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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,
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
Volt
The units of the electric potential
Downward
when the electric field is directed __ point B at a lower potential than point A
loses potential energy
When a positive test charge moves from A to B, the charge-field system
Electric field lines
always point in the direction of decreasing electric potential.
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.
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.
Voltage
Electric potential is also called applied to a device or across a device is the same as the potential difference across the device.
Electron-Volts
Another unit of energy that is commonly used in atomic and nuclear physics is the electron-volt
One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude (an electron or a proton) is moved through a potential difference of 1 volt.
1 eV = 1.60 x 10-19 J
Parallel-plate capacitor
This configuration of plates is called a parallel-plate capacitor
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
Outward
An isolated positive point charge produces a field directed radially__
Positive
If the two charges are the same sign, U is ___ and work must be done to bring the charges together.
Negative
If the two charges have opposite signs, U is ___ and work is done to keep the charges apart
More than two charges
If there are ___, then find U for each pair of charges and add them.
Equipotential lines
are the dashed blue lines.
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.
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
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.
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.
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.
Capacitance Parallel Plates
Each plate is connected to a terminal of the battery (source of potential difference).
A
is the area of each plate, and the area of each plate is equal
Q
is the charge on each plate, equal with opposite signs.
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
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.
Oil Filled
Common for high-voltage capacitors A number of interwoven metallic plates are immersed in silicon oil.
Electrolytic
Used to store large amounts of charge at relatively low voltages
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.
Electric current (/)
is the rate of flow of charge through some region of space.
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
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
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.
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.
P
is the resistivity at some reference temperature T
T
is usually taken to be 20° c
a
is the temperature coefficient of resistivity
SI units of a are °C-1
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.
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.
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
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
Superconductors
A class of materials and compounds whose resistances fall to virtually zero below a certain temperature, Tc.
Tc
is called the critical temperature.
The value of Tc is sensitive to
chemical composition
pressure
molecular structure
Power
is the rate at which the energy is delivered to the resistor.
given by the equation P = I AV