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## 1.

Republic of KazakhstanMinistry of Education and Science

Kazakh-British Technical University

Faculty of Power and Oil and Gas Industry

Physical Engineering Department

Physics 1

Voronkov Vladimir Vasilyevich

## 2. Lecture 9

Insulators and Conductors in electric field.

Capacitance, Dielectrics.

Current, resistance.

Electromotive Force.

## 3. Conductors and Insulators

• Electrical conductors are materials in whichsome of the electrons are free, that are not

bound to atoms and can move relatively freely

through thematerial.

• Electrical insulators are materials in which all

electrons are bound to atoms and can not

move freely through the material.

## 4. Capacitance

• The capacitance C of a capacitor isdefined as the ratio of the magnitude of

the charge on either conductor to the

magnitude of the potential difference

between the conductors:

• Note: net charge of a capacitor is zero. A capacitor

consists of 2 conductors, and Q is the charge on one of

each, and correspondingly –Q is the charge on the other.

• Do not confuse C for capacitance with C for the unit

coulomb.

• Usually V is taken instead of DV for simplicity.

## 5. Parallel – Plate Capacitor

A parallel-plate capacitorconsists of two parallel

conducting plates, each of

area A, separated by a

distance d. When the

capacitor is charged the

plates carry equal

amounts of charge. One

plate carries positive

charge, and the other

carries negative charge.

## 6.

• Using the Gauss theorem we can find that thevalue of the electric field between plates is

• The magnitude of the potential difference between

the plates equals:

• And finally:

• So the capacitance of a parallel-plate capacitor is

• Here A is the area of each plate, d is the distance

between plates.

## 7. Capacitance of various Capacitors

## 8.

• The electric field between the plates of a parallel-platecapacitor is uniform near the center but nonuniform near

the edges.

• That’s why we applied formula for electric field between

two infinite uniformly charged planes:

## 9. Parallel Combination of Capacitors

• Ceq=C1+C2• Qnet=Q1+Q2

• V=V1=V2

## 10. Parallel Combination of Capacitors

• The equivalent capacitance of a parallel combinationof capacitors is the algebraic sum of the individual

capacitances and is greater than any of the individual

capacitances.

• Ceq=C1+C2+C3+…

• The total charge on capacitors connected in parallel is

the sum of the charges on the individual capacitors:

• Qnet=Q1+Q2+Q3+…

• The individual potential differences across capacitors

connected in parallel are the same and are equal to

the potential difference applied across the

combination:

• V=V1=V2=V3=…

## 11. Series Combination of Capacitors

• Q=Q1=Q2• V=V1+V2

• 1

## 12. Series Combination of Capacitors

• The charges on capacitors connected in series are the same:• Q=Q1=Q2=Q3=…

• The total potential difference across any number of capacitors

connected in series is the sum of the potential differences

across the individual capacitors:

• Vnet=V1+V2+V3+…

• The inverse of the equivalent capacitance is the algebraic

sum of the inverses of the individual capacitances and the

equivalent capacitance of a series combination is always less

than any individual capacitance in the combination:

## 13. Capacitors Parallel-Series Combinations:

• Let’s calculate theequivalent

capacitance step by

step, using the

mentioned above

properties of

capacitors:

• First we merge parallel

capacitors into one:

using that

Cparallel=C1+C2+…

## 14. 1. Merging parallel capacitors:

## 15. 2. Joining serial capacitors:

• And finally we• In circles we have • Then we

join the two

merged capacitors: join series

parallel

conductors:

conductors into

one:

## 16. Energy Stored in a Charged Capacitor

If a capacitor has charge Q then it’s differenceof potentials V is V=Q/C, then the work dW,

necessary to transfer small charge dq from one

capacitor’s conductor to another is:

Then the total work required to charge the

capacitor from q = 0 to final charge q = Q is

## 17. Energy Stored in a Charged Capacitor

• The work done in charging the capacitorappears as electric potential energy U stored in

the capacitor

• Here U is the energy, stored in the capacitor,

DV – difference of potentials on the capacitor

• This result applies to any capacitor, regardless

of its geometry.

## 18. Energy in a Capacitor

Usually V is used instead of DV for thedifference of potentials, then the expressions

for energy, stored in a capacitor is:

## 19. Energy in Electric Fields

• Let’s take a parallel-plate capacitor:• V - the potential difference between the

plates of a capacitor,

• d - distance between the plates,

• A – the area of each plate,

• E - the electric field between the plates of

a capacitor. Then V=Ed.

• Then the energy of the electric field in the

capacitor is:

## 20. Energy density of Electric Field

• The volume, occupied by the electric fieldis Ad, then the energy density of the

electric field is:

• The energy density in any electric field is

proportional to the square of the

magnitude of the electric field at a given

point.

## 21. Dielectrics

• Many materials (like paper, rubber, plastics,glass …) do not conduct electricity easily – we

call them insulators.

• But they modify the electric field they are placed

in, that’s why they are called dielectrics.

• E0 – the electric field without the dielectric

• E – the electric field in the presence of the

dielectric

• k – the dielectric constant

## 22. Dielectric strength

• The dielectric strength equals themaximum electric field that can exist in a

dielectric without electrical breakdown.

Note that these values depend strongly on

the presence of impurities and flaws in the

materials.

## 23.

## 24. Atomic Description of Dielectrics

• Dielectric can be made up ofpolar molecules. The dipoles

are randomly oriented in the

absence of an electric field.

• When an external Electric

field is applied, its molecules

partially align with the field.

Now the dielectric is

polarized.

## 25. Polar and Nonpolar molecules of Dielectric

• The molecules of the dielectric can be polar ornonpolar.

• The case of polar molecules are considered in the

previous slide.

• If the molecules of the dielectric are nonpolar then the

electric field produces some charge separation in

every molecule of the dielectric, and an induced dipole

moment is created. These induced dipole moments

tend to align with the external field, and the dielectric

is polarized.

• Thus, we can polarize a dielectric with an external field

regardless of whether the molecules are polar or

nonpolar.

## 26. Dielectric polarization

• The degree of alignment of the moleculeswith the electric field depends on

temperature and on the magnitude of the

electric field.

• In general, the alignment increases with

decreasing temperature and with

increasing electric field.

## 27. Induced Electric field in Dielectric

• When an external field E0is applied, a torque is

exerted on the dipoles,

causing them to partially

align with the field.

• That’s why dielectric’s

molecules produces

induced electric field Eind,

opposite to the external E0.

## 28. Capacitor with Dielectric

• So the electric field is k times less in a capacitorwith a dielectric, its dielectric constant is k:

• Then, the potential difference is k times less:

without dielectric:

V0 =E0d

with dielectric:

V=Ed= E0d/k.

V=V0/k.

## 29.

• As the charge Q on the capacitor is notchanged:

• C0=Q/V0,

V=V0/k

• C=Q/V=kC0V0/V0=kC0

C=kC0

• So the capacitance increases in k if a

dielectric completely fills the distance

between the plates of a capacitor.

## 30. Usage of Dielectrics in Capacitors

• Insulating materials have k>1 and dielectricstrength greater than that of air, so usage

of dielectrics has following advantages:

– Increase in capacitance.

– Increase in maximum operating voltage.

– Possible mechanical support between the

plates, which allows the plates to be close

together without touching, thereby decreasing

d and increasing C.

## 31. Electric Current

• Electric current (or just current) is defined as the totalcharge that passes through a given cross-sectional area

per unit time.

• Current can be composed of

– moving negative charges such as electrons or negatively

charged ions;

– moving positive charges such as protons or positively charged

ions.

DQ - the amount of charge passing through the cross

sectional area of a wire

DT - a time interval of the passing.

The average current is:

• The instantaneous current is:

## 32. Current direction

• By convention the direction of the currentis the direction of positive charges would

move.

## 33. Ohm’s Law

• Ohm’s law states that• For many materials the resistance is

constant over a wide range of potential

differences:

V = IR.

• Resistance is defined as the opposition to

the flow of electric charge.

## 34. Electromotive Force

• A device with the ability to maintain potentialdifference between two points is called a

source of electromotive force (emf). The

most familiar sources of emf are batteries and

generators.

• Batteries convert chemical energy into electric

energy.

• Generators transforms mechanical energy into

electric energy.

• Since emf is work per unit charge, it is

expressed in the same unit as potential

difference: the joule per coulomb, or volt.

## 35. Units in Si

Capacitance

Current

Resistance

Electro motive force (emf)

Energy density

C

I

R

e

uE

F=C/V

A=C/s

Ohm=V/A

V

J/m3=kg/(m*s2)