Current•Current, I, is the rate of flow of electric charge, dQ/dt is the instantaneous current•It is measured in Coulombs/Second•Unit is Ampere (amp, or A) 1 C
1 A1 S
•The direction of current is the direction that positive charges would flow•Or the opposite of the direction that negative charges flow
+ + +
- - -
I
•There must be a net transport of charge to have a current.
Quiz
A) To the rightB) To the leftC) Up D) DownE) None of the above
•Suppose we have a current from a flow of electrons to the right.
•In what direction is the current?•In what direction is the electric field?
- - -
Quiz
+2
+2
+2
A) To the rightB) To the leftC) Up D) DownE) None of the above
•Suppose we have a current from a flow of Calcium (+2) ions
•In what direction is the current?•In what direction is the electric field?
Current Density•Current Density, J, is the amount of current flow through a unit area
IJ
A
Area ACurrent I
•Note: For a fixed area, the current density is independent of shape
•Remember: Current has a direction!
•Assuming uniform current parallel to dA
Current: Details
Area ACurrent I
•When thinking about current flow, think about fluid flow.
•Remember that a conductor at equilibrium has no field inside
•For there to be a current one cannot be at equilibrium
•There has to be a potential difference, otherwise for every carrier moving in one direction another one is moving in the opposite•Think about fluid flow: there has to be a potential difference for fluid to flow otherwise water is stagnate.
Current: Flow
Area A
•When thinking about current flow, think about fluid flow.•The flow in equals the flow out•So the current in equals the current out
Current I
I1I2
I3
I1= I2+ I3
Quiz
Area ACurrent I
•In which of the following situations is the magnitude of the current the largest
+ +
-
7C/s 3C/s
5C/s 5C/s 1C/s
6C/s2C/s
+ +
- -
A B C D
Microscopic Description of Current: Qualitative
•Microscopically current is due to the movement of charge carriers
•In the Drude model, the electrons diffuse in the absence of an applied field
Electron Gas
When a field is applied, the symmetry of the “motion” of the electrons is broken and there is a net drift.
Microscopic Description of Current: Math
m
EnqJ
2
•Assume uniform motion and density of charge carriers
A
•The charge in a wire of length L can be calculated
q=(nAL)e, for electrons
•The total charge moves through a cross-section in:t=L/v ; v is the drift velocity
Microscopic Description of Current: Math
m
EnqJ
2
•Assume uniform motion and density of charge carriers
A
•I=q/t=nALev/L =nAev
•This implies (J=I/A) that J=(ne)v
ne is the charge carrier density
Conductivity•In most materials, electric field is required to make the current move
•the current is proportional to the electric field, and the conductivity
•The conductivity is a property of the material
EJ Empirically, EJ
•the resistivity is the reciprocal of the conductivity, nothing more!
Current I
Electric Field E
Resistance•Define resistance as the ratio of the voltage to the current
Area A
Length L
Electric Field E
Current I
V IR
•Resistance is measured in units of Ohms ()
1 V1
1 A
•Resistance is always positive•Current always flows from positive to negative
•Note: This is not Ohm’s law! We can (in principle) always use this
Resistance vs Resistivity•Resistivity is how much a material impedes current
Current I
•For particularly easy cases, the relationship can be calculated:•(homogenous, isotropic conductors with a uniform field and a uniform cross-section)
EJ
•Resistance is how much an object impedes current
A
LR
Current I
Electric Field E
Quiz
A)Inew=0.5IB)Inew=2IC)Inew=4ID)Inew=0.25I
•Suppose start with a piece of wire in a circuit connected to a battery, and some current I flows. Now suppose replace that wire with a wire of the same length but twice the radius. How is the new current, Inew related to the original current?
Resistance and Temperature•Resistance and hence conductivity is a function of temperature
0 is the resistivity at temperature T0 (typically 20 C) is the temperature coefficient of resistivity
001
LR T T
A
0 01R T T
•The linear relationship is approximate, but allows one to measure temperature very accurately
To
Ohm’s Law
•The resistance R is a constant irregardless of the applied potential
Area A
V IR
•This is equivalent to saying that the resistivity of the material is independent of the applied field
EJ
Nonohmic materials
•If the resistance R depends on the magnitude or direction ofthe potential difference, than the material is nonohmic
Area A
V IR
•Semiconducting diodes good example:current is essentially zero until some cutoff potential is
achieved and then the current rises expontentially with the potential. One could say that the resistance is infinite until a cutoff voltage is reach and then the resistance decreases as the voltage is raised
Microscopic Description of Ohm’s law
•Microscopically current is due to the movement of charge carriers
When a field is applied, the symmetry of the “motion” of the electrons is broken and there is a net drift.
m
EnqJ
2
nqvJ
We can rewrite this in a different form,atv
m
Fa qEF
Put this all together and,
We also now know what the conductivity andresistivity are.
Superconductors•A superconductor has a critical temperature below which the resistance drops to zero!!!
•So once a current is set up in them, the current persists for years!
•Cool industrial applications:•Superconducting magnets
•Used in NMR /MRI•In medicine to image people and animals •In materials science to image/identify materials•In chemistry to identify molecules•In structural biology to study macromolecular structures•In biophysics to study macromolecular dynamics, assembly and function
Power Consumed by a Resistor
E–
+
V = 0
V = E
I = E/RR
dUP
dt d
Q Vdt
dQ
Vdt
I V
P I V
2
2 VP RI
R
