Download Electrical Energy & Current

Electrical Energy & Current
Introduction to Electric PE, Electric
Potential, and Potential Difference
 Intro to Electric Potential
Electrical Potential Energy
 PE 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 energy
ME = KE + PEgrav + PEelastic + PEelectric
Electric PE in a Uniform Electric
Field
 A 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 Energy
 Recall 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 = Fd
Since F = qE (E = F/q)
W = qEd
PEb-PEa= -qEd
 ΔPE = -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 = mgh
 m is mass
 g is gravitational field
 h is distance above a reference point
 PEelect = -qEd
 q is charge
 E is electric field strength
 d is distance from reference point
 The (-) sign indicates the PEelect will increase for –q and decrease
for +q
 Using dimensional analysis, what is the unit of PEelect?
Potential Difference
 Electric potential is the ratio of PEelect to charge q
PEelect
V
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?
Potential difference
 The change in electric potential
 The difference in electrical potential between two points
PEelect
V 
q
 Is the work that must be done against electric forces to move
a charge from one point to another divided by the charge
Potential Difference
 Unit is the volt (V)
PEelect
V 
q
J
1V 
C
Potential Difference in a Uniform
Electric Field
 Varies in a uniform field with displacement from a reference
point
 Where d is displacement parallel to the field
 Use this equation to determine potential difference between
two points in a field
V  Ed
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
q
V  k C
r
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 charge
 Keep track of signs!
Sample Problem
 As 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 Capacitance
 Capacitors are devices that store electrical PE
 Often constructed of parallel metal plates
 When connected to a battery, the plates become charged
 When fully charged, ∆Vcap = ∆Vbat
Capacitance
 Ability of a conductor to store energy in the form of
separated charges
Q
C
V
 Unit of capacitance is the farad, F
Coulomb
1 Farad  1
Volt
Capacitance of a Parallel Plate
Capacitor in a Vacuum
 A is the area of the plates
 E0 is permittivity constant for
a vacuum
 = 8.85 x 10-12 C2/Nm2
A
C  0
d
Dielectric Materials
 Insulating material placed
between the plates of a
capacitor
 Increases the ability of a
capacitor to carry a charge
Discharging a Capacitor
 Capacitors are devices that
store charge
 When discharge, they release
charge
 Computer keyboards are an
example of capacitors in
action
Capacitance of a Sphere
 R is radius
 Because 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)
Q
R
Csphere 

V kC
Energy and Capacitors
PE Stored in a Charged Capacitor
1
PE  QV
2
1
2
PE  C V 
2
2
Q
PE 
2C
Current and Resistance
 Current is the rate of movement of charge
 Rate of movement of electrons through a cross-sectional area
Q
I
t
coulomb
1ampere  1
second
Sample Problem
 If 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 Current
 Depending upon the circumstances, either positive, negative,




or both can move.
Particles that move are called charge carriers
By 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 easily
 Electrons in metals
 Ions in solution (electrolytes)
Conventional Direction of Current
Drift Velocity
http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif
 Recall the structure of metals
 Valence electrons move about randomly due to their thermal
energy
 Their net movement is zero
 But if an electric field is established in the wire, there is a net
movement of electrons against the electric field (toward +)
 Drift velocity animation
Drift Velocity
Consider motion of an
electron through a wire
 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 velocity
Slow: e.g. in a copper wire carrying a 10.0 A current,
vdrift = 2.46 x 10-4 m/s
Resistance to Current
 Opposition to electric
current
 Unit of electrical resistance
is the ohm (Ω)
 More commonly known as
Ohm’s law
V
R
I
volt
1 ohm  1
amp
V  IR
Ohmic and Non-ohmic Materials
 Materials 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 (nonlinear
 Diodes are constructed of
non-ohmic materials
Other Factors Affecting Resistance
17.4 Electric Power
 A potential difference (∆V) is necessary to cause current (I)
 Batteries supply chemical energy (PEchem) which can be
converted into electical PE
 Generators convert mechanical energy into electrical PE
 E.g. hydroelectric power plants
 Coal or natural gas powr plants
 Nuclear power plants
Direct and Alternating Current
 DC current flows in one direction only
 Electrons move toward the (+) terminal
 Conventional 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 AC
 DC
 constant
 uni-directional
 AC
 not constant
 bi-directional
Energy Transfer
 In a DC circuit
 Electrons leave the battery
with high PE
 Lose PE as flow through the
circuit
 Regain PE when returned to
battery
 (battery supplies PE through
electrochemical reactions)
Electric Power
W PE
P

t
t
PE
V 
 PE  qV
q
qV
q
P
Since
I
t
t
P  IV
 The rate of conversion
of electrical energy
 SI unit is the watt (W)
Other Formulas for Power
Beginning with P  IV
Using Ohm' s Law...
PI R
2

V 
P
2
R
Kilowatt-hours
 How utility companies measure energy consumed
 Is the energy delivered in one hour a constant rate of one kW
 1kWh=3.6 x 106 J
 What is the cost to light a 100 W light bulb for 1 full day if the
electric utility rate is $0.0600 per kWh?
100 W  24 h  2400 Wh  2.4 kWh
$0.0600
2.4 kWh 
 $0.144
kWh
Transmission Lines
 Transit at high voltage and
low current to minimize
energy lost during
transmission
 Compare the equations….
 P = I 2R
 P = I∆V