Electrical Energy & Current. Introduction to Electric PE, Electric Potential, and Potential...
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Transcript of 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