Basic Definition
A capacitor is an electronic component that stores electrical energy in an electric field.
It consists of two conductive plates separated by an insulating material (dielectric).
When a voltage is applied across the plates, positive and negative charges accumulate on opposite plates, creating a potential difference and storing energy.
The amount of charge a capacitor can store per unit voltage is called its capacitance, represented by \(C\), and is measured in farads (F).
The potential difference (V) is directly proportional to the electric field hence we can say,
\(\begin{array}{l}Q\propto V\end{array} \)
\(\begin{array}{l}Q=CV\end{array} \)
Capacitance equals charge stored per unit voltage.
\(\begin{array}{l}C=\frac{Q}{V}\end{array} \)
Where:
- C = Capacitance in farads (F)
- Q = Charge in coulombs (C)
- V = Voltage in volts (V)
Units of Capacitance
The SI unit of capacitance is the farad (F). Other common units include microfarads (μF), nanofarads (nF), and picofarads (pF).
- 1 mF (millifarad) = 10−3 F
- 1 μF (microfarad) =10−6 F
- 1 nF (nanofarad) = 10−9 F
- 1 pF (picofarad) = 10−12 F
Formula
Some common formula related to capacitance
Energy Stored in a Capacitor
\(E = \frac{1}{2} C V^2\)
Capacitance of a Parallel Plate Capacitor
\(C = \varepsilon_0 \varepsilon_r \frac{A}{d}\)
where
- A = plate area,
- d = distance between plates,
- \(\varepsilon_0\) = permittivity of free space,
- \(\varepsilon_r\) = relative permittivity of dielectric.
Equivalent Capacitance in Series
\(\frac{1}{C_\text{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \ldots\)
Equivalent Capacitance in Parallel
\(C_\text{eq} = C_1 + C_2 + C_3 + \ldots\)
Voltage Across Each Capacitor in Series
\(V_n = \frac{Q}{C_n}\)
Energy Density in an Electric Field
\(u = \frac{1}{2} \varepsilon E^2\)
where (E) is the electric field intensity.
Capacitive Reactance (AC Circuits)
\(X_C = \frac{1}{2 \pi f C}\)
where (f) is frequency in hertz.
Time Constant in an RC Circuit
\(\tau = R C\)
It represents the time taken for the voltage or charge to change by about 63%.