CBSE Class 12th Physics Notes: Electrostatic Potential and Capacitance (Part ‒ II)

Important revision notes of Chapter 2 - Electrostatic Potential and Capacitance are available in this article. Important concepts related to electrostatic potential are already covered in part I, in part II we will mainly focus on concepts related to dielectric and electric capacitance.

•     Dielectrics

•     Types of dielectrics

•     Dielectric Polarization

•     Capacitor

•     Capacitance of a Capacitor

•     Capacitance of an Isolated Conducting Sphere

•     Parallel Plate Capacitor and Its Capacitance

•     Combination of Capacitors

•     Effect of Conductors in Capacitor

•     Effect of Dielectrics in Capacitor

•     Energy Stored in Capacitor

•     Total Energy of the combination of capacitors

•     Energy Density or Energy per Unit Volume

•     Common Potential of charge capacitors

•     Energy dissipated when two charged capacitors are connected

Dielectrics:

Dielectrics are non-conducting substances. In contrast to conductors, they have no (or negligible number of) charge carriers.

Types of dielectrics:

Dielectrics are of two types:

(i) Non-Polar Dielectrics: When the centre of positive charge coincides with the centre of negative charge in a molecule, e.g., Nitrogen, Oxygen, CO₂ etc.

(ii) Polar Dielectrics: When the centre of positive and negative charges do not coincide because of the asymmetric shape of the molecules, e.g., NH₃, HCl etc.

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Dielectric Polarization:

In a dielectric, this free movement of charges is not possible. It turns out that the external field induces dipole moment by stretching or re-orienting molecules of the dielectric. The collective effect of all the molecular dipole moments is net charges on the surface of the dielectric which produce a field that opposes the external field. Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field. It only reduces it. The extent of the effect depends on the nature of the dielectric.

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Capacitor:

It is an arrangement of primarily two conductors for storing large amount of electric charge.  

Capacitance of a Capacitor:

Capacitance (C) of a capacitor is defined as ratio of charge (Q) given to the potential difference (V) applied across the conductors, i.e., C = Q/V.

The SI unit of capacitance is farad (F).

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Capacitance of an Isolated Conducting Sphere:

The capacitance (C) of an isolated conducting sphere of radius (r) is given by C = 4 π ∈_o r.

Parallel Plate Capacitor and Its Capacitance:

A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.  The two plates have charges Q and –Q.

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Parallel plate capacitor is an arrangement of two large metal plates of area A each kept parallel to each other at a distance d apart. If the space between the plates is vaccum (or air) then the capacitance of such an arrangement is given by,

Combination of Capacitors

We can combine several capacitors of capacitance C₁, C₂,…, C_n to obtain a system with some effective capacitance C. The effective capacitance depends on the way the individual capacitors are combined. Two simple possible ways are:

Capacitors in Series:

In series arrangement the magnitude Q of charge on each plate is same

Capacitors in Parallel

In parallel arrangement the potential difference across the each capacitor will remain same.

C_Equivalent = C₁ + C₂ + C₃ . . . + C_n

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Effect of Conductors in Capacitor

When a parallel plate capacitor is partially filled with a metallic slab of thickness t < d, its capacitance will be:

Effect of Dielectrics in Capacitor

When a dielectric slab of dielectric constant K having thickness t < d is placed between the plates of parallel plate capacitor.

The capacitance of the capacitor will be,

Energy Stored in Capacitor

Energy stored (U) in capacitor (C) charged to a potential difference V is given as,

Total Energy of the combination of capacitor:

Series combination:

Parallel combination:

Energy Density or Energy per Unit Volume:

The energy density or energy stored per unit volume of a charged capacitor is given by

Common Potential of charged capacitors

If C₁and C₂ are capacitors charged to potentials V₁ and V₂ respectively. These capacitors are connected by a conducting wire, charges flow from higher potential to lower potential. This flow of charge will continue till their potentials become equal. There will no charge is lost in sharing and their common potential is given by,

Energy dissipated when two charged capacitors are connected

If U₁ is the total energy before sharing of charges and U₂ is total energy after sharing of charges then,

CBSE Class 12th Physics Notes: Electrostatics Potential and Capacitance (Part - I)