Capacitor
A capacitor is a passive electronic component that stores electrical energy in an electric field between two conducting plates separated by an insulating material called a dielectric. The capacitance (measured in farads) quantifies how much charge a capacitor stores per unit voltage. Capacitors are widely used in circuits for filtering, energy storage, timing, and coupling or decoupling signals.
Key Formula
C = Q / V = (epsilon_0 × epsilon_r × A) / d
LaTeX: C = \dfrac{Q}{V} = \dfrac{\varepsilon_0 \varepsilon_r A}{d}
| Symbol | Meaning | Unit |
|---|---|---|
| C | Capacitance | Farad (F) |
| Q | Charge stored | Coulomb (C) |
| V | Voltage across capacitor | Volt (V) |
| ε₀ | Permittivity of free space (8.85 × 10⁻¹²) | F/m |
| εᵣ | Relative permittivity of dielectric | Dimensionless |
| A | Area of each plate | Square metre (m²) |
| d | Separation between plates | Metre (m) |
Worked Example
Problem
A parallel-plate capacitor with plate area 0.02 m² and plate separation 0.5 mm uses a dielectric with εᵣ = 4. Find its capacitance and the charge stored at 100 V.
Solution
Step 1: d = 0.5 mm = 5 × 10⁻⁴ m. Step 2: C = (ε₀ × εᵣ × A) / d = (8.85 × 10⁻¹² × 4 × 0.02) / (5 × 10⁻⁴). Numerator: 8.85 × 10⁻¹² × 4 × 0.02 = 7.08 × 10⁻¹³. C = 7.08 × 10⁻¹³ / 5 × 10⁻⁴ = 1.416 × 10⁻⁹ F ≈ 1.42 nF. Step 3: Q = C × V = 1.416 × 10⁻⁹ × 100 = 1.416 × 10⁻⁷ C.
Answer
C ≈ 1.42 nF; Q ≈ 142 nC
Common Capacitor Types and Their Characteristics
| Type | Capacitance Range | Voltage Rating | Typical Application |
|---|---|---|---|
| Ceramic | 1 pF – 100 µF | Up to 5 kV | Decoupling, RF circuits |
| Electrolytic (Al) | 1 µF – 100,000 µF | Up to 500 V | Power supply filtering |
| Film (polyester) | 1 nF – 100 µF | Up to 2 kV | Timing, audio circuits |
| Tantalum | 0.1 µF – 1000 µF | Up to 50 V | Portable electronics |
| Supercapacitor | 1 F – 10,000 F | Up to 5 V | Energy storage, EVs |
Interactive Tools
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Related Terms
Inductor
An inductor is a passive electrical component, typically a coil of wire, that stores energy in a magnetic field when current flows through it and opposes changes in current through electromagnetic induction. Its inductance (measured in henries) quantifies the ratio of the magnetic flux linkage to the current. Inductors are essential in filters, oscillators, transformers, and switching power supplies.
Electric Current
Electric current is the rate of flow of electric charge through a conductor, measured as the amount of charge passing a cross-section per unit time. It is the fundamental quantity that drives electrical circuits and powers all electronic devices. In metallic conductors, current arises from the drift of free electrons, while in electrolytes and plasma it involves the movement of ions.
Electrical Power
Electrical power is the rate at which electrical energy is transferred or consumed by a device, equal to the product of the voltage across it and the current through it. It determines how quickly a device does work or dissipates energy as heat, light, or motion. Power is critical in the design of electrical systems, from household appliances rated in watts to large industrial generators rated in megawatts.
From Latin "capacitas" meaning "the ability to hold" or "capacity", derived from "capere" (to hold). The device was originally called a "condenser" in the 18th century; "capacitor" became standard in the 20th century. The unit Farad honours British physicist Michael Faraday (1791–1867).