Download Lecture 07: Current Flow - Purdue Physics

PHYS219 Fall semester 2014
Lecture 07: Current Flow
Dimitrios Giannios
Purdue University
Electro Dynamics
The Study of Charge in Motion
So far, we have studied static charges at well defined
positions → understanding of electrostatic forces,
electric fields, and potential differences.
What happens when charge is permitted to move?
What rules govern the flow of charge?
Define Electric Current I as the rate of flow of net
charge through a surface.
The charge can be carried by anything that has a net charge: electrons,
ions, molecules, particles, etc..
Surface
-q4
+q1
+q2
+x
-x
+q5
-q3
+x
I=
q1 + q2 + (−q3) −
−q4 + q5
Δt
Δt
Clock
0
Current need not be confined to
wire.
Units of I: [C/s = Ampere = A]
Note that mathematically, -q moving
in +x direction is equivalent to +q
moving in –x direction
When current flows through a wire
I
Definition of Conventional Current
I
By definition, the direction of current flow for
either case is the same.
Current – Orders of Magnitude
• 1 x 10-12 A = 1 pA (about 107 e-/s)
•10 x 10-9 A = 10 nA (leakage current in transistors)
• 1 x 10-6 A = 1 A (typical input current to IC)
• 1 x 10-3 A =1 mA (humans can feel this)
•~0.02 A = 20 mA (muscle contraction)
•50 x 10-3 A = 50 mA (painful to humans)
• ~0.1 A = 100 mA (death)
•~ 1 A (current thru 100 W light bulb)
•103-104 A (lightning bolt)
What Drives Current Flow?
A potential difference develops across the terminals of a battery
EMF = ElectroMotive Force =
Analogy to Water Flow
What factors limit
the flow of water?
What factors limit
the flow of charge?
Resistance to Flow: The ratio of the potential energy difference
across a conductor to the current flowing through it.
Currents on Earth and the universe
Currents are not only on wires!
currents require free charges  Plasma
(gas at temperature of million-billion K!)
I
Fusion Device (Tokamak)
Astrophysical Currents
(and instabilities!)
Microscopically, how does the current
flow in a wire?
Net drift velocity
of electron due to
applied electric
field
I
vd
E
E= -Δ V/ Δ s
-
Atom 1
Atom 5
FE
Atom 6
Atom 4
Atom 2
Atom 3
+
+
+
+
+
+
+
+
+
E
A few nanometers (1 nm = 1 x 10-9 m)
I
Current and Drift Velocity
• Current is related to the drift velocity
vd = -
I
neA
where: A= wire cross section, n= number density of
electrons, I=current
• For a household size copper wire carrying 1 A of
current, the drift velocity is about -0.01 m/s!
• There is no perceptible time delay between when
you push a switch and when the light comes on
• The speed of the electric current is equal to the
speed of electromagnetic radiation in the wire
• This is nearly the speed of light
Ohm’s Law
I
I
ΔV
UNITS :
R = V/A = Ohm [Ω]
current flows and electrical resistance
9.0 V
360 mA
What determines resistance R for a wire?
(constant over
entire length)
Units: L (m); A(m2); ρ(Ω∙m); R(Ω)
Electrical Resistivity (ρ)
Some materials, like metals, offer little resistance to current flow.
Other materials, like plastic, offers high resistance to current flow.
Resistivity is used to quantify how much a given material resists
the flow of current.
Resistivity is a property of a
material.
Distinguish between resistivity and
resistance
•Resistivity is a property
of a material.
•Resistance of a component
depends on BOTH
geometry as well as the
resistivity of the material
from which it is made.
R=ρL/A
Three wires, same length & material
different cross-sections
A=d2
A=½ base*height
=½d∙d√3/2=d2√3/4
d
L
60◦
60◦
d
d
d
d√3/2
A=π(d/2)2
American Wire Gauge (AWG)
Determine the resistance of a 100
meter length of 12 AWG (2.052 mm
diameter) solid wire made of the
following materials:
a.copper (resistivity = 1.67x10-8 Ω•m):
b.aluminum (resistivity = 2.65x10-8 Ω•m)
c.iron (resistivity = 9.71x10-8 Ω•m)
Area = π R2= π (0.002052m/2)2=3.31 x 10-6 m2
Can a copper wire and an
aluminum wire of the same
length have the same
resistance?
RCopper = ρCu L/A = (1.67 x 10-8 Ω m) 100m/(3.31 x 10-6 m2) = 0.504 Ω
RAluminun = ρAl L/A = (2.65 x 10-8 Ω m) 100m/(3.31 x 10-6 m2) = 0.801 Ω
Riron = ρFe L/A = (9.71 x 10-8 Ω m) 100m/(3.31 x 10-6 m2) = 2.93 Ω
A wire has a resistance R. If the length of the wire is doubled
and the radius is also doubled, what is the new resistance?
2
1
L
2L
2r
4r