Transcript resistivity
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) 1C 1A 1S •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 •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? A) To the right B) To the left C) Up D) Down E) None of the above - - - 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? A) To the right B) To the left C) Up D) Down E) None of the above +2 +2 +2 Current Density •Current Density, J, is the amount of current flow through a unit area I J A •Assuming uniform current parallel to dA •Note: For a fixed area, the current density is independent of shape •Remember: Current has a direction! Current I Area A 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. Current I Area A 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 Current I I2 I1 I1= I2+ I3 Area A Quiz •In which of the following situations is the magnitude of the current the largest 3C/s 7C/s + + 5C/s A 2C/s Current I + 6C/s + 5C/s 1C/s - - B C D Area A 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 •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 nq 2 E J m 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 nq 2 E J m Conductivity •In most materials, electric field is required to make the current move •the current is proportional to the electric field, and the conductivity J E J E Empirically, •The conductivity is a property of the material •the resistivity is the reciprocal of the conductivity, nothing more! Electric Field E Current I Resistance •Define resistance as the ratio of the voltage to the current V IR •Resistance is measured in units of Ohms () 1V 1 1A •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 Current I Length L Area A Resistance vs Resistivity •Resistivity is how much a material impedes current •Resistance is how much an object impedes current J E •For particularly easy cases, the relationship can be calculated: •(homogenous, isotropic conductors with a uniform field and a uniform cross-section) L R A Electric Field E Current Current II 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? A)Inew=0.5I B)Inew=2I C)Inew=4I D)Inew=0.25I Resistance and Temperature •Resistance and hence conductivity is a function of temperature L 0 R 1 T T0 R0 1 T T0 A •0 is the resistivity at temperature T0 (typically 20 C) • is the temperature coefficient of resistivity o T •The linear relationship is approximate, but allows one to measure temperature very accurately Ohm’s Law V IR •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 J E Area A Nonohmic materials V IR •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 Area as theA 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. J nqv We can rewrite this in a different form, F qE v at F a m Put this all together and, nq 2 E J m We also now know what the conductivity and resistivity 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 V=E + E – R I = E/R P I V V=0 dU d dQ P QV V I V dt dt dt 2 V 2 P RI R