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 C1 A

1 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

IJA

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

EnqJ2

•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

EnqJ2

•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 IElectric 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 V11 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

ALR

Current IElectric 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

001LR 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

EnqJ2

nqvJ

We can rewrite this in a different form,atv

mFa 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

dUPdt

d Q Vdt

dQ Vdt

I V

P I V

22 V

P RIR