1. Ohm’s Law Physics 102 Professor Lee Carkner Lecture 14

2. PAL #13 Capacitors  0.005 C stored on capacitor at 1000 volts  What is capacitance?  Q= CV  C = Q/V = 0.005/1000 = 5X10 -6 F = 5  F  Jury-rig a replacement out of metal foil and Teflon coating (k = 2.1, thickness = 0.01 mm).  C =  0 A/d  A = Cd/  0 = (5X10 -6 )(0.00001)/(2.1)(8.85X10 -12 )  A = 2.69 m 2  How can such a device be portable?  Roll it up, making sure the foil won’t short

3. 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

4. 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

5. 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

6. Circuit Theory  There are three key variables used in circuit theory:    V provides energy and causes charges to move   Energy can be extracted from the current due to resistance (symbol: R)

7. Current  The current is the flow rate of charge and is defined as: I =  Q/  t   The current is carried by charged particles called charge carriers 

8. 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)  However, the electrons do not move in a straight line   Note that the electrons are not pushing each other, they just react to the potential   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

9. Resistivity  If you apply the same  V to several different types of materials you get different currents  Why?   They have different resistivities (symbol  )   Resistivity is a property of a particular type of material rather than of a particular wire

10. 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)

11. Simple Circuit

12. Ohm’s Law  How much current do you get if you put a potential difference V across a wire with resistance R? I = V/R   This relationship is called Ohm’s Law  Commonly written as: V = IR  Ohm’s law is very important, memorize it!   Every individual piece of a circuit obeys Ohm’s law

13. 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

14. Energy in Electric Circuits   As the charges flow (as current) they convert the potential energy to kinetic energy   We should be able to relate the potential difference, current and resistance to the energy produced

15. Energy Dispersion Rate  Each charge that passes through the battery gains energy that it will later lose as heat   Each charge then gives up its energy so the total power (energy per second) depends on the rate of charge flow or current   V = P

16. Power  Using Ohm’s law (  V = IR) we can write:  In general we will know the values of R (since it depends on the properties of the resistor) and  V (since we should know the voltage of our source or battery) 

17. Lightbulbs  A common circuit element is the lightbulb   Household lightbulbs are rated in watts   In the US, most power outlets produce 120 volts of potential difference   Those that do not use a transformer

18. Conservation of Charge   If a current flows through a single wire, the value of the current must be the same everywhere   Otherwise charge would be gained or lost

19. Conservation of Energy  Each resistor has a  V associated with it   The sum of the voltage drops across all circuit elements on a single wire must be equal to the potential difference across the ends of the wire   All wires connected between the same two points must have the same  V  Since the change in potential energy is the same for each

20. Resistors in Series  All resistors in series have the same current (I)   Since  V eq is the sum of all the individual  V, R eq must be the sum of all of the individual R:  R eq = R 1 + R 2 + R 3 …  Resistors in series add  V eq R1R1 R2R2 I

21. Resistors in Parallel  All resistors in parallel have the same  V   Since the current through each is I =  V/R and I eq =  V/R eq :  1/R eq = 1/R 1 + 1/R 2 + 1/R 3... VV R1R1 R2R2 I eq I1I1 I2I2

22. Next Time  Read: 19.1-19.4, 18.6, 19.7  Homework: Ch 18, P 7, 35, Ch 19, P 5, 9