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1

**Electrical Potential Energy**

When a test charge is placed in an electric field, it experiences a force

The work done within the charge field system by the electric field on the charge through an infinitesimal displacement is

As this work is done by the field, the change in potential energy is

For a finite displacement of the charge from A to B,

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Electric Potential

The potential energy per unit charge, is the electrical potential

The electrical potential is

The potential is a scalar quantity. Because energy is a scalar

As a charged particle moves in an electric field,

The equations for electric potential between two points A and B can be simplified if the electric field is uniform

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Volt

The units of the electric potential

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Downward

when the electric field is directed __ point B at a lower potential than point *A*

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loses potential energy

When a *positive *test charge moves from *A* to *B*, the charge-field system

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**Electric field lines**

always point in the direction of **decreasing **electric potential.

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**Equipotentials**

Point

*B*is at a lower potential than point*A*Points

*A*and*C*are at the same potential.All points in a plane perpendicular to a uniform electric field are at the same electric potential.

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**Equipotential surface**

is given to any surface consisting of a continuous distribution of points having the same electric potential.

must always be perpendicular to the electric field lines passing through them.

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Voltage

Electric potential is also called applied to a device or across a device is the same as the potential difference across the device.

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**Electron-Volts**

Another

**unit of energy**that is**commonly used in atomic and nuclear physics**is the electron-voltOne

**electron-volt**is defined as the*energy a charge-field system**gains or loses**when a*through a potential difference of 1 volt.*charge of magnitude (an electron or a proton) is moved*1 eV = 1.60 x 10-19 J

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**Parallel-plate capacitor**

This **configuration of plates** is called a parallel-plate capacitor

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**Potential and Point Charges**

The potential difference between points *A* and *B* will be

The electric potential is independent of the path between points and It is customary to choose a reference potential of

Then the potential due to a point charge at some point is

The electric potential due to several point charges

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**Outward**

An** isolated positive point charge** produces a field directed radially__

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Positive

If the two charges are the **same sign**, *U *is **___ **and work must be done to bring the charges together.

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Negative

If the two charges have **opposite signs**, *U *is **___ **and work is done to keep the charges apart

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More than two charges

If there are **___**, then find *U *for each pair of charges and add them.

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**Equipotential lines**

are the **dashed blue lines**.

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**E and V for a Point Charge**

The electric field lines are the

**brown lines**.The electric field is

**radial**.Er =-dV/dr

The equipotential lines are everywhere perpendicular to the field lines.

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19

**Capacitors**

- are devices that store electric charge.

- Examples of where capacitors are used include:

radio receivers

filters in power supplies

to eliminate sparking in automobile ignition systems

energy-storing devices in electronic flashes

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Makeup of a capacitor

A capacitor consists of

**two conductors.**These conductors are called

**plates**.When the conductor is charged, the plates carry charges of

*equal magnitude and opposite directions*.

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**Capacitance**

*(*** C**) of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the potential difference between the conductors.

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**SI unit** of capacitance

**farad (F)**. The farad is a large unit, typically you will see**microfarads (mF) and picofarads (pF)**.The capacitance will always be a positive quantity

The capacitance of a given capacitor is constant.

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**Capacitance Parallel Plates**

Each plate is connected to a terminal of the battery (source of potential difference).

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*A*

is the area of each plate, and the area of each plate is equal

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*Q*

is the charge on each plate, equal with opposite signs.

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Dielectric

is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitance and Increase the maximum operating voltage. Dielectrics include rubber, glass, and waxed paper

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**Tubular**

Metallic foil may be interlaced with thin sheets of paraffin-impregnated paper or Mylar.

The layers are rolled into a cylinder to form a small package for the capacitor.

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**Oil Filled**

Common for high-voltage capacitors A number of interwoven metallic plates are immersed in silicon oil.

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**Electrolytic**

Used to store large amounts of charge at relatively low voltages

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**Electrolyte**

A solution that conducts electricity by virtue of motion of ions contained in the solution.

When a voltage is applied between the foil and the electrolyte, a thin layer of metal oxide is formed on the foil.

This layer serves as a

**dielectric.**

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**Electric current (/)**

is the rate of flow of charge through some region of space.

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**Current density**

Is the current density of a conductor. It is defined as the current per unit area.

*J = I / A**J is uniform and**A**is perpendicular to the direction of the current.**J has SI units of A/m^2*

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**Conductivity**

A current density and an electric field are established in a conductor whenever a potential difference is maintained across the conductor.

The constant of proportionality, o, is called the conductivity of the conductor

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**Ohm’s Law**

states that for many materials, the ratio of the current density to the electric field is a constant o that is independent of the electric field producing the current.

Mathematically, J=oE or V=IR

Materials that obey this law are said to be ohmic.

Most metals obey this law

Materials that do not obey this law are said to be

*nonohmic*.

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35

**Resistance of conductor**

The quantity

**R**= /oA is called the resistance of the conductor.Defined as the ratio of the potential difference across a conductor to the current in the conductor:

SI units of resistance are ohms

Resistance in a circuit arises due to collisions between the electrons carrying the current with the fixed atoms inside the conductor.

Most electric circuits use circuit elements called resistors to control the current in the various parts of the circuit.

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*P*

is the resistivity at some reference temperature T

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*T*

is usually taken to be 20° c

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*a*

is the temperature coefficient of resistivity

SI units of a are **°C-1**

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39

**Resistors**

Most electric circuits use circuit elements called resistors to control the current in the various parts of the circuit.

Can be built into integrated circuit chips.

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**Values of resistors are normally indicated by colored bands.**

The first two bands give the first two digits in the resistance value.

The third band represents the power of ten for the multiplier band.

The last band is the tolerance.

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**Resistors in Series**

For a series combination of resistors, the currents are the same in all the resistors

The potential difference will divide among the resistors

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**Consequence of Conservation of Energy**

The equivalent resistance has the same effect on the circuit as the original combination of resistors.

If one device in the series circuit creates an open circuit, all

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**Superconductors**

A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, T

*c*.

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**T c**

is called the critical temperature.

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**The value of T c is sensitive to**

chemical composition

pressure

molecular structure

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**Power**

is the rate at which the energy is delivered to the resistor.

given by the

**equation**P = I AV

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