Capacitors

A capacitor is a device used to store electrical energy in the form of an electrostatic field. It consists of two conducting plates separated by an insulating material known as a dielectric.

Functions and Uses of Capacitors

• Energy Storage: Storing electrical energy for quick release.
• Tuning: Used in radio and TV receiver circuits for selecting specific frequencies.
• Smoothing: Converting pulsating DC from rectifiers into steady DC in power supplies.
• Blocking DC: Allowing AC to pass while blocking DC signals in electronic circuits.
• Flash Photography: Releasing stored energy rapidly to power a flash tube.

Capacitance of a Capacitor

Capacitance (C) is defined as the ratio of the charge (Q) on one of the plates to the potential difference (V) between them. The formula is: C = Q / V. The SI unit is the Farad (F). Since the Farad is a very large unit, we often use microfarads (μF), nanofarads (nF), and picofarads (pF).

Parallel Plate Capacitors

For a parallel plate capacitor, the capacitance is determined by the physical characteristics of the plates and the material between them. The capacitance is given by: C = (εο εr A) / d.

Factors Affecting Capacitance

• Area of Plates (A): Capacitance is directly proportional to the common area of the plates. (C ∝ A)
• Distance between Plates (d): Capacitance is inversely proportional to the separation distance. (C ∝ 1/d)
• Nature of Dielectric (ε): Capacitance depends on the permittivity of the material between the plates. Introducing a dielectric with a higher relative permittivity (εr) increases capacitance.

Arrangement of Capacitors

Capacitors in Series

When capacitors are connected in series, the charge (Q) on each capacitor is the same, but the total potential difference is split. The equivalent capacitance (C_T) is calculated as: 1/C_T = 1/C₁ + 1/C₂ + 1/C₃.

Capacitors in Parallel

When capacitors are connected in parallel, the potential difference (V) across each is the same, but the charge is distributed. The total capacitance is the sum: C_T = C₁ + C₂ + C₃.

Energy Stored in a Capacitor

The work done in charging a capacitor is stored as electrical potential energy (W). The formulas are:

• W = ½ QV
• W = ½ CV²
• W = ½ Q² / C