacitors, 10 μF and 15 μF, are connected in series. What is the total capacitance?
1/C_total = 1/C₁ + 1/C₂
1/C_total = 1/10 + 1/15
1/C_total = 3/30 + 2/30 = 5/30
C_total = 30/5
C_total = 6 μF
When to Use It
Use the capacitance formula when you need to:
- Determine how much charge a capacitor can store
- Calculate the voltage across a charged capacitor
- Combine capacitors in series or parallel circuits
- Design timing circuits, filters, and power supplies
Energy stored in a capacitor is E = ½CV².
Note that capacitor combination rules are the opposite of resistor rules: capacitors in parallel add directly, while those in series use the reciprocal formula.
Key Notes
- Fundamental relationship: Q = CV: Charge stored Q (coulombs) equals capacitance C (farads) times voltage V. Farads are enormous in practice — most capacitors are measured in microfarads (µF), nanofarads (nF), or picofarads (pF).
- Parallel plate capacitor: C = εA/d: Capacitance increases with plate area A and permittivity ε, and decreases with plate separation d. Dielectric materials between the plates increase ε (and therefore C) compared to vacuum — this is why ceramic and electrolytic capacitors can achieve large capacitance in small packages.
- Capacitive reactance: X_C = 1/(2πfC): At DC (f = 0), reactance is infinite — capacitors block DC. At high frequencies, reactance approaches zero — capacitors pass AC easily. This makes capacitors ideal for coupling AC signals while blocking DC bias.
- Series vs parallel: Capacitors in parallel: C_total = ΣCᵢ (plates effectively add). In series: 1/C_total = Σ(1/Cᵢ) — total capacitance is less than any individual. This is the opposite of resistors and a common source of errors.
- Applications: Capacitors are used in power supply smoothing (filter ripple), timing circuits (RC time constant τ = RC), DRAM memory cells, touchscreens (capacitive sensing), motor start/run circuits, audio crossovers, and defibrillators (storing then releasing high energy).