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# Current

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1. I + + + - - - 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) • The direction of current is the direction that positive charges would flow • Or the opposite of the direction that negative charges flow • There must be a net transport of charge to have a current.

2. - - - Quiz • 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? • To the right • To the left • Up • Down • None of the above

3. Quiz • 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? • To the right • To the left • Up • Down • None of the above +2 +2 +2

4. Current Density • Current Density, J, is the amount of current flow through a unit area • Assuming uniform current parallel to dA • Note: For a fixed area, the current density is independent of shape • Remember: Current has a direction! Area A Current I

5. Current: Details • 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. Area A Current I

6. Current I Current: Flow • When thinking about current flow, think about fluid flow. • The flow in equals the flow out • So the current in equals the current out I3 I2 I1 Area A I1= I2+ I3

7. Quiz • In which of the following situations is the magnitude of the current the largest 3C/s 2C/s 6C/s 7C/s + + + + 5C/s 1C/s 5C/s - - - A C D B Area A Current I

8. 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.

9. Microscopic Description of Current: Math • Assume uniform motion and density of charge carriers • 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 A L

10. Microscopic Description of Current: Math • Assume uniform motion and density of charge carriers • I=q/t=nALev/L =nAev • This implies (J=I/A) that J=(ne)v ne is the charge carrier density A L

11. Conductivity • In most materials, electric field is required to make the current move • the current is proportional to the electric field, and the conductivity Empirically, • The conductivity is a property of the material • the resistivity is the reciprocal of the conductivity, nothing more! Electric Field E Current I

12. Resistance • Define resistance as the ratio of the voltage to the current • Resistance is measured in units of Ohms () • 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 Electric Field E Area A Current I Length L

13. Electric Field E Current I Resistance vs Resistivity • Resistivity is how much a material impedes current • Resistance is how much an object impedes current • For particularly easy cases, the relationship can be calculated: • (homogenous, isotropic conductors with a uniform field and a uniform cross-section) Current I

14. Quiz • 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? • Inew=0.5I • Inew=2I • Inew=4I • Inew=0.25I

15. 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 • The linear relationship is approximate, but allows one to measure temperature very accurately

16. Ohm’s Law • The resistance R is a constant irregardless of the applied potential • This is equivalent to saying that the resistivity of the material is independent of the applied field Area A

17. Nonohmic materials • If the resistance R depends on the magnitude or direction of • the potential difference, than the material is nonohmic • 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 Area A

18. 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. We can rewrite this in a different form, Put this all together and, We also now know what the conductivity and resistivity are.

19. 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

20. I = E/R Power Consumed by a Resistor V = E + E R – V = 0