1. Current PH 203 Professor Lee Carkner Lecture 10

2. 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

3. Why is a dielectric useful in a capacitor? A)It keeps the plates from touching B)It increases the conductivity of the plates C)It increases the charge that can be stored per volt D)a and c only E)a, b, and c

4. 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

5. 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)

6. Current  The current is the flow rate of charge and is defined as: i = dq/dt   The current is carried by charged particles called charge carriers   We draw the current as the direction positive particles would travel in

7. Charge Conservation   If a current comes to a junction and splits into two currents, those two must sum up to equal the original  This is true no matter how many branches or junctions, or how they arranged  Note that a single wire with no junctions has the same current everywhere

8. Junctions  Before doing any circuit problem, always identify the junctions   It has to make a choice   Things in series cannot have a junction between them 

9. 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

10. Current Density  Current is contained within a wire that is full of charges   We can combine the current and area to find the current density, J  In amperes per square meter  J is a vector in the same direction as the current

11. Speed of Electrons  How fast are the charges moving?   What is q?  A wire of length L and area A has a volume LA   What is t?  We can then the define the drift speed, v d as length divided by the time to move through the length, t  v d = L/t  v d = Li/q = Li/neLA = i/neA

12. Drift Speed  Each electron moves at the drift speed v d = i/neA   For large electron densities in thick wires we get a small v d  The electrons don’t need a large speed to get a large current because there are so many of them

13. Electron Motion

14. 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   The direction of the current is opposite the motion of the electrons  Convention is based on the positive charge, but protons don’t normally move

15. Resistivity   Why?  The materials resist the flow of current   Good conductors have low resistivity, good insulators have high resitivities  Resistivity is a property of a particular type of material rather than of a particular wire

16. Resistance  The total resistance of the material also depends on its size   The resistance can be written as: R =  (L/A)   The units of resistance are ohms (volts per ampere)

17. Temperature and Resistance  Resistors convert energy from the current into heat   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

18. Temperature Dependence  How does the resistance change with temperature?  We use the relationship:  –  0 =  0  (T – T 0 )  Where:    0 is the resistivity at some reference temperature T 0  Usually T 0 = 293 K (room temperature)   We look up  0 and  in tables

19. Superconductivity  If we set up a current in a wire and then take away the battery the current fades to zero   If the resistance was zero the current would keep flowing even without a battery   Such materials are called superconductors  Resistance generally decreases with decreasing T 

20. Next Time  No class Friday  For Monday:  Read 26.4-26.9  Problems: Ch 26, P: 9, 22, 26, 36, 40