2. Announcements

3. Conductivity In most materials, electric field is required to make the current move and to maintain a current the current density is proportional to the electric field, and the conductivity  The conductivity is a property of the material Empirically, the resistivity is the reciprocal of the conductivity, nothing more!

4. Resistance Define resistance as the ratio of the voltage to the current Area A Length L Electric Field E Current I 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

5. 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) Resistance is how much an object impedes current Current I Electric Field E

6. Resistance and Temperature Resistance and hence conductivity is a function of temperature  0 is the resistivity at temperature T 0 (typically 20 C)  is the temperature coefficient of resistivity The linear relationship is approximate, but allows one to measure temperature very accurately

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

8. Quiz A)I new =0.5I B)I new =2I C)I new =4I D)I new =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, I new related to the original current?

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

10. 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.

11. 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

13. Circuits – more symbols wire (conductor) capacitor switch battery +– ground (V = 0) resistor EE – +  V = 0  V = E I= E /R RR

14. Batteries An ideal battery creates a voltage difference between the two sides +– R E If we can neglect the internal resistance in the battery, the current in this simple circuit is just: An ideal emf source has no internal resistance so the potential difference is constant

15. emf An emf source is something creates a potential difference and is doing so does work on charge carriers Battery Electrical generator! Consider what happens to a charge that makes this circuit: A bit of charge,dq, goes around the circuit in a time, dt, and so work, dW, must be done by the emf source to move the charge across the potential R E +–

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