Physics

# Capacitance

Electric capacitors:

• Capacitors are charge storing devices.
• Capacitance of a capacitor is the ratio of charge(Q) given and the potential (V) to which it is raised.
• The SI unit of capacitance is Farad and its CGS unit is Stat farad.
• The dimensional formula of electrical capacitance is []
• The capacitance of spherical conductor is : where R is the radius of the conductor.
• The capacitance of concentric spherical capacitor is: where 'b' is the radius of outer sphere and 'a' is the radius of inner sphere.
• The capacitance of the earth is farad = 712F

Parallel plate capacitor:

• It is the simplest capacitor where two conductors are separated by insulator/dielectric.
• The capacitance is given by: where A is the area of each plate, d is distance between them and K is the dielectric constant.
• The capacitance does not depend on material of plates, charge given to plates, potential difference between the plates.
• The value of C depends on size, shape and relative position of the two coatings of the capacitor. It also depends on the medium separating the two coatings.
• When the space between the plates is partially filled with medium of dielectric constant K and thickness t then capacitance becomes:

Combination of capacitors:

• Series combination:
• Parallel combination:

Dielectric in series:

• The capacitance of a parallel plate capacitor having a number of slabs of thickness and dielectric constants respectively in between is:

Dielectric in parallel:

• When a number of dielectric slabs of same thickness(d) and different areas of cross section having dielectric constants respectively are placed between the plates of a parallel plate capacitor, its capacitance is given by:

Energy stored in a capacitor:

Energy density: where E is the electric field intensity

Some important relations:

1. Regrouping of capacitors:
• When like plates are joined:

Loss in energy =

• When unlike plates are joined:

Loss in energy =

1. For charging a capacitor:

1. For discharging a capacitor: