electrical energy & current. introduction to electric pe, electric potential, and potential...

Electrical Energy & Current

Introduction to Electric PE, Electric Potential, and Potential DifferenceIntro to Electric Potential

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

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

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

W = FdSince F = qE (E = F/q)W = qEdPEb-PEa= -qEdΔPE = -qEd

PE as a charge moves in a uniform electric field

Movement of charge

+ charge - charge

Along E Loses PE(where + “wants” to

go)

Gains PE

Opposite E Gains PE Loses PE(where – “wants” to

go)

Similarity of PEelectric and PEg

PEg = mghm is massg is gravitational fieldh is distance above a reference point

PEelect = -qEdq is chargeE is electric field strengthd is distance from reference pointThe (-) sign indicates the PEelect will increase for –q

and decrease for +qUsing dimensional analysis, what is the unit of

PEelect?

Potential DifferenceElectric potential 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

The unit of electric potential is what?

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

q

PEV elect

Potential DifferenceUnit is the volt (V)

q

PEV elect

C

J V 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

Potential Difference at a Point Near a Charge

One point is near the charge

The other point is at infinity

Use this equation to find the potential difference at a single point

r

qkV C

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 = 8.0 cm

in a uniform field of 350 N/C, it loses 4.5 x 10-18 J of potential energy.

What is the magnitude of the charge?What is the potential difference between the

two points a and b?

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

CapacitanceAbility of a conductor to store energy in the

form of separated charges

Unit of capacitance is the farad, F

V

QC

Volt

Coulomb 1Farad 1

Capacitance of a Parallel Plate Capacitor in a VacuumA is the area of the

platesE0 is permittivity

constant for a vacuum

= 8.85 x 10-12 C2/Nm2

d

AC 0

Dielectric MaterialsInsulating material

placed between the plates of a capacitor

Increases the ability of a capacitor to carry a charge

Discharging a CapacitorCapacitors are

devices that store charge

When discharge, they release charge

Computer keyboards are an example of capacitors in action

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 Capacitors

C

QPE

VCPE

VQPE

2

2

12

1

2

2

PE Stored in a Charged Capacitor

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 = 2.46 x 10-4 m/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

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 ∆V constantly switch

Causing constant reversal of current, e.g. 60 Hz

Rapid 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

Compare the equations….

P = I2RP = I∆V