Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force

Сентябрь 14, 2022

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Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force

Содержание

2. Lecture 9 Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force.
3. Conductors and Insulators Electrical conductors are materials in which some of the electrons are free, that
4. Capacitance The capacitance C of a capacitor is defined as the ratio of the magnitude of
5. Parallel – Plate Capacitor A parallel-plate capacitor consists of two parallel conducting plates, each of area
6. Using the Gauss theorem we can find that the value of the electric field between plates
7. Capacitance of various Capacitors
8. The electric field between the plates of a parallel-plate capacitor is uniform near the center but
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 combination of capacitors is the algebraic
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
13. Capacitors Parallel-Series Combinations: Let’s calculate the equivalent capacitance step by step, using the mentioned above properties
14. 1. Merging parallel capacitors:
15. 2. Joining serial capacitors: In circles we have merged capacitors: Then we join series conductors: And
16. Energy Stored in a Charged Capacitor If a capacitor has charge Q then it’s difference of
17. Energy Stored in a Charged Capacitor The work done in charging the capacitor appears as electric
18. Energy in a Capacitor Usually V is used instead of ΔV for the difference of potentials,
19. Energy in Electric Fields Let’s take a parallel-plate capacitor: V - the potential difference between the
20. Energy density of Electric Field The volume, occupied by the electric field is Ad, then the
21. Dielectrics Many materials (like paper, rubber, plastics, glass …) do not conduct electricity easily – we
22. Dielectric strength The dielectric strength equals the maximum electric field that can exist in a dielectric
24. Atomic Description of Dielectrics Dielectric can be made up of polar molecules. The dipoles are randomly
25. Polar and Nonpolar molecules of Dielectric The molecules of the dielectric can be polar or nonpolar.
26. Dielectric polarization The degree of alignment of the molecules with the electric field depends on temperature
27. Induced Electric field in Dielectric When an external field E0 is applied, a torque is exerted
28. Capacitor with Dielectric So the electric field is k times less in a capacitor with a
29. As the charge Q on the capacitor is not changed: C0=Q/V0, V=V0/k C=Q/V=kC0V0/V0=kC0 C=kC0 So the
30. Usage of Dielectrics in Capacitors Insulating materials have k>1 and dielectric strength greater than that of
31. Electric Current Electric current (or just current) is defined as the total charge that passes through
32. Current direction By convention the direction of the current is the direction of positive charges would
33. Ohm’s Law Ohm’s law states that For many materials the resistance is constant over a wide
34. Electromotive Force A device with the ability to maintain potential difference between two points is called
36. Скачать презентацию

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Lecture 9
Insulators and Conductors in electric field.
Capacitance, Dielectrics.
Current, resistance.
Electromotive Force.

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Conductors and Insulators
Electrical conductors are materials in which some 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.

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Capacitance
The capacitance C of a capacitor is defined 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 ΔV for simplicity.

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Parallel – Plate Capacitor
A parallel-plate capacitor consists 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.

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Using the Gauss theorem we can find that the value 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.

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Capacitance of various Capacitors

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The electric field between the plates of a parallel-plate capacitor 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:

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Parallel Combination of Capacitors
Ceq=C1+C2
Qnet=Q1+Q2
V=V1=V2

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Parallel Combination of Capacitors
The equivalent capacitance of a parallel combination of

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=…

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Series Combination of Capacitors
Q=Q1=Q2
V=V1+V2
1

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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:

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Capacitors Parallel-Series Combinations:
Let’s calculate the equivalent capacitance step by step, using

the mentioned above properties of capacitors:
First we merge parallel capacitors into one: using that Cparallel=C1+C2+…

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1. Merging parallel capacitors:

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2. Joining serial capacitors:
In circles we have merged capacitors:
Then we join

series conductors:

And finally we join the two parallel conductors into one:

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Energy Stored in a Charged Capacitor
If a capacitor has charge Q

then it’s difference of 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

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Energy Stored in a Charged Capacitor
The work done in charging the

capacitor appears as electric potential energy U stored in the capacitor
Here U is the energy, stored in the capacitor,
ΔV – difference of potentials on the capacitor
This result applies to any capacitor, regardless of its geometry.

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Energy in a Capacitor
Usually V is used instead of ΔV for

the difference of potentials, then the expressions for energy, stored in a capacitor is:

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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:

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Energy density of Electric Field
The volume, occupied by the electric field

is 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.

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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

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Dielectric strength
The dielectric strength equals the maximum 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.

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Atomic Description of Dielectrics
Dielectric can be made up of polar 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.

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Polar and Nonpolar molecules of Dielectric
The molecules of the dielectric can

be polar or nonpolar.
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.

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Dielectric polarization
The degree of alignment of the molecules with 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.

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Induced Electric field in Dielectric
When an external field E0 is 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.

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Capacitor with Dielectric
So the electric field is k times less in

a capacitor with 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.

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As the charge Q on the capacitor is not changed:
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.

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Usage of Dielectrics in Capacitors
Insulating materials have k>1 and dielectric strength

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.

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Electric Current
Electric current (or just current) is defined as the total

charge 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.
ΔQ - the amount of charge passing through the cross sectional area of a wire
ΔT - a time interval of the passing.
The average current is:
The instantaneous current is:

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Current direction
By convention the direction of the current is the direction

of positive charges would move.

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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.

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Electromotive Force
A device with the ability to maintain potential difference 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.

Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force

Содержание

Lecture 9Insulators and Conductors in electric field.Capacitance, Dielectrics. Current, resistance.Electromotive Force.

Conductors and InsulatorsElectrical conductors are materials in which some of the

CapacitanceThe capacitance C of a capacitor is defined as the ratio

Parallel – Plate Capacitor A parallel-plate capacitor consists of two parallel conducting

Using the Gauss theorem we can find that the value of

Capacitance of various Capacitors

The electric field between the plates of a parallel-plate capacitor is

Parallel Combination of Capacitors Ceq=C1+C2Qnet=Q1+Q2V=V1=V2

Parallel Combination of CapacitorsThe equivalent capacitance of a parallel combination of

Series Combination of CapacitorsQ=Q1=Q2V=V1+V21

Series Combination of CapacitorsThe charges on capacitors connected in series are

Capacitors Parallel-Series Combinations:Let’s calculate the equivalent capacitance step by step, using

1. Merging parallel capacitors:

2. Joining serial capacitors:In circles we have merged capacitors:Then we join

Energy Stored in a Charged Capacitor If a capacitor has charge Q

Energy Stored in a Charged Capacitor The work done in charging the

Energy in a Capacitor Usually V is used instead of ΔV for

Energy in Electric FieldsLet’s take a parallel-plate capacitor:V - the potential

Energy density of Electric FieldThe volume, occupied by the electric field

DielectricsMany materials (like paper, rubber, plastics, glass …) do not conduct

Dielectric strengthThe dielectric strength equals the maximum electric field that can

Atomic Description of DielectricsDielectric can be made up of polar molecules.

Polar and Nonpolar molecules of DielectricThe molecules of the dielectric can

Dielectric polarizationThe degree of alignment of the molecules with the electric

Induced Electric field in DielectricWhen an external field E0 is applied,

Capacitor with DielectricSo the electric field is k times less in

As the charge Q on the capacitor is not changed:C0=Q/V0, V=V0/k C=Q/V=kC0V0/V0=kC0C=kC0So

Usage of Dielectrics in CapacitorsInsulating materials have k>1 and dielectric strength

Electric CurrentElectric current (or just current) is defined as the total

Current directionBy convention the direction of the current is the direction

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

Electromotive ForceA device with the ability to maintain potential difference between

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