1. Current PH 203 Professor Lee Carkner Lecture 10

2. Circuit Theory   We have already discussed potential difference   This charge motion is called the current (symbol: i)  Energy can be extracted from the current due to resistance (symbol: R)

3. Current  i = dq/dt  The units are amperes (amps) or coulombs per second   The most common charge carrier is the electron, but,  We draw the current as the direction positive particles would travel in

4. Charge Conservation   If a current comes to a junction and splits into two currents, those two must sum up to equal the original i 0 = i 1 + i 2   Note that a single wire with no junctions has the same current everywhere

5. Junctions   A junction is where the current splits  It has to make a choice  Note that “bends” are not junctions   Things in parallel must have a junction at each end

6. Inside a Wire  What goes on inside a current carrying wire?   An applied potential difference makes them want to move in a certain direction (against the field)   They undergo many collisions and move in a random walk  Electrons do not move freely, directly or rapidly

7. Current Density   Most wires can be thought of as cylinders with a particular radius and cross sectional area, A  We can combine the current and area to find the current density, J J = i/A   J is a vector in the same direction as the current

8. Speed of Electrons  How fast are the charges moving?   What is q?   If n is the number of electrons per unit volume than the total charge is q= neLA  What is t?   v d = L/t  But t = q/i and q = neLA v d = Li/q = Li/neLA v d = i/neA

9. Current Conundrums  The drift speed is very small (~mm per second), yet the effect of current is felt instantaneously   Electrons move randomly, yet current flows in only one direction  Between collisions they get back on track   Convention is based on the positive charge, but protons don’t normally move

10. Resistivity   Why?  The materials have different internal structures and thus resist the flow of current differently  They have different resistivities (symbol  )   Resistivity is a property of a particular type of material rather than of a particular wire

11. Resistance   Short, wide wires have less resistance than long, narrow wires  The resistance can be written as: R =  (L/A)   The units of resistance are ohms (volts per ampere)  Resistance tells how much current we will get for a given potential difference (R = V/i)

12. Temperature and Resistance   Electronic devices get hot!  Temperature also affects electronic properties   This increased random motion means collisions are more frequent and it is harder for current to flow  Resistance generally increases with temperature

13. Temperature Dependence   We use the relationship:  –  0 =  0  (T – T 0 )  Where:    0 is the resistivity at some reference temperature T 0    is the temperature coefficient of resistivity  We look up  0 and  in tables

14. Temperature Versus Resistance for a Metal

15. Semiconductors  Insulators have no free electrons   Conductors have many free electrons   Semiconductors are materials that have electrons that are moderately bound   Adding electrical or thermal energy can free the electrons and increase conductivity  At higher temperatures the larger thermal motions are offset by the greater availability of free electrons

16. Semiconductors and Temperature

17. Superconductivity   The wire’s resistance slows down the electrons   Like a frictionless surface  Such materials are called superconductors  Resistance generally decreases with decreasing T 

18. Next Time  Read 26.4-26.9  Problems: Ch 26, P: 9, 22, 26, 36, 40

19. Consider a spherical capacitor. Which of the following would increase the capacitance the most (assuming no other changes)? A)Doubling the radius of the inner sphere B)Doubling the radius of the outer sphere C)Doubling the radius of both inner and outer spheres D)a and b tie E)None of the these changes would increase C

20. Consider a pair of metal plates separated by an air gap that acts as a capacitor. How could the amount of charge on the plates be increased for a given voltage? A)Replace the air with vacuum B)Replace the air with a copper plate C)Replace the air with cardboard D)Increase the separation of the plates E)Use round plates instead of square ones

21. If the voltage across a capacitor is doubled, the amount of energy stored on the capacitor, A)Is halved B)Stays the same C)Is doubled D)Is tripled E)Is quadrupled