Honors Physics

Electrical Potential EnergyPE associated with a charge due to its

position in an electric field.Analogous to PEg

PEg of an object results from its position in a gravitational field (mgh)

Is a component of mechanical energyME = KE + PEgrav + PEelastic + PEelectric

Similarity of PEelectric and PEgPEg = mgh

m is massg is gravitational field (ag)h is distance above a reference point

PEelect = -qEdq is chargeE is electric field strengthd is component of displacement in the direction of

the electric field from reference pointUsing dimensional analysis, what is the unit of

PEelect?

Electric WorkWhenever a force moves an object, work is

done on the object.When an electric force moves a charge, work

is done on that charge.It is the electric field, E, that exerts force on

a chargeTherefore, the electric field, E, does work on

a charge.This results in a change in PEelect.

Electric PE in a Uniform Electric FieldA uniform field is one that has the same

magnitude and direction at all points, such as between two parallel plates

Remember: electric field lines are always directed from away from positive and toward negative

Electric Potential EnergyRecall that ΔPE = -W When charge q is released at

point a, electric force will move the charge to b, i.e.

The electric field does work on the charge q

Electric Potential EnergyW = FdSince F = qE (remember

E = F/q)W = qEdPEb-PEa= -qEdΔPE = -qEdSignificance of the (-) sign:

PEelect Increases if charge is (-)Decreases if charge is (+)

PE as a charge moves in a uniform electric field

Movement of charge

+ charge - charge

Along E Loses PE Gains PE

Opposite E Gains PE Loses PE

ΔPE = -qEd

Negative sign indicates that PE will increase if the charge is negative and decrease if the charge is positive

Potential DifferenceElectric potential (V) is the ratio of PEelect to

charge q

Represents the work needed to move a charge against electric forces from a reference point to some other point in an electric field, divided by the charge

The SI units of electric potential are what? Which is a …?

q

PEV elect

Potential differenceThe change in electric potentialThe difference in electrical potential between

two points

Is the work that must be done against electric forces to move a charge from one point to another divided by the charge

Is the change in energy per unit charge

q

PEV elect

Potential DifferenceUnit is the volt (V)

Remember: PEelect is a quantity of energyElectrical potential is a measure of energy per

unit chargePotential difference describes change in

energy per unit charge

q

PEV elect

?

? volt 1

Potential Difference in a Uniform Electric FieldVaries in a uniform field with displacement

from a reference pointWhere d is displacement parallel to the fieldUse this equation to determine potential

difference between two points in a field

EdV

q

PEVqEdPE

So,

and

Potential Difference at a Point Near a Charge

r

qkV C

One point is near the charge

The other point is at infinity

Electric potential due to multiple charges

Electric potentials are scalar quantities (whew!)So….Total potential at some point in a field is the

simple sum of the potentials due to each chargeKeep track of signs!

Sample ProblemAs a charge moves xa = 4.0 cm to xb = 6.0 cm

in a uniform field of 350 N/C, it loses 4.5 x 10-

16 J of potential energy.What is the magnitude of the charge?

6.4 x 10-17CWhat is the potential difference between the

two points a and b?

-7.0V

Ed

PEqqEdPE

EdVq

PEV

or

17.2 CapacitanceCapacitors are devices that store electrical

PEOften constructed of parallel metal platesWhen connected to a battery, the plates

become chargedWhen fully charged, ∆Vcap = ∆Vbat

Schematic Representation of a Capacitor and Battery

Intro to Capacitor

Construction of a CapacitorParallel platesParallel plates

separated by an insulator (dielectric material) rolled into a cylinder saves space

CapacitanceAbility of a conductor to store energy in the

form of separated charges

Unit of capacitance is the Farad, named for Michael Faraday1F = 1C/V1 Farad is a large amount of capacitance so…Often use pF, nF, or µF

Supplemental instruction on capacitanceView on your own, ~ 17 min.

V

QC

Capacitance of a Parallel-Plate Capacitor in a VacuumWhen no material exists

between the platesε0 is the permittivity of the

medium between the platesA measure of ability to

develop an electrical field, permitting transfer of charges

ε0 in a vaccuum is 8.85 x 10-

12 C2/Nm2

d

AC 0

Dielectric MaterialsMaterials placed

between the plates of a capacitor can increase capacitance.

Typically these are insulating materials

d

AC 0

Dielectric Constants (K)Dielectric materials

have different values of “dielectric constant” (K).

Increase capacitance

d

AKC 0

Performance of Dielectric MaterialsMolecules of the dielectric are

polarizableAs charge builds on the

capacitor plates, dielectric molecules orient to the electric field

This effectively reduces the charge on the plates….

allowing more charge to be carried by each plate

Capacitor DischargeThe opposite of

charging, releasing stored charge

Electrical potential of the capacitor is used to do electrical work such as …

The flash of a cameraSignaling the stroke of a

computer keyboard

Capacitance of a SphereR is radiusBecause the earth has a large

radius, it has a very large capacitance

i.e., the earth can accept or supply a very large amount of charge without changing its electrical potential

This is why the earth is “ground,” (reference point for measuring potential differences)

Csphere k

R

V

QC

Energy and CapacitorsBecause work is

done to move charges to and from opposite plates…

A charged capacitor holds electrical potential energy

PE stored in a charged capacitor is equal to the (–) work done to charge it

2

2

1

Since

2

1

VCPE

VCQV

QC

VQPEW

Breakdown voltageVoltage at which discharge begins, i.e.

charges move

Energy and CapacitorsPE Stored in a Charged Capacitor

C

QPE

VCPE

VQPE

2

2

2

1

2

12

1

Current and ResistanceCurrent is the rate of movement of chargeRate of movement of electrons through a

cross-sectional area

second

coulomb11ampere

t

QI

Sample ProblemIf current flowing through a light bulb is

0.835 A, how long does it take for 1.67 C of charge to pass through the filament of the bulb?

2.00 seconds

Conventional Direction of CurrentDepending upon the circumstances, either

positive, negative, or both can move.Particles that move are called charge carriersBy convention, direction of current is defined as

the direction a positive charge moves or would move if it could.

In metals, only electrons can move.Good conductors permit charge carriers to

move easilyElectrons in metalsIons in solution (electrolytes)

Conventional Direction of Current

Drift Velocity

Recall the structure of metalsValence electrons move about randomly due

to their thermal energyTheir net movement is zeroBut if an electric field is established in the

wire, there is a net movement of electrons against the electric field (toward +)

Drift velocity animation

http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif

Drift Velocity

It is the electric field that exerts force and thereby sets charge carriers in motion

E propagates very rapidly (near speed of light)Charge carriers move more slowly, in an

erratic path,Called drift velocitySlow: e.g. in a copper wire carrying a 10.0 A

current, vdrift = 0.246 mm/s

Consider motion of an electron through a wire

Resistance to CurrentOpposition to

electric currentUnit of electrical

resistance is the ohm (Ω)

More commonly known as Ohm’s law

amp

volt 1 ohm 1

I

VR

IRV

Ohmic and Non-ohmic MaterialsMaterials which follow

ohm’s law are ohmic materials

Resistance is constant over a wide range of potential differences (linear)

Non-ohmic materials have variable resistance (non-linear)

Diodes are constructed of non-ohmic materials

Other Factors Affecting Resistance

Function of ResistanceFrom Ohm’s Law, changing resistance can change

current

So, if current needs to be reduced in a circuit, you can increase the resistance

In many cases, ∆V is constant, so changing resistance is the only option for reducing current.

IRV

Electrical Resistance in the BodyElectrical resistance is reduced as the

body becomes wet or sweatsThis is due to the greater availability of

ions to conduct currentPractical applications:

Your body is more susceptible increased current when wet

Lie detectors EKGs, etc

PotentiometersDevices that have variable resistance

“Pots”Applications

Control knobs on electronic devices

Stereos, dimmer switches, joy sticks, etc.

17.4 Electric PowerA potential difference (∆V) is necessary to

cause current (I)Batteries supply chemical energy (PEchem)

which can be converted into electical PEGenerators convert mechanical energy into

electrical PEE.g. hydroelectric power plantsCoal or natural gas powr plantsNuclear power plants

Direct and Alternating CurrentDC current flows in one direction onlyElectrons move toward the (+) terminalConventional current directed from (+) to (-)AC current

Terminals of source of ΔV constantly switchCausing constant reversal of current, e.g.

60 HzRapid switching causes e-s to vibrate rather

than have a net motion.

DC and ACDC

constant uni-directional

AC not constant bi-directional

Energy TransferIn a DC circuitElectrons leave the

battery with high PELose PE as flow

through the circuitRegain PE when

returned to battery(battery supplies PE

through electrochemical reactions)

Electric PowerThe rate of

conversion of electrical energy

SI unit is the watt (W)

VIP

It

q

t

VqP

VqPEq

PEV

t

PE

t

WP

Since

Other Formulas for Power

R

VP

RIP

VIP

2

2

Law... sOhm' Using

with Beginning

Kilowatt-hoursHow utility companies measure energy

consumedIs the energy delivered in one hour a constant

rate of one kW1kWh=3.6 x 106 JWhat is the cost to light a 100 W light bulb for

1 full day if the electric utility rate is $0.0600 per kWh?

$0.144kWh

$0.0600kWh 2.4

kWh 2.4 Wh2400h 24 W100

Transmission LinesTransit at high

voltage and low current to minimize energy lost during transmission

P=I2R