Chapter 19. Dielectric Properties – Material Science and Metallurgy

19

Dielectric Properties

19.1 INTRODUCTION

A dielectric material is an electrically insulating material (non-metallic) and it exhibits an electric dipole structure. Electrically charged positive and negative dipoles are separated on a molecular or atomic level. The properties of dielectrics are due to polarization of the substance of dielectric. Due to polarization, dielectric stores energy and makes it available when electric field is reversed.

The effectiveness of a dielectric is measured by its ability to store energy and is expressed in terms of ‘dielectric constant’. The ability of a dielectric to withstand electric field without losing its insulating property is known as ‘dielectric strength’. Because of this ability, it is used in capacitance.

A good dielectric must retain a large percentage of energy stored in it, when the field is reversed. Dielectrics are characterized by high resistivity, negative temperature coefficient and a large insulation resistance.

Dielectrics with high dielectric constant are extremely useful in all branches of electrical engineering. Polymers like nylon, PVC, bakelite, polyethylene and ceramics like glass, mica, porcelain and steatite are commonly used as dielectrics.

19.2 DIELECTRIC BEHAVIOUR

A dielectric material is an electrically insulating material. It exhibits or can be made to exhibit an electric dipole structure. In a dipole, there is a separation of positively and negatively charged entities at atomic or molecular level.

A dipole may be induced or created in an atom or molecule, which is electrically symmetric. In a symmetric atom, the overall spatial distribution of electrons is symmetric in relation to the positively charged nucleus as shown in Figure 19.1.

Now, all the atoms constantly vibrate and cause short-lived distortions of electrical symmetry resulting in small electric dipoles as shown in Figure 19.2. One of these dipoles can produce a displacement of electron distribution of a nearby atom or molecule, which makes second one also to become a dipole.

Figure 19.1 Electron Cloud Around Nucleus

Figure 19.2 Electric Dipoles

A dipole moment arises from net positive and negative charges of a dipole. As a result of dipole interactions with electric field, dielectric materials are used in capacitors.

When an electric field is applied across a capacitor, one plate is positively charged and the other is negatively charged, with electric field directed from positive to negative.

Capacitance, C = Q/V, where Q is the quantity of charge stored on any of the two plates and V is the voltage applied across the capacitor. Units of capacitance are coulombs per volt or Farads (F).

Consider a parallel plate capacitor as shown in Figure 19.3. There is vacuum between the two plates. Electric field V is applied between the two plates as shown in Figure 19.3.

Figure 19.3 Parallel Plate Capacitor

Capacitance of a parallel plate capacitor, C = Є0A/L, where A is the area enclosed between the two plates, L is the distance between the plates, Є0 is the permittivity of a vacuum and a universal constant = 8.85 × 10−12 F/m. Now, a dielectric medium is inserted between the two plates as shown in Figure 19.4.

Figure 19.4 Dielectric Medium Between Two Plates

   Capacitance,

C = ЄA/L,

where Є is the permittivity of a dielectric medium, which is greater than Є0.

 

   Relative permittivity,

k = Є/Є0,

which is also called as dielectric constant.

Now, k > 1 represents the increase in charge storing capacity of a dielectric medium between the plates. The ability of a dielectric to withstand electric fields without losing insulating property is known as ‘dielectric strength’.

 

   Dielectric strength,

ζ = V/L, = V/m

Dielectric constant and dielectric strength (kV/mm) for some materials are given in Table 19.1.

19.3 DIPOLE MOMENT AND POLARIZATION

An electric dipole moment, p is associated with each dipole, which is equal to the charge on each pair × separation distance between positive and negative charge as shown in Figure 19.5. If +q is the charge on one dipole element, −q is the charge on another dipole and d is the separation distance, then

 

   Dipole moment,

p = q.d

Figure 19.5 Polarization Vector, p on a Dipole

Dipole moment is a vector, p directed from negative to positive charge. In the presence of an electric field, ζ = V/L (voltage per unit distance between the capacitor plates), electric field acts on electric dipole to orient with the applied field. This phenomenon is known as ‘polarization’, which is shown in Figure 19.6. For a capacitor, surface charge density, D or the amount of charge per unit area (C/m2) is proportional to the applied electric field, ζ.

 

Table 19.1 Dielectric Constant and Dielectric Strength

Figure 19.6 Polarization: Final Dipole Alignment with the Field

In a vacuum, surface charge density, D0 = Є0ζ. In the case of a dielectric medium, charge density, D = Єζ. For a capacitor containing n plates, the capacitance, C = Є0kA (n − 1)/L, where A is the area between the plates, k is the dielectric constant, L is the separation between the plates and Є0 is the permittivity of vacuum, which is equal to 8.85 × 10−12 F/m. Sometimes, D is also known as dielectric displacement. When a dielectric is introduced and an electric field is applied, the entire solid within the plates becomes polarized.

Surface charge density on the plates of a capacitor can be represented by, D = Є0ζ + P, where P is polarization.

 

P = DЄ0ζ = ЄζЄ0ζ = ζ(ЄЄ0) = ζЄ0 (k − 1)

Units of P are the same as that of D, i.e C/m2.

Example 19.1   Sodium chloride has a polarization of 4.33 × 10−8 C/m2 in an electric field of 950 V/m. Calculate the dielectric constant k for NaCl.

Solution:

 

    Polarization,

      P

=

(k − 1) Є0ζ,

 


k − 1


=

Dielectric constant,      k = 6.15

Example 19.2   A parallel plate capacitor has an area of 7.74 × 10−4 m2, and a plate separation of 2.2 mm, across which a potential of 10 V is applied. Dielectric constant of the material is 6.02. Calculate (1) the capacitance, (2) magnitude of charge stored on each plate, (3) dielectric displacement and (4) polarization.

Solution:

Permittivity of dielectric medium,

 

 

Є

=

0 = 6.02 × 8.85 × 10−12 F/m

 

 

=

53.227 × 10−12 F/m

Area of the plate,

 

A = 7.74 × 10−4 m2

Separation,

L = 0.0022 m
  1. Capacitance,
  2. Charge stored,

     

    Q = CV = 1.874 × 10−11 × 10 = 1.874 × 10−10 C

     

  3. Dielectric displacement,
  4. Polarization,

     

     


    P


    =

     

     

    =

    2.0194 × 10−7 C/m2

19.4 POLARIZATION OF AN ELECTRIC FIELD

When an electric field is applied to a material, dipoles are induced within the atomic or molecular structure. During polarization, dipoles are aligned along the direction of the field. In addition, any permanent dipoles already present in the material are also aligned with the field.

Polarization, P = Ncqd, where Nc is the number of charge carriers, q is the electronic charge and d is the distance between the dipoles. P = qd, i.e. total electronic charge × distance between the dipoles.

There are three mechanisms that cause polarization. They are as follows:

  1. Electronic polarization
  2. Ionic polarization
  3. Orientation polarization

19.4.1 Electronic Polarization

Electronic polarization is induced in all atoms. This polarization results from the displacement of centre of the negatively charged electron cloud relative to the positively charged nucleus of the atom by an electric field. It is found in all dielectric materials and exists under an applied electric field as shown in Figure 19.7.

Figure 19.7 Electronic Polarization

19.4.2 Ionic Polarization

This polarization occurs only in ionic materials. An applied electric field acts to displace cations in one direction and anions in the opposite direction, which gives rise to a net dipole moment, pi as shown in Figure 19.8.

Dipole moment on each pair, pi = q.di, where di is the relative displacement and q is the magnitude of each dipole charge.

Figure 19.8 Ionic Polarization

19.4.3 Orientation Polarization

It is a temperature-dependent process in which hydrocarbon molecules align themselves in the direction of applied field. By increasing the temperature, the alignment becomes random. The CH3Cl molecule carrying dipole moment gets aligned in this way even without an electric field. The positive and negative charges do not coincide in this molecule.

Some materials contain natural dipoles. When a field is applied, the dipoles rotate to line up with the imposed field. When the field is removed, the dipoles remain in alignment, causing permanent polarization. Figure 19.9 shows an orientation polarization.

Figure 19.9 Orientation Polarization

19.5 FREQUENCY DEPENDENCE OF DIELECTRIC CONSTANT

In many applications, ac power is used and the applied electric field reverses direction continuously. Dielectric material is subjected to polarization by an ac electric field. With each reversal of voltage, the dipoles attempt to reorient with the field—a process that requires a finite time. Relaxation frequency is taken as the reciprocal of this minimum orientation time. A dipole cannot keep switching orientation if the relaxation frequency, fr is less than the frequency of applied voltage, fa. Under these circumstances, a dipole cannot contribute to the dielectric constant. Figure 19.10 shows dependence of k (dielectric constant) on field frequency, fa for three types of polarization, i.e. orientation, ionic and electronic.

Figure 19.10 shows that the dielectric constant, k is independent of frequency in a particular range of frequencies for a certain type of polarization, but when polarization mechanism ceases to function, there is abrupt change in the dielectric constant.

Figure 19.10 Variation of Dielectric Constant with Frequency, fa

19.6 EFFECT OF TEMPERATURE ON DIELECTRIC CONSTANT

Under increased temperature, permanent dipoles acquire greater mobility and polarize more easily giving higher value of dielectric constant, but moderately higher temperatures may cause the dielectric to breakdown and produce changes in crystal structure to a less polar condition, which greatly reduces polarization.

19.7 DIELECTRIC LOSSES

When a dielectric material is polarized in an ac electric field, some energy is dissipated as heat. The fraction of energy lost during each reversal is the dielectric loss. Energy loss is mainly due to the following factors:

  1. Current leakage: Losses due to current leakage are low if the electrical resistivity is high.
  2. Dipole friction: This occurs when reorientation of the dipoles is difficult as in complex organic molecules.
  3. At lower frequencies, losses are high because dipoles have time to move. At higher frequencies, losses are low because dipoles do not move at all.

A frequency can be purposely selected so that the dielectric materials with permanent dipoles have high dielectric loss and the materials that polarize only by electronic or ionic means have a low dielectric loss. Consequently, the permanent dipole materials heat but other materials remain cool. Figure 19.11 shows the influence of frequency on dielectric loss.

Example: Microwave ovens are used to cure many polymeric adhesives while joining two materials. Adhesive has a high loss factor but the materials to be joined have low loss factor, and the heat produced in adhesive due to dielectric loss initiates the thermosetting reaction.

Figure 19.11 Influence of Frequency on Dielectric Loss

19.8 DIELECTRIC BREAKDOWN

The voltage per unit thickness of insulating material that can be sustained by an insulating material before it breaks down is known as ‘dielectric strength’ and a good insulating material must possess high dielectric strength.

Following factors are responsible for the breakdown of a dielectric:

  1. Intrinsic breakdown: This occurs when electrons from valence band crossover forbidden gap, Eg, under the action of applied voltage and enter into conduction band. In this process, a large induction current and very high local field is created. This failure is known as Zener breakdown. Intrinsic breakdown can occur at lower voltage also if impurities are present in the dielectric material.
  2. Thermal breakdown: If the heat dissipation is poor, heat produced by electrical energy gets accumulated and the dielectric may melt. This breakdown is more severe in dc than in ac field.
  3. Electrochemical breakdown: If the leakage current increases due to larger mobility of ions at elevated temperature, the dielectric gets converted into oxides, decreasing the insulation resistance, for example, breakdown of rubber.
  4. Defect breakdown: Due to detrimental effects of moisture and pores on the surface of the dielectric material, this type of breakdown occurs. Glazing of surface may eliminate this breakdown. Fire-proof silica and high-strength mica are used to provide good surface finish.
  5. Discharge breakdown: This occurs due to the presence of gas bubbles in the solid and their collapse under the applied field. Gaseous atoms get ionized at lower potential than the solid atoms, causing deterioration.

Example 19.3   The dielectric strength of a natural rubber is 40 kV/mm at 60 Hz. Calculate the thickness of insulation on a wire carrying 25 kV to sustain breakdown.

Solution:

 

    Dielectric strength,

ζ

=

V/L = 40 kV/mm

    Voltage in wire

 

=

25 kV

    Thickness of insulation

 

=

25 × 1/40

 

 

=

0.625 mm

19.9 FERROELECTRICITY

Ferroelectricity is a result of spontaneous alignment of electric dipoles, which exhibit a strong mutual interaction. A ferroelectric crystal lacks the centre of symmetry but must contain a unique non-equivalent direction necessary for unique direction of polarization. Above Curie point of temperature, ferroelectric crystal loses its ferroelectric behaviour. This is due to the thermal vibration of a particular amplitude, which destroys an ordered array of induced ionic dipoles. Until Curie temperature, there is sharp increase in dielectric constant, but after this point the dielectric constant suddenly drops.

The most important ferroelectric materials are as follows:

  1. Rochelle salt (tetrahydrate of potassium tartrate)
  2. Barium titanate (BaTiO3)
  3. Strantium titanate (SrTiO3)
  4. KDP (potassium dihydrogen phosphate)
  5. Potassium niobate (KNbO3)
  6. Lead zirconate titanate (PbZrO3TiO3)

Whenever high dielectric constant is required, ferroelectric materials are used. When Lead zirconate titanate is used as a dielectric material for capacitors, size becomes much smaller in comparison to the capacitor made from paper or mica. Moreover, high value of electromechanical coupling constant of ferroelectrics makes them highly useful for piezoelectric transducers. But in frequency determination devices, still quartz is used. All ferroelectric materials are piezoelectric also, but not all piezoelectric materials are ferroelectrics. For example, quartz is a piezoelectric material but not a ferroelectric material. Ferroelectric lithium niobate is used as an electro-optic material, whose index of refraction is controlled by an electric field. Ferroelectrics are employed in the form of polycrystalline ceramics for most technical applications.

If a ferroelectric material is heated above its Curie temperature and then allowed to cool slowly in powerful electric field, then preferred orientation of the domains in each of the crystal is maintained. This type of material with a net permanent polarization acts like a pseudo-single crystal (Table 19.2).

 

Table 19.2 Properties of Some Ferroelectric Materials

Material Polarization (C/m2) Curie Temperature (°C)

KH2PO4

0.05
−148

BaTiO3

0.25
122

KNbO3

0.30
436

PbTiO3

0.50
490
19.10 PIEZOELECTRICITY

When a crystal is strained, an electric field is generated in it. This phenomenon is known as ‘piezoelectricity’. As a result of this field, a potential difference develops across the sample, which can be measured. The inverse effect is that an applied field produces strain in the sample, which has also been observed in a piezoelectric crystal. This piezoelectricity is very small. A field of 1000 V/cm in a quartz crystal (SiO2) produces a strain of only 10−7. Conversely, even a small strain produces enormous electric fields. The piezoelectric effect is often used to convert electrical energy into mechanical energy and vice versa. Piezoelectric crystal is used as a transducer. For example, an electric signal applied to the ends of a quartz rod generates mechanical waves in the rod. Quartz is the most commonly used piezoelectric material in transducer applications.

The microscopic origin of piezoelectricity lies in the displacement of ionic charge within the crystal. In the absence of any strain, the distribution of charge at the lattice sites is symmetric, and no electric field is present. But, when the crystal is strained, the charge is displaced. If the charge distribution is no longer symmetric, then a net polarization occurs and a concomitant electric field is developed.

19.11 DIELECTRIC MATERIALS

Most of the dielectric materials used for capacitors are classified into three categories as follows:

  1. Liquids composed of polar molecules
  2. Polymers
  3. Ceramics

All these possess permanent dipoles that move easily in an electric field and have high dielectric constant. Water has a high dielectric constant but is corrosive in nature, relatively conductive and difficult to use in capacitors. Organic oils and wax are more effective. These materials contain long-chain molecules, which serve as dipoles and are easily aligned. Often these are impregnated into papers.

In amorphous polymers, segments of chains possess sufficient mobility to cause polarization. Capacitors very often use polyesters (as Mylar), polystyrenes, polycarbonates and cellulose (paper) as dielectrics. Glass is an amorphous substance used as dielectric material.

Polymers with asymmetric chains have higher dielectric constant, even though the chains may not align easily during polarization. Polyvinyl chloride and polystyrene have dielectric strength greater than that of polyethylene. For polymers, dielectric constant lies between 2.2 and 4.0.

Barium titanate (BaTiO3), a crystalline ceramic, has a asymmetric structure at room temperature. Titanium ion is displaced slightly from the centre of the unit cell, causing the crystal to be tetragonal and permanently polarized. In ac field, there is rapid response of titanium ion to move back and forth to assure that polarization is aligned with the field. Barium titanate has extraordinarily high dielectric constant.

Ceramics provide excellent insulation because of their high dielectric strength and excellent thermal stability. Widely used ceramics are glass, alumina, quartz, mica and asbestos, which have a dielectric constant up to 12. The mineral rutile (TiO2) possesses very high values of dielectric constant.

Piezoelectric materials include titanates of barium and lead; lead zirconate (PbZrO3), ammonia dihydrogen phosphate (NH4H2PO4) and quartz. Rochelle salt (tetrahydrate of potassium phosphate), strantium titanate (SrTiO3), potassium dihydrogen phosphate (KDP) and potassium niobate (KNbO3) are ferroelectric materials. Formvar is a suitable insulating material at low-temperature applications. It is the trade name of polyvinylformal.

19.12 PRACTICAL DIELECTRICS

Solid dielectrics are the most commonly used dielectrics in electrical engineering and many solids are very good insulators also. Common examples of dielectrics are porcelain, glass and many plastics. Air, nitrogen and sulphur hexafluoride are the three most commonly used gaseous dielectrics. Following are some other examples of dielectrics:

  1. Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment.
  2. Mineral oil is extensively used in electrical transformers as a fluid dielectric and to assist in cooling. Electrical grade castor oil is used in high-voltage capacitors to prevent corona discharge and to increase capacitance.
  3. Since dielectrics resist the flow of electricity, the surface of the dielectric may retain stranded excess electrical charge. This may occur accidentally when the dielectric is rubbed (triboelectric effect). This is useful in Van de Graff generator, but destructive in electrostatic discharge.
  4. Specially processed dielectrics called ‘electrets’ may retain excess internal charge or ‘frozen in ‘polarization’. They have a semi-permanent external electric field and are the electrostatics equivalent to magnets.
  5. Some dielectrics can generate a potential difference, when subjected to a mechanical stress or strain. These materials are called ‘piezoelectric materials’.
  6. Some ionic crystals and polymer dielectrics exhibit a spontaneous dipole moment, which can be reversed by an externally applied electric field. This behaviour is called ‘ferroelectric effect’. Ferroelectric materials often have high dielectric constant, making them useful for capacitors.
KEY POINTS TO REMEMBER
  • A dielectric material is an electrically insulating material exhibiting an electric dipole structure.
  • Positively and negatively charged dipoles are separated on atomic or molecular level.
  • As a result of dipole interaction with electric field, dielectric material is used in capacitors.
  • Capacitance, C = Q/V, i.e. the ratio of quantity of charge stored on any of the two plates and applied voltage.
  • Capacitance, C = Є0A/L, where Є0 is the permittivity in a vacuum, which is equal to 8.85 × 10−12 F/m, A is the area between the plates, L is the distance between the two plates or thickness of dielectric.
  • Dielectric constant, k = Є/Є0, i.e. the ratio of permittivity of dielectric medium and vacuum.
  • In a vacuum, charge density, D0 = Є0ζ.
  • In a dielectric medium, charge density, D = Єζ, where ζ is the density of electric field.
  • Polarization, P = ζЄ0 (k − 1) in C/m2.
  • Polarization, P = Ncqd, where Nc is number of charge carriers, q is electronic charge and d is distance between the dipoles.
  • Electronic polarization results from the displacement of centre of the negatively charged electron cloud relative to the positively charged nucleus of an atom by an electric field.
  • Ionic polarization: Applied electric field displaces cations in one direction and anions in opposite direction, giving rise to a dipole moment.
  • Orientation polarization: When an electric field is applied, natural dipoles of some materials rotate to line up with the imposed field. After the removal of the field, the dipoles remain in alignment.
  • When the frequency of the applied electric field is more than the relaxation frequency of dipoles, the polarization mechanism ceases to function.
  • With increased temperature, the permanent dipole acquires greater mobility and polarizes more easily, resulting in higher dielectric constant.
  • When a dielectric material is polarized in an ac electrical field, some energy is dissipated as heat. The fraction of energy lost during each reversal is the dielectric loss. The current leakage and dipole friction are the main causes of dielectric loss.
  • The voltage per unit thickness of insulating material that can be sustained by an insulating material before it breaks down is known as dielectric strength.
  • Intrinsic breakdown: Due to large induction current and very high local field.
  • Thermal breakdown: Due to poor heat dissipation, electrical energy gets accumulated, causing melting of the dielectric.
  • Electro-chemical breakdown: Due to elevated temperature, dielectric gets converted into oxide, resulting in decrease in insulation resistance.
  • Discharge breakdown: Due to the collapse of gas bubbles present in the solid under the applied field.
  • Ferroelectricity is the result of spontaneous alignment of electric dipoles, which has a strong mutual interaction. Rochelle salt, barium titanate, KDP, potassium niobate, strantium titanate and lead zirconate titanate are ferroelectrics.
  • When a crystal is strained, an electric field is generated or vice versa, which is known as piezoelectricity. Quartz crystal is piezoelectric.
  • Organic oils and wax are effective as capacitors.
  • Polyester, polystyrene, polycarbonates and cellulose are used as dielectrics.
  • Ceramics as glass, porcelain, alumina, quartz, mica and asbestos are excellent dielectric materials with excellent thermal stability and high dielectric constant.
  • Formvar is a suitable insulating material for low-temperature applications.
  • Electrets are specially processed dielectrics, which may retain excess internal charge or frozen in polarization.
MULTIPLE CHOICE QUESTIONS
  1. Dielectric losses are due to
    1. Current leakage
    2. Dipole friction, which is a correct statement
    1. Both (A) and (B)
    2. Neither (A) nor (B)
    3. Only (A)
    4. Only (B)
  2. If Q = charge, V = voltage, then capacitance C is given by
    1. Q.V
    2. Q/V
    3. V/Q
    4. None of these
  3. Dielectric constant for mica at 60 Hz is
    1. 8
    2. 4.0
    3. 2.6
    4. None of these
  4. If V is the voltage, ζ is the field density, Є0 is the permittivity for vacuum, then in vacuum charge density, D0 is
    1. Є0V
    2. Є0ζ
    3. V/Є0
    4. None of these
  5. If the capacitance, C = 2 × 10−9 F, voltage applied is 100 V, then charge stored, Q is
    1. 2 × 10−11 C
    2. 2 × 10−8 C
    3. 2 × 10−7 C
    4. None of these
  6. If fr is the relaxation frequency and fa is the applied frequency, then at what stage polarization mechanism ceases to function
    1. fa < fr
    2. fa = fr
    3. fa > fr
    4. None of these
  7. Which of the following statements is correct?
    1. At lower frequencies losses are high because dipoles have time to move
    2. At higher frequencies, losses are low because the dipoles do not move at all
    1. Both (A) and (B)
    2. (A) only
    3. (B) only
    4. None of these
  8. Match the lists of reasons and types of breakdown

     

    I
    II

      I Poor heat dissipation

    (A) Electrochemical breakdown

     II Dielectric converted in oxide

    (B) Discharge break down

    III Collapse of gas bubbles

    (C) Defect break down

    IV Detrimental effect of moisture

    (D) Thermal break down

     

             I

    II

    III

    IV

    (a)  A

    D

     B

     C

    (b)  D

    A

     B

     C

    (c)  D

    A

     C

     B

    (d)  None of these

     

     

     

  9. Curie temperature of lead titanate is
    1. −148°C
    2. 122°C
    3. 436°C
    4. 490°C

Answers

1. (a)

2. (b)

3. (a)

4. (b)

5. (c)

6. (c)

7. (c)

8. (b)

9. (d)

 

REVIEW QUESTIONS
  1. What is the difference between a dielectric and an insulator?
  2. Define the terms dielectric constant, dielectric strength and dielectric loss.
  3. Explain polarization and describe three types of polarization with the help of neat sketches.
  4. Discuss the phenomenon of polarization taking place in a capacitor connected to a dc supply.
  5. Enumerate the factors leading to dielectric loss.
  6. What is breakdown voltage of a capacitor?
  7. What is spontaneous polarization?
  8. State the difference between polar and nonpolar materials.
  9. Explain the difference between ferroelectricity and piezoelectricity.
  10. What is dipole moment and what is polarization?
  11. With the help of a neat graph between dielectric constant and applied frequency, explain the effect of frequency on dielectric constant for three types of polarization.
  12. Compare the dielectric constants of polymers and ceramics.
PRACTICE PROBLEMS
  1. The polarization P of a dielectric material positioned within a parallel plate capacitor is to be 1 × 10−6 C/m2.
    1. What must be the dielectric constant if an electric field of 5 × 104 V is applied?
    2. What will be the dielectric displacement D?

    Ans. (3.26, 1.44 × 10−6 C/m2)

  2. A charge of 3.5 × 10−11 C is to be stored on each plate of a parallel plate capacitor having an area of 160 mm2 and a plate separation of 3.5 mm.
    1. What voltage is required if a material having a dielectric constant of 5.0 is positioned within the plates and what is the capacitance?
    2. What voltage is required if a vacuum is there in between the plates?
    3. What is polarization in part (a)?

    Ans. (17.3 V, 2.023 ×10−12 F; 86.5 V, 0.404 × 10−12 F/m, P = 1.75 × 10−7 C/m2)

  3. A barium titanate crystal is inserted in a parallel plate condenser of plate dimensions 10 × 10 mm2. A capacitance of 10−9 F is noticed when the plates are separated by 2 mm. Taking Є0 = 8.85 × 10−12 F/m, determine the dielectric constant of the crystal.

     

    Ans. (2260)

  4. Capacitor has a capacitance of 0.019 F, when a wax paper (Єp = 1.85) between electrodes of aluminium foil is used. The wax paper is to be replaced by a plastic film (Єp = 2.15) of same dimensions. Taking the other factors to be equal, obtain the change in capacitance.

     

    Ans. (0.0117 F increase)

  5. A layer of porcelain is 80 mm long, 20 mm wide and 1 μm thick. Calculate its capacitance taking k = 6.

     

    Ans. (0.85 × 10−7 F)