Capacitors Concept Page - 1

Definition

Capacity of Accumulator

The capacity of Accumulator is measured by the quantity of charge which can be obtained from the cell before discharging the latter.
It is given by,
1 Ampere Hour = 1 Ampere * Hour
                     =1ampere×3600second$=1ampere\times 3600second$
                      =3600Coulomb$=3600Coulomb$
If the capacity of cell is 40 ampere-hour, it means that 1 ampere current can be drawn from the given cell for 40 hours or 0.4 ampere for 100 hours.
Small currents should be drawn for long duration. If the large is drawn then cell may stop working.

Formula

Capacitance of parallel plate capacitor

We know that C=QΔV$C={\displaystyle \frac{Q}{\mathrm{\Delta }V}}$
But Q=σA$Q=\sigma A$ and ΔV=Ed$\mathrm{\Delta }V=Ed$
putting these values in capacitance formula we get
C=ϵoAd$C={\displaystyle \frac{{ϵ}_{o}A}{d}}$
Where, A = Area of plate, d = Distance between capacitor plates

Definition

Electrical capacitance of a conductor

Capacitance is the constant of proportionality relating charge to the potential difference between the conductors in a capacitor.
Q=CV$Q=CV$
C=Q/V$C=Q/V$
where C$C$ is the capacitance, Q$Q$ is the charge contained and V$V$ is the potential difference.
The SI Unit of capacitance isCoulombVolt${\displaystyle \frac{Coulomb}{Volt}}$ or Common unit is Farad.1CoulombVolt=1Farad$1{\displaystyle \frac{Coulomb}{Volt}}=1Farad$

Definition

Capacitance

The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required

Definition

Capacitor and Capacitance

A capacitor is combination of 2 conductors which are electrically isolated from each other as well as from their surroundings.
The capacitance C is defined as : qV${\displaystyle \frac{q}{V}}$
Where q = Charges on plates/conductors
V = potential difference across the plates

Definition

Capacitors and their examples

A capacitor is a system of two conductors separated by an insulator used to store electrical energy temporarily in an electric field. For example, on printed circuit boards two wires running parallel to each other on opposite sides of the board form a capacitor. 

Example

Moving dielectric slab

A capacitor is formed of two square plates, each of dimensions a$a$ , separation d$d$, connected to a battery. There is a dielectric medium of permittivity between the plates. The dielectric medium is pulled out at speed x˙$\dot{x}$ . Calculate the current in the circuit as the battery is recharged.

When the dielectric slab is moved a distance x$x$, the capacitance is
εa(a−x)d+ε0axd=εa2−(ε−ε0)axd${\displaystyle \frac{\epsilon a(a-x)}{d}}+{\displaystyle \frac{{\epsilon }_{0}ax}{d}}={\displaystyle \frac{\epsilon a^2-(\epsilon -{\epsilon }_0)ax}{d}}$
The charge held by the capacitor is then
Q=[εa2−(ε−ε0)axd]V$Q=[{\displaystyle \frac{\epsilon a^2-(\epsilon -{\epsilon }_0)ax}{d}}]V$
If the dielectric is moved out at speed x˙$\dot{x}$ , the charge held by the capacitor will increase at a rate
Q˙=−(ε−ε0)ax˙Vd$\dot{Q}={\displaystyle \frac{-(\epsilon -{\epsilon }_0)a\dot{x}V}{d}}$

Definition

Parallel plate capacitor

A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. 

Definition

Factors affecting capacitance

The capacitance C$C$ depends only on:
1. The shape and size of capacitor plates - Geometric configuration
2. The distance between 2 plates - Separation distance
3. The medium present between 2 plates

Definition

Potential difference between the plates of a parallel plate capacitor

For a uniform electric field, the potential difference between the plates of a capacitor(for air in between) is  :
V=Ed=QdAϵ0

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