Dielectric Strength

      We know that,  E = V/d

      So, as the voltage on the capacitor is increased with a given thickness (d) or the thickness (d) is reduced with a given voltage (V), the electric intensity E increases.

      This intensity represents the force exerted on the charge on the molecules or the dielectric material.

      As E is increased, the centre of the positive charges is pushed in the direction of E and centre of the negative charges in the opposite direction.

      Now, every dielectric medium has its capacity to withstand the increasing E. If the applied voltage and hence E is increased beyond a certain limit, then forces on the molecules become sufficiently large. The electrons break away from the molecules causing ionization and free charges.

      The material then conducts due to ionization and the charge recombine, thereby vanish from the capacitor plates. The capacitor can no more hold the charge and is said to be breakdown. The dielectric medium is said to be punctured and becomes useless from using it as a dielectric.

      The ability of an insulating medium to resist its breakdown when a voltage is increased across it, is called its dielectric strength.

      This depends upon the temperature of the material and presence of air pockets and imperfections in the molecules arrangement of that material. It is generally expressed in kV/cm of kV/mm.

Note: The voltage at which the dielectric medium of the capacitor breakdown is known as breakdown voltage of the capacitor.

      The factors affecting the dielectric strength are,

1. Temperature

2. Type of material

3. Size, thickness and shape of the plates.

4. Presence of air pockets in the material.

5. Moisture content of the material.

6. Molecules arrangement of the material.

      Dielectric strength and dielectric constants of some materials are quoted below from published literature.

     The dielectric strength varies as thickness of dielectric material hence the range of values are given in the table . the value indicates that if material is subjected to electric field more than specified dielectric strength then it will breakdown.

1.1 Dielectric Leakage and Losses

      If there is no leakage of current in the dielectric and the insulation is perfect, then the charge on the capacitor plates can be held on for hours.

      The fact however remains that the insulation resistance of most of the dielectric materials is only of the order of megaohms and hence charge on the capacitor leaks leaks away through the insulating material in a few minutes.

Note: In any case, it is dangerous to touch a charge capacitor even after it is disconnect from the supply.

      In case of d.c. a practical capacitor is considered to be a charge strong device in parallel with a leakage resistance(R) as shown in the Fig 2.

     Further, when the voltage applied to the capacitor is alternating, due to molecular friction of dipoles created in the material, the value of R becomes frequency dependent. The loss due to molecular friction is called dielectric loss.

Capacitance of a Parallel Plate Capacitor

      Consider a parallel plate plate capacitor, fully charged as shown in the Fig 1.

      The area of each plate X and Y is say A m² and plates are separated by distance 'd'.

      The relative permittivity of the dielectric used in between is say ε_r.

      Let Q be the charge accumulated on plate X, then the flux passing through the medium is Ψ = Q.

      The electric field intensity.

Note: when the capacitor is fully charged, the potential difference across it is equal to the voltage applied to it.

Relation between Charge and Applied Voltage

      AS seen earlier, the charge on capacitor plates depends on the applied voltage. Let 'V' be the voltage applied to the capacitor and 'Q' be the charge accumulated on the capacitor plates, then mathematically, it can be written as,

      The constant of proportionality 'C' is called capacitance of the capacitor, defined earlier.

      From the above expression, the capacitance is defined as the ratio of charge acquired to attain the potential difference between the plates. It is the charge required per unit potential difference. It is measured in unit farads.

      One farad capacitance is defined as the capacitance of a capacitor which requires a charge of one coulomb to establish a potential difference of one volt between its plates.

      The capacitance is symbolically denoted as shown in the Fig 1.

      For practical use, the farad is too large unit and hence, micro farad (µF), nano farad (nF) and pico farad (Pf) are commonly used.

Action of a Capacitor

      Consider a capacitor formed by two flat metal plates X and Y, facing each other and separated by an air gap or other insulating material used as a dielectric medium. There is no electrical contact or connection between them. Such a capacitor is called parallel plate capacitor.

      Consider a circuit in which such a capacitor across a battery with the help of a switch 'S' and a galvanometer 'G' in series. The arrangement is shown in the Fig 1.

      Let us see what happens when the switch 'S' is closed. As soon as the switch 'S' is closed, the positive terminal of the battery attracts some of the free electrons from the plate 'X' of the capacitor. The electrons are then pumped from positive terminal of the battery to the negative terminal of the battery due to e.m.f. of the battery. Now, negative terminal and electrons are repelled by the negative terminal to the plate 'Y' of the capacitor.

      The action is shown in Fig 2. 

  

      So, plate 'X' become positively charged while plate 'Y' becomes negatively charged. The flow of electrons constitutes a current, in the direction opposite to the flow of electrons. This is the conventional current called charging current of the capacitor as shown in the Fig. this can be experienced from the momentary deflection of the galvanometer 'G'. Because of this, there builds a potential difference across 'X' and 'Y'. There builds an electric field between the two fields.

      But this potential difference across the plates, acts as a counter e.m.f. and starts opposing the movement of the electrons. The magnitude of this potential difference is proportional to the charge that accumulates on the plates. When this potential difference becomes equal to the battery e.m.f., the flow of electrons ceases.

      If under such condition, the battery is disconnected then the capacitor remains in the charged condition, for a long time. It stores an electrical energy and can be regarded as a reservoir of electricity. Now, if a conducting wire is connected across the two plates of capacitor, with the galvanometer in series, then galvanometer shows a momentary deflection again but in the opposite direction.

      This is due to the fact that electrons rush back to plate X from plate Y through the wire. So, there is a rush of current through the wire. This is called discharging current of a capacitor. Thus, the energy stored in the capacitor is released and is dissipated in the form of the heat energy in the resistance of the wire connected.

      The direction of the conventional current is always opposite to the flow of electrons. If the voltage of the battery is increased, the deflection of the galvanometer also increases the time of charging and discharging.

Note: so, charge on the capacitor is proportional to the voltage applied to it.