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

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Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №1Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №2Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №3Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №4Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №5Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №6Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №7Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №8Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №9Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №10Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №11Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №12Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №13Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №14Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №15Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №16Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №17Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №18Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №19Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №20Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №21Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №22Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №23Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №24Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №25Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №26Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №27Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №28Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №29Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №30Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №31Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №32Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №33Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №34Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №35
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Republic of Kazakhstan Republic of Kazakhstan Ministry of Education and Science Kazakh-British Technical University Faculty of Power and Oil and Gas Industry Physical Engineering Department Physics 1 Voronkov Vladimir Vasilyevich
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Republic of Kazakhstan Republic of Kazakhstan Ministry of Education and Science Kazakh-British Technical University Faculty of Power and Oil and Gas Industry Physical Engineering Department Physics 1 Voronkov Vladimir Vasilyevich

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Lecture 9 Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force.
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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.
Описание слайда:
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 V for simplicity.
Описание слайда:
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 V 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.
Описание слайда:
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 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.
Описание слайда:
Using the Gauss theorem we can find that the value of the electric field between plates is 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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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. 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:
Описание слайда:
The electric field between the plates of a parallel-plate capacitor is uniform near the center but nonuniform near the edges. 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
Описание слайда:
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=…
Описание слайда:
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 Q=Q1=Q2 V=V1+V2 1

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Series Combination of Capacitors
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Series Combination of Capacitors

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Capacitors Parallel-Series Combinations:
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Capacitors Parallel-Series Combinations:

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1. Merging parallel capacitors:
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1. Merging parallel capacitors:

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

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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
Описание слайда:
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, V – difference of potentials on the capacitor This result applies to any capacitor, regardless of its geometry.
Описание слайда:
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, V – 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 V for the difference of potentials, then the expressions for energy, stored in a capacitor is:
Описание слайда:
Energy in a Capacitor Usually V is used instead of V 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:
Описание слайда:
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.
Описание слайда:
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
Описание слайда:
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.
Описание слайда:
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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Insulators and Conductors in electric field. Capacitance, Dielectrics. Current, resistance. Electromotive Force, слайд №23
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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.
Описание слайда:
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.
Описание слайда:
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.
Описание слайда:
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.
Описание слайда:
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.
Описание слайда:
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: 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.
Описание слайда:
As the charge Q on the capacitor is not changed: 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.
Описание слайда:
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. Q - the amount of charge passing through the cross sectional area of a wire T - a time interval of the passing. The average current is: The instantaneous current is:
Описание слайда:
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. Q - the amount of charge passing through the cross sectional area of a wire T - 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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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.
Описание слайда:
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.
Описание слайда:
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.

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Units in Si Capacitance C F=C/V Current I A=C/s Resistance R Ohm=V/A Electro motive force (emf) V Energy density uE J/m3=kg/(m*s2)
Описание слайда:
Units in Si Capacitance C F=C/V Current I A=C/s Resistance R Ohm=V/A Electro motive force (emf) V Energy density uE J/m3=kg/(m*s2)

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